The Facts On File

DICTIONARYof

PHYSICS

The Facts On File

DICTIONARYof

PHYSICS

Edited byJohn Daintith

Richard Rennie

Fourth Edition

The Facts On File Dictionary of PhysicsFourth Edition

Copyright © 2005, 1999 by Market House Books Ltd

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Library of Congress Cataloging-in-Publication DataThe Facts On File dictionary of physics. — 4th ed. / [edited by]

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PREFACE

This dictionary is one of a series designed for use in schools. It is intended for stu-dents of physics, but we hope that it will also be helpful to other science students andto anyone interested in science. Facts On File also publishes dictionaries in a varietyof disciplines, including biology, chemistry, forensic science, marine science, mathe-matics, space and astronomy, and weather and climate.

The Facts On File Dictionary of Physics was first published in 1980 and the thirdedition was published in 1999. This fourth edition of the dictionary has been exten-sively revised and extended. The dictionary now contains over 2,800 headwords cov-ering the terminology of modern physics. A totally new feature of this edition is theinclusion of over 1,000 pronunciations for terms that are not in everyday use. Anumber of appendixes have been included at the end of the book containing usefulinformation, including a list of chemical elements, a periodic table, a list of symbols,a number of useful conversion tables, and a Greek alphabet. There is also a list ofWeb sites and a bibliography. A guide to using the dictionary has also been added tothis latest version of the book.

We would like to thank all the people who have cooperated in producing this book.A list of contributors is given on the acknowledgments page. We are also grateful tothe many people who have given additional help and advice.

v

ACKNOWLEDGMENTS

Consultant Editors (First and Second Editions)

Eric Deeson M.Sc., F.C.P., F.R.A.S.J. W. Warren B.Sc.

Contributors

Roger Adams B.Sc.Jane Craig B.Sc., A.R.C.S.Sue Flint B.Sc.B. W. Lowthian B.Sc., Ph.D.Carol Russell B.Sc.Michael S. Slater B.Sc.James M. Struthers B.Sc.Thomas A. Shields B.A., C.S.A.M. Welton B.Sc.

Pronunciations

William Gould B.A.

NoteUnless otherwise stated, the melting and boiling points given in the dictionary areat standard pressure. Relative densities of liquids are at standard pressure with theliquid at 20°C relative to water at 4°C. Relative densities of gases are relative toair, both gases being at standard temperature and pressure.

The following abbreviations are used in the text:

p.n. proton number(atomic number)

r.a.m. relative atomic mass(atomic weight)

m.p. melting pointb.p. boiling point

vi

CONTENTS

Preface v

Acknowledgments vi

Guide to Using the Dictionary viii

Pronunciation Key x

Entries A to Z 1

Appendixes

I. The Periodic Table 270

II. The Chemical Elements 271

III. Symbols for Physical 273Quantities

IV. The Greek Alphabet 273

V. Conversion Factors

Length 274

Area 274

Volume 274

Mass 275

Force 275

Work and Energy 276

Pressure 276

VI. Web Sites 277

Bibliography 278

vii

GUIDE TO USING THE DICTIONARY

The main features of dictionary entries are as follows.

HeadwordsThe main term being defined is in bold type:

aberration A defect in an optical systemsuch that the image is not a true picture ofthe object.

PluralsIrregular plurals are given in brackets after the headword.

spectrum (pl. spectra) ... A range of elec-tromagnetic radiation emitted or absorbedby a substance under particular circum-stances.

VariantsSometimes a word has a synonym or alternative spelling. This is placed in brackets afterthe headword, and is also in bold type:

eyepiece (ocular) The lens or combina-tion of lenses nearest the eye in an opticalinstrument.

Here, ‘ocular’ is another word for eyepiece. Generally, the entry for the synonym consistsof a simple cross-reference:

ocular See eyepiece.

AbbreviationsAbbreviations for terms are treated in the same way as variants:

electron spin resonance (ESR) Abranch of microwave spectroscopy ....

The entry for the synonym consists of a simple cross-reference:

ESR See electron spin resonance.

Multiple definitionsSome terms have two or more distinct senses. These are numbered in bold type

abundance 1. The relative amount of agiven element among others; for example,the abundance of oxygen in the Earth’scrust is approximately 50% by weight.2. The amount of a nuclide (stable or ra-dioactive) relative to other nuclides of thesame element in a given sample.

viii

Cross-referencesThese are references within an entry to other entries that may give additional useful in-formation. Cross-references are indicated in two ways. When the word appears in the de-finition, it is printed in small capitals:

accommodation The action of the EYE

in changing its focal power. …

In this case the cross-reference is to the entry for ‘eye’.

Alternatively, a cross-reference may be indicated by ‘See’, ‘See also’, or ‘Compare’, usu-ally at the end of an entry:

angular momentum Symbol: L Theproduct of the moment of inertia of a bodyand its angular velocity. See also rotationalmotion.

Hidden entriesSometimes it is convenient to define one term within the entry for another term:

charcoal An amorphous form of carbonmade by… Activated charcoal is charcoalheated to…

Here, ‘activated charcoal’ is a hidden entry under charcoal, and is indicated by italic type.The entry for ‘activated charcoal’ consists of a simple cross-reference:

activated charcoal See charcoal.

PronunciationsWhere appropriate pronunciations are indicated immediately after the headword, en-closed in forward slashes:

ablation /ab-lay-shŏn/ The burningaway of the outer surface of .…

Note that simple words in everyday language are not given pronunciations. Also head-words that are two-word phrases do not have pronunciations if the component words arepronounced elsewhere in the dictionary.

ix

/a/ as in back /bak/, active /ak-tiv//ă/ as in abduct /ăb-dukt/, gamma /gam-ă//ah/ as in palm /pahm/, father /fah-ther/,/air/ as in care /kair/, aerospace /air-ŏ-

spays//ar/ as in tar /tar/, starfish /star-fish/, heart

/hart//aw/ as in jaw /jaw/, gall /gawl/, taut /tawt//ay/ as in mania /may-niă/ ,grey /gray//b/ as in bed /bed//ch/ as in chin /chin//d/ as in day /day//e/ as in red /red//ĕ/ as in bowel /bow-ĕl//ee/ as in see /see/, haem /heem/, caffeine

/kaf-een/, baby /bay-bee//eer/ as in fear /feer/, serum /seer-ŭm//er/ as in dermal /der-măl/, labour /lay-ber//ew/ as in dew /dew/, nucleus /new-klee-ŭs//ewr/ as in epidural /ep-i-dewr-ăl//f/ as in fat /fat/, phobia /foh-biă/, rough

/ruf//g/ as in gag /gag//h/ as in hip /hip//i/ as in fit /fit/, reduction /ri-duk-shăn//j/ as in jaw /jaw/, gene /jeen/, ridge /rij//k/ as in kidney /kid-nee/, chlorine /klor-

een/, crisis /krÿ-sis//ks/ as in toxic /toks-ik//kw/ as in quadrate /kwod-rayt//l/ as in liver /liv-er/, seal /seel//m/ as in milk /milk//n/ as in nit /nit/

/ng/ as in sing /sing//nk/ as in rank /rank/, bronchus /bronk-ŭs//o/ as in pot /pot//ô/ as in dog /dôg//ŏ/ as in buttock /but-ŏk//oh/ as in home /hohm/, post /pohst//oi/ as in boil /boil//oo/ as in food /food/, croup /kroop/, fluke

/flook//oor/ as in pruritus /proor-ÿ-tis//or/ as in organ /or-găn/, wart /wort//ow/ as in powder /pow-der/, pouch

/powch//p/ as in pill /pil//r/ as in rib /rib//s/ as in skin /skin/, cell /sel//sh/ as in shock /shok/, action /ak-shŏn//t/ as in tone /tohn//th/ as in thin /thin/, stealth /stelth//th/ as in then /then/, bathe /bayth//u/ as in pulp /pulp/, blood /blud//ŭ/ as in typhus /tÿ-fŭs//û/ as in pull /pûl/, hook /hûk//v/ as in vein /vayn//w/ as in wind /wind//y/ as in yeast /yeest//ÿ/ as in bite /bÿt/, high /hÿ/, hyperfine /hÿ-

per-fÿn//yoo/ as in unit /yoo-nit/, formula /form-yoo-lă//yoor/ as in pure /pyoor/, ureter /yoor-ee-ter//ÿr/ as in fire /fÿr/

x

Bold type indicates a stressed syllable. In pronunciations, a consonant is sometimes dou-bled to prevent accidental mispronunciation of a syllable resembling a familiar word; forexample, /ass-id/ (acid), rather than /as-id/ and /ul-tră- sonn-iks/ (ultrasonics), rather than/ul-tră-son-iks/. An apostrophe is used: (a) between two consonants forming a syllable, asin /den-t’l/ (dental), and (b) between two letters when the syllable might otherwise be mis-pronounced through resembling a familiar word, as in /th’e-ră-pee/ (therapy) and /tal’k/(talc). The symbols used are:

Pronunciation Key

ab- A prefix used with a practical electri-cal unit to name the corresponding electro-magnetic unit. For example, theelectromagnetic unit of charge is called theabcoulomb. Compare stat-.

aberration A defect in an optical systemsuch that the image is not a true picture ofthe object. For instance, colored fringesmay appear, the image may not be focused,or the shape may show distortion. Tech-niques of aberration correction exist; thesecan, however, be complex and costly.

Chromatic (color) aberration is foundwith a single lens; mirrors do not sufferfrom chromatic aberration. Because dis-persion always accompanies refractive de-viation, the ‘red’ image will be farther fromthe lens than the ‘blue’. Consequently, theimage is surrounded by colored fringes.Chromatic aberration is corrected by form-ing a compound lens, whose elements havedifferent refractive constants.

Spherical aberration always occurswith rays that are distant from the axis andincident on a spherical mirror or lens. It isthe cause of the caustic curve. Sphericalaberration is corrected by using parabolicreflecting and refracting surfaces.

Astigmatism affects rays neither closenor parallel to the axis. The cone of raysthrough a lens from an off-axis object doesnot focus at a point. Instead, two images inthe form of short lines are formed at differ-ent distances from the lens. Between thetwo the image appears blurred. Mirrorsforming images of off-axis points show asimilar defect. The best method of mini-mizing astigmatism is to reduce the aper-ture with stops, thus allowing light onlythrough the center of the lens.

Coma is rather similar in cause, effect,and correction to astigmatism. After re-

fraction by a lens, a cone of rays from anoff-axis object tends to have a tadpole-shaped section because of coma.

Distortion is the result of differences ina lens’ magnifying power between differentaxes. Reduction of aperture is the normalsolution to both coma and distortion.

ablation /ab-lay-shŏn/ The burning awayof the outer surface of a satellite, shuttle,space probe or missile on re-entering theEarth’s atmosphere. The term originallyapplied to meteors.

absolute expansion See expansivity.

absolute humidity The mass of watervapor per unit volume of air, usually mea-sured in micrograms per cubic meter.Compare relative humidity. See also hu-midity.

absolute permeability See permeability.

absolute permittivity See permittivity.

absolute refractive index See refractiveindex.

absolute temperature Symbol: T A tem-perature expressed on the thermodynamic(ideal gas) scale, measured from absolutezero. If θ is the temperature on a Celsiusscale calibrated against the InternationalPractical Temperature Scale, then:

T = θ + 273.15See also temperature scale.

absolute unit A unit defined in terms offundamental quantities (such as length,mass, time, and electric charge).

absolute zero The zero value of thermo-

1

A

absorbance

2

dynamic temperature; 0 kelvin or–273.15°C.

absorbance /ăb-sor-băns, -zor-/ (opticaldensity) The logarithm of absorptance. Seeabsorptance.

absorptance /ăb-sorp-tăns, -zorp-/ Sym-bol: α The ratio of the radiant or luminousflux absorbed by a body or material to theincident flux. It was formerly called the ab-sorptivity.

absorption A process in which a gas istaken up by a liquid or solid, or in which aliquid is taken up by a solid. In absorption,the substance absorbed goes into the bulkof the material. Solids that absorb gases orliquids often have a porous structure. Theabsorption of gases in solids is sometimescalled sorption. Compare adsorption.

absorption band See band spectrum

absorption coefficient See Lambert’slaw.

absorption of radiation No mediumtransmits radiation without some energyloss. This loss of energy is called absorp-tion. The energy is converted to some otherform within the medium. See also Lam-bert’s law.

absorption spectrum See spectrum.

absorptivity /ab-sorp-tiv-ă-tee, -zorp-/See absorptance.

abundance 1. The relative amount of agiven element among others; for example,the abundance of oxygen in the Earth’scrust is approximately 50% by mass.2. The amount of a nuclide (stable or ra-dioactive) relative to other nuclides of thesame element in a given sample. The nat-ural abundance is the abundance of a nu-clide as it occurs naturally. For instance,chlorine has two stable isotopes of masses35 and 37. The abundance of 35Cl is75.5% and that of 37Cl is 24.5%. For someelements the abundance of a particular nu-clide depends on the source.

abundance ratio The ratio of the numberof atoms of an isotope to the number ofatoms of another isotope of the same ele-ment in a sample. See abundance.

a.c. See alternating current.

acceleration Symbol: a The SI unit of lin-ear acceleration is the meter per second persecond (m s–2). The SI unit of angular ac-celeration is the radian per second per sec-ond (rad s–2). 1. When considering motionin one dimension, and in unscientificusage, acceleration means rate of increaseof speed. This is a scalar quantity, whichcan be positive or negative. Negative val-ues mean that the speed is decreasing andmay be called deceleration or retardation.2. In scientific study of motion in two orthree dimensions acceleration means rateof change of velocity; a = dv/dt. This is avector quantity having magnitude (whichis always positive) and direction. When-ever speed changes (increasing or decreas-ing), or direction changes, or both speedand direction change, this is an accelera-tion.

By Newton’s second law the net force Facting on a body of mass m gives it an ac-celeration a where F = ma.

See equations of motion; Newton’slaws of motion.

acceleration due to gravity See acceler-ation of free fall.

acceleration of free fall (acceleration dueto gravity; gravitational acceleration)Symbol: g The constant acceleration of amass moving freely (without friction orany other force) close to the surface of theEarth. This acceleration is measured withrespect to the nearby surface of the Earthso is not exactly equal to the accelerationtoward the center, because of the cen-tripetal acceleration of the reference point.On correcting for this small error g is ameasure of the gravitational field strength,the force on unit mass. The force mg issometimes called the weight.

The value of g decreases on going up-ward from the surface and increases ongoing down a mine. It increases slightly on

going from the equator toward the poles,because of the effects of rotation and theslight flattening of the Earth at the poles.Certain geological features cause smalllocal differences, the detection of whichmay be useful in prospecting for minerals,especially oil. The standard value assumedfor g is 9.806 65 m s–2. For rough calcula-tions one can assume g = 10 m s–2.

See Newton’s law of universal gravita-tion, weight.

accelerator A device for acceleratingcharged particles to high energies so thatthey are able to penetrate to the nuclei ofatoms in a target, causing nuclear reac-tions. The earliest accelerator was inventedby Cockcroft and Walton and was firstused to accelerate protons toward a targetof lithium.

Two types are now in use. In LINEAR AC-CELERATORS the particles are accelerated ina straight line. Cyclic accelerators use mag-netic fields to keep the particles moving incircular or spiral paths. Examples of cyclicaccelerators are the cyclotron, the synchro-cyclotron, and the betatron.

acceptor /ak-sep-ter, -tor/ See semicon-ductor.

acceptor circuit See resonance.

accommodation The action of the EYE inchanging its focal power. The normal eyehas a high power (short focal distance) forviewing close objects; it relaxes to lowpower for very distant objects. Accommo-dation is accomplished by muscles in a ringround the lens of the eye, which are able tochange the shape of the lens. The AMPLI-TUDE OF ACCOMMODATION decreases withage – the power range is around 11diopters at age 10 and 1 diopter at age 70.Thus the distance between far point andnear point decreases with age. This effect ispresbyopia.

accumulator (secondary cell; storage bat-tery) An electric cell or battery that can becharged by passing an electric currentthrough it. The chemical reaction in the cellis reversible. When the cell begins to run

down, current in the opposite directionwill convert the reaction products backinto their original forms. The most com-mon example is the lead-acid accumulator,used in vehicle batteries.

achromat /ak-rŏ-mat/ An achromaticlens.

achromatic color /ak-rŏ-mat-ik/ A colorthat has no hue; i.e. black, white, or gray.

achromatic lens A compound lens whoseelements differ in refractive constant inorder to minimize chromatic aberration.Simple achromatic doublets are formed bycombining two lenses of different glass.The condition for achromatism is:

ω1P1 + ω2P2 = 0where ω1 and ω2 are the dispersive powersof the glasses of the lenses, and P1 and P2are the powers of the lenses. Achromaticlenses are corrected for chromatic aberra-tion at two different wavelengths. See alsoapochromatic lens.

aclinic line /ay-klin-ik/ (magnetic equator)See isoclinic line.

acoustics The study of the productionand properties of sounds. The term is alsoused to describe the way in which sound isreproduced in practical situations.

acoustoelectronics /ă-koos-toh-i-lek-tron-iks/ The branch of electronics thatdeals with sound waves at the frequenciesof microwaves.

actinic radiation /ak-tin-ik/ Radiationthat can cause a chemical reaction; for ex-ample, ultraviolet radiation is actinic.

actinium /ak-tin-ee-ŭm/ A soft silvery-white radioactive metallic element that isthe first member of the actinoid series. Itoccurs in minute quantities in uraniumores. It can be produced by neutron bom-bardment of radium and is used as a sourceof alpha particles. The metal glows in thedark.

Symbol: Ac; m.p. 1050±50°C; b.p.3200±300°C; r.d. 10.06 (20°C); p.n. 89;

3

actinium

most stable isotope 227Ac (half-life 21.77years).

actinometer /ak-tă-nom-ĕ-ter/ An instru-ment for measuring the intensity of radia-tion.

actinon /ak-tă-non/ See emanation.

action 1. An out-dated term for force. Seereaction.2. The product of kinetic energy timestime, or momentum times displacement,integrated along the path of a body. It hasthe dimensions of mass times the square oflength over time, the same as for angularmomentum. The Planck constant is some-times called Planck’s constant of action.

action at a distance A type of interactionbetween two bodies such that each influ-ences the other through space. The descrip-tions of gravity by Newton’s law andelectrostatics by Coulomb’s law are exam-ples of action at a distance. Theories basedupon action at a distance do not have amechanism for explaining how the forcegets across space from one body to theother, and it is usual to describe such phe-nomena using field theories.

activated charcoal See charcoal.

activation analysis A method used foranalyzing materials in which a very smallsample of the material is bombarded withneutrons. A nucleus of the material cap-tures a neutron to form an excited nucleuswith a nucleon number one higher thanthat of the original nucleus. The wave-length of gamma rays emitted by the ex-cited nucleus returning to its ground stateenables the element to be identified. Thetechnique is very sensitive and can detectconcentrations of a few parts per million.

activity Symbol: A For a radioactive sub-stance, the average number of atoms disin-tegrating per unit time.

acuity, visual The ability of the eye to seeseparately two points close to each other. Itis a measure of the resolving power of the

eye’s optical system and depends on thedensity of cells in the retina. The maximumacuity of the normal human eye is around0.5 minutes of arc – points separated bythis angle at the eye should be seen as sep-arate. See resolution.

additive process A process of color mix-ing by addition. See color.

adhesion A force of attraction betweenatoms or molecules of different substances.For example, adhesion between water mol-ecules and glass creates a MENISCUS. Seecapillary action.

adiabatic change /ad-ee-ă-bat-ik/ Achange taking place in a system that hasperfect thermal insulation, so that heatcannot enter or leave the system and energycan only be transferred by work. In prac-tice, a close approximation to an adiabaticchange can be achieved by the processbeing too rapid for significant heat trans-fer, or by the large scale of the system (e.g.a large volume of air in the atmosphere).

In an adiabatic expansion of a gas, me-chanical work is done by the gas as its vol-ume increases and the gas temperaturefalls. For an ideal gas undergoing a re-versible adiabatic change it can be shownthat

pVγ = K1Tγp1–γ = K2

and TVγ–1 = K3where K1, K2, and K3 are constants and γ isthe ratio of the principal specific heat ca-pacities. Compare isothermal change.

adiabatic demagnetization A method ofproducing temperatures close to absolutezero. A sample of a paramagnetic salt iscooled in liquid helium in a strong magne-tizing field. The sample is then thermallyisolated by pumping away the helium, andthe magnetic field is removed. The sampledemagnetizes itself at the expense of its in-ternal energy so that the temperature falls.Temperatures of the order of a millikelvincan be obtained.

admittance Symbol: Y The reciprocal ofimpedance, measured in siemens (S). It is a

actinometer

4

measure of the response of an electric cir-cuit to an alternating signal. See also im-pedance.

adsorbent /ad-sor-bĕnt, -zor-/ The sub-stance on whose surface ADSORPTION oc-curs.

adsorption /ad-sorp-shŏn, -zorp-/ Aprocess in which a layer of atoms or mol-ecules of one substance forms on the sur-face of a solid or liquid. All solid surfacestake up layers of gas from the surroundingatmosphere. The adsorbed layer may beheld by chemical bonds (chemisorption) orby weaker van der Waals’ forces (ph-ysisorption). Compare absorption.

advanced gas-cooled reactor See gas-cooled reactor.

advection /ad-vek-shŏn/ The transfer ofmatter such as water vapor or heat throughthe atmosphere as a result of horizontalmovement of an air mass.

aerial See antenna.

aerodynamics The branch of physicsconcerned with the movement of gases andthe motion of solid objects in gases (usuallyair). It is applied to the flight of birds andinsects, and (particularly) to various kindsof aircraft. See drag; lift; Reynold’s num-ber; turbulent flow.

aerogenerator An electric generator dri-ven by wind power.

aerosol A dispersion of small particles ofsolid or droplets of liquid in a gas.

aether /ee-th’er/ See ether.

after-image An image seen after the eye’sretina has been exposed for a time to an in-tense or stationary light source. It may benegative or positive, or appear in comple-mentary colors.

agate /ag-it, -ayt/ A crystalline form of sil-ica used, because of its hardness, in makingknife edges in balances, pendulums, etc.

age of the Earth An age of approxi-mately 4.5 billion years. The Earth isthought to have formed, like the rest of theplanets, soon after the solar system itselfwas formed. Early calculations in the 19thcentury based on rates of cooling gavemuch lower estimated ages. Present esti-mates are based on radioactive dating ofrocks. The original estimates were too lowbecause they did not allow for radioactiv-ity in the Earth’s core.

age of the universe An age of approxi-mately 13.7 billion years since the BIG

BANG. This figure has been arrived at bycareful analysis of the cosmic microwavebackground radiation in the early years ofthis century.

agonic line /ă-gon-ik, ay-/ See isogonicline.

AGR Advanced gas-cooled reactor. Seegas-cooled reactor.

air column A long column of air in whichstanding waves can be set up. This type ofcolumn is used in musical instrumentsbased on pipes. If both ends of the pipe areopen there are antinodes at both ends. Ifone end is open and the other end is closedthere is a node at the closed end and an an-tinode at the open end.

airfoil A lifting wing on an aircraft, or an-imal, or the cross-sectional shape of such awing.

air pressure The PRESSURE OF THE ATMOS-PHERE at any point on Earth or in theEarth’s atmosphere.

air wedge An arrangement producing lo-calized interference patterns by reflectionat the two sides of a wedge-shaped film ofair (as between two glass slides at anangle). Newton’s rings (variable wedgeangle) and thin films (zero wedge angle)produce similar effects. In an air wedge thefringes (with monochromatic light, wave-length λ) are light and dark bands parallelto the thin edge of the wedge. A brightfringe occurs when 2t + λ/2 = mλ, t being

5

air wedge

the thickness and m an integer. For a darkfringe 2t = mλ. See also interference.

albedo /al-bee-doh/ The ratio of theamount of light reflected from a surface tothe amount of incident light.

alcohol thermometer A liquid-in-glassthermometer that uses ethanol as its work-ing substance. The ethanol commonly con-tains a red or blue dye to make the liquidmore visible. See also thermometer.

allotropy /ă-lot-rŏ-pee/ The existence of asolid substance in different physical forms.Tin, for example, has metallic and non-metallic crystalline forms. Carbon has twocrystalline allotropes: diamond andgraphite.

alloy A mixture of two or more metals(e.g. bronze or brass) or a metal with smallamounts of non-metals (e.g. steel). Alloysmay be completely homogeneous mixturesor may contain small particles of one phasein the other phase.

alpha decay A type of radioactive decayin which the unstable nucleus emits a he-lium nucleus. The resulting nuclide has amass number decreased by 4 and a protonnumber decreased by 2. An example is:

282

86Ra → 2

82

62Rn + 24He

The particles emitted in alpha decay arealpha particles. Streams of alpha particlesare alpha rays or alpha radiation. Theypenetrate a few centimeters of air at STP ora metal foil of mass/area a fewmilligram/cm2. See also beta decay.

alternating current (a.c.) Electric currentthat regularly reverses its direction. In thesimplest case, the current varies with time(t) in a simple harmonic manner, repre-sented by the equation I = I0sin2πft, f beingthe frequency. Alternating current can bedescribed by its peak value I0, or by itsroot-mean-square value IRMS (= I0/√2 for asine wave). In the USA it is 220 V (RMS) ata frequency of 60 hertz. In the UK, themains electricity supply is also alternating,about 250 V (RMS) at a frequency of 50hertz. Compare direct current.

alternating-current circuit A circuitcontaining a resistance R, capacitance C,and inductance L, with an alternating volt-age supply, is called an LCR circuit. Thesimplest type is one in which L, C, and Rare all in series. The impedance of such acircuit is given by

Z = √[(XL – XC)2 + R2]where XL is the reactance of the inductor(2πfL), and XC is the reactance of the ca-pacitor (½πC). The current I is given byV/Z. There is a phase difference betweenthe current in the circuit and the voltage.Current lags behind voltage by a phaseangle φ:

tanφ = (XL – XC)/RSee also resonance.

alternator A generator for producing analternating electric current.

altimeter /al-tim-ĕ-ter/ An instrument formeasuring altitude – that is, the heightabove a certain reference level (usuallymean sea-level). Because atmospheric pres-sure varies with altitude, an aneroidbarometer can be used as an altimeter. Seebarometer.

albedo

6

interferingwave trains

air

path difference = 2t + λ /2(for very small angles )

t

Air wedge

R LC

~

Alternating-current circuit

aluminum A soft moderately reactivemetal. Aluminum has the electronic struc-ture of neon plus three additional outerelectrons. There are numerous minerals ofaluminum; it is the most common metallicelement in the Earth’s crust (8.1% by mass)and the third in order of abundance.

Symbol: Al; m.p. 660.37°C; b.p.2470°C; r.d. 2.698 (20°C); p.n. 13; r.a.m.26.981539.

AM See amplitude modulation.

Amagat’s experiments /ah-mah-gah/ SeeAndrews’ experiments.

amalgam /ă-mal-găm/ An alloy of mer-cury with one or more other metals. Amal-gams may be liquid or solid.

americium /am-ĕ-rish-ee-ŭm/ A highlytoxic radioactive silvery element of theactinoid series of metals. A transuranic ele-ment, it is not found naturally on Earth butis synthesized from plutonium. 241Am hasbeen used in gamma-ray radiography.

Symbol: Am; m.p. 1172°C; b.p.2607°C; r.d. 13.67 (20°C); p.n. 95; moststable isotope 243Am (half-life 7.37 × 103

years).

ammeter /am-mee-ter/ A meter used tomeasure electric current. Ammeters have tohave low resistance as they are connectedin series in the circuit. Commonly, moving-coil instruments are used with shunt resis-tors to increase the current range. Foralternating current a rectifier is necessary.Moving-iron instruments can be used bothfor d.c. and a.c. High-frequency currentsmay be measured with a hot-wire instru-ment.

amorphous /ă-mor-fŭs/ Denoting a solidthat has no crystalline structure; i.e. there isno long-range ordering of atoms. Manysubstances that appear to be amorphousare in fact composed of many tiny crystals.Soot and GLASS are examples of truly amor-phous materials.

amount of substance Symbol: n A phys-ical quantity that is a measure of the num-

ber of entities present in a substance. Seemole.

ampere /am-pair/ Symbol: A The SI baseunit of electric current, defined as the con-stant current that, maintained in twostraight parallel infinite conductors of neg-ligible circular cross section placed onemeter apart in vacuum, would produce aforce between the conductors of 2 × 10–7

newton per meter. The ampere is namedfor the French physicist and mathematicianAndré Marie Ampère (1775–1836).

ampere balance See current balance.

ampere-hour Symbol: Ah A unit of elec-tric charge equal to the charge transferredthrough a conductor in one hour by a cur-rent of one ampere. It is equal to 3.6coulombs.

Ampère–Laplace law /ahm-pair lah-plahs/ See Ampère’s law.

Ampère’s law 1. (Ampère–Laplace law)The elemental force, dF, between two cur-rent elements, I1dl1 and I2dl2, parallel toeach other at a distance r apart in freespace is given by:

d = µ0I1d1l1I2dl2sinθ/4πr2

Here µ0 is the permeability of free spaceand θ is the angle between either elementand the line joining them.2. The principle that the sum or integral ofthe magnetic flux density B times the pathlength along a closed path round a current-carrying conductor is proportional to thecurrent I. For a circular path of radius rround a long straight wire in a vacuum,B.2πr = µ0I. (µ0 is the magnetic permeabil-ity of free space.) Ampère’s law enables thevalue of B inside a solenoid to be calculatedusing the equation B = nµ0I, where n is thenumber of turns per unit length. See alsoMaxwell’s equations.

ampere-turn /am-pair tern/ Symbol: AtThe SI unit of magnetomotive force(m.m.f.) equal to the magnetomotive forceproduced by a current of one ampere flow-ing through one turn of a conductor. Seealso magnetic circuit.

7

ampere-turn

amplification factor See triode.

amplifier A device that increases an elec-trical signal applied to it as an input. If theinput is an alternating voltage, the outputvoltage has a similar waveform with an in-creased amplitude.

The ratio of the output signal to theinput signal (called the gain), will usuallyvary with the signal frequency. Amplifiersare usually designed to give a particularcurrent, voltage, or power gain over the re-quired frequency range. Some circuits con-taining a number of amplifying stages cancope with frequencies from 0 hertz (steadydirect current) to radiofrequencies. Inmodern solid-state electronics, all of theamplifier circuit components, includingmany individual amplifying stages, aremanufactured in a single integrated circuit.

amplitude The maximum value of a vary-ing quantity from its mean or base value. Inthe case of a simple harmonic motion – awave or vibration – it is half the maximumpeak-to-peak value.

amplitude modulation (AM) A type ofmodulation in which the amplitude of aCARRIER WAVE is modulated by an imposedsignal, usually at audio frequency.

In this way communication of a signalis made between two distant points using aradio transmission as carrier. When thecarrier wave is received the audio compo-nent is extracted by the process of DEMOD-ULATION, and the original sound may bereproduced.

amplitude of accommodation Theeye’s range of accommodation in terms of

refractive power (often measured indiopters). It is given by (1/u1 – 1/u2), whereu1 is the distance from the near point to thelens and u2 is the distance from the farpoint to the lens.

amu /ay-em-yoo/ See atomic mass unit.

analyzer A device for determining theplane of polarization of plane-polarized ra-diation. Maximum intensity is transmittedif the plane is parallel with the analyzer’sdirection of polarization; the intensity is aminimum (theoretically zero) if the two areperpendicular. For visible radiation, ana-lyzers are usually Polaroid sheets or Nicolprisms.

anastigmatic lens /an-ă-stig-mat-ik, an-as-tig-/ A lens designed so as to minimizeits astigmatic aberration. Anastigmaticlenses have different curvatures in differentdirections; the surface of an anastigmaticlens is part of a toroid.

AND gate See logic gate.

Andrews’ experiments Experimentsperformed (1863) on the effect of pressureand temperature on carbon dioxide andnamed for the Irish physical chemistThomas Andrews (1813–85). Andrewsused two thick-walled glass capillary tubes,one containing dry carbon dioxide and theother dry nitrogen. The top end of eachtube was closed and the bottom end con-tained a plug of mercury to trap the gas.The bottom ends of the tubes were sealedinto a case containing water, and pressurecould be applied by means of a pair ofscrews. In this way Andrews achieved pres-

amplification factor

8

signal wave carrier wave modulated wave

Amplitude modulation

sures up to above 10 MPa. The nitrogenwas used to measure the pressure by as-suming that it obeyed Boyle’s law. The ap-paratus was surrounded by a constanttemperature bath, so that isothermals (p–Vcurves) could be plotted at different tem-peratures.

In this way Andrews showed the behav-ior near the critical temperature, and theliquefaction of carbon dioxide by pressurebelow the critical temperature. Similar ex-periments were done on carbon dioxideand other gases by the French physicistEmile Hilaire Amagat (1841–1915).

anechoic chamber /an-ek-oh-ik/ (deadroom) A room designed so that there is lit-tle or no reflection of sound from its inter-nal walls. The walls are covered withpyramid shapes so that stationary wavesare not produced between parallel sur-faces. They are coated with absorbing ma-terial. Anechoic chambers are used forexperiments in acoustics.

anemometer /an-ĕ-mom-ĕ-ter/ An instru-ment for measuring wind speed. A simpletype consists of several cups or vanes at-tached to a vertical shaft that rotates whenthe cups/vanes are forced round by thewind. The shaft can be geared to a pointerto give a direct reading of wind speed on adial.

aneroid (non-liquid) barometer /an-ĕ-roid/ See barometer.

angle of deviation See deviation.

angle of dip See inclination.

angle of incidence The angle between aray incident on a surface and the normal tothe surface at the point of incidence.

angle of polarization See Brewsterangle.

angle of reflection The angle between aray reflected by a surface and the normal tothe surface at the point of reflection.

angle of refraction The angle between aray refracted at the surface between twomedia and the normal to the surface at thepoint of refraction.

angstrom /ang-strŏm/ Symbol: Å A unitof length defined as 10–10 meter. Theangstrom was formerly used for expressingwavelengths of light or ultraviolet radia-tion or for interatomic distances and thesizes of molecules. The angstrom is namedfor the Swedish physicist Anders JonasÅngstrom (1814–74).

angular acceleration Symbol: α The ro-tational acceleration of an object about anaxis:

α = dω/dt or α = d2θ/dt2

Here ω is angular velocity; θ is angular dis-placement. Angular acceleration is directlyanalogous to linear acceleration, a. See alsoequations of motion; rotational motion.

angular displacement Symbol: θ The ro-tational displacement of an object about anaxis. If the object (or a point on it) movesfrom point P1 to point P2 in a plane per-pendicular to the axis, θ is the angle P1OP2,where O is the point at which the perpen-dicular plane meets the axis. See also rota-tional motion.

angular frequency (pulsatance) Symbol:ω The number of complete rotations perunit time. A simple harmonic motion offrequency f can be represented by a pointmoving in a circular path at constantspeed. The foot of a perpendicular from the

9

angular frequency

gas

unsaturated vaporliquid + saturated

vapor

liqu

id

V (arbitrary units)

P(a

tmo

sph

eres

)

100

80

60

40

Andrew’s isothermal for CO2

point to a diameter of the circle movesbackward and forward along the diameterwith simple harmonic motion. The angularfrequency of this motion is 2πf, where f isthe frequency. The unit is the radian persecond.

angular magnification (magnifyingpower) Symbol: M The ratio of the anglesubtended at the eye by an image to thatsubtended by the object: M = θ1/θ0. The ob-ject and image are considered to be at theiractual positions, except in the case of mi-croscopes. Here it is conventional to mea-sure θ0 for the object at the standardnear-point distance (250 mm from theeye). The maximum useful magnifyingpower depends on the resolving power ofthe viewing system – i.e. the acuity of theeye or the grain of the photographic emul-sion. See also magnification.

angular momentum Symbol: L Theproduct of the moment of inertia of a bodyand its angular velocity. See also rotationalmotion.

angular velocity Symbol: ω The rate ofchange of angular displacement: ω = dθ/dt.See also rotational motion.

anharmonic oscillator /an-har-mon-ik/A system whose vibration, while still peri-odic, cannot be described in terms of sim-ple harmonic motions (i.e. sinusoidalmotions). In such cases, the period of oscil-lation is not independent of the amplitude.

anion /an-ÿ-ŏn, -on/ A negatively chargedion, formed by addition of electrons toatoms or molecules. In electrolysis anionsare attracted to the positive electrode (theanode). Compare cation.

anisotropy /an-ÿ-sot-ŏ-pee/ A medium isanisotropic if a certain physical quantitydiffers in value in different directions.Most crystals are anisotropic electrically;important polarization properties resultfrom differences in transmission of electro-magnetic radiation in different directions.Compare isotropy.

annealing /ă-neel-ing/ The process ofheating a solid to a temperature below themelting point, and then cooling it slowly.Annealing removes crystal imperfectionsand strains in the solid.

annihilation A reaction between a parti-cle and its antiparticle; for example, be-tween an electron and a positron. Theenergy released is equal to the sum of therest energies of the particles and their ki-netic energies. In order that momentum beconserved two photons are formed, mov-ing away in opposite directions. This radi-ation (annihilation radiation) is in thegamma-ray region of the electromagneticspectrum. The quantum energy is about0.51 MeV.

Annihilation also can occur between anucleon and its antiparticle. In this casemesons can be produced.

annual variation The direction andstrength of the Earth’s magnetic field atany point changes with time. This must beallowed for by navigators. One suchchange is a variation with a period of ayear, but there are others. The amplitude ofthe annual variation is greatest duringmaximum sun-spot activity. See alsoEarth’s magnetism; magnetic variation.

annular eclipse See eclipse.

anode /an-ohd/ In electrolysis, the elec-trode that is at a positive potential with re-spect to the cathode. In any electricalsystem, such as a discharge tube or a solid-state electronic device, the anode is the ter-minal at which electrons flow out of thesystem.

anomalous dispersion The refractiveindex of a transparent medium normallyincreases as the wavelength is reduced.There is then a range of wavelengths (usu-ally in the ultraviolet) in which the radia-tion is absorbed fairly strongly. Such littleradiation as is transmitted in this regionshows anomalous dispersion, that is the re-fractive index decreases as the wavelengthis reduced. See dispersion.

angular magnification

10

anomalous expansion An increase involume resulting from a decreased temper-ature. Most liquids increase in volume astheir temperature rises. The density of theliquid falls with increased temperature.Water, however, shows anomalous behav-ior. Between 0 and 4°C the density in-creases with increasing temperature.

antenna (aerial) (pl. antennae) A devicesuch as a wire, rod or dish used to transmitor receive radio waves. The simplest type isa rod of ferrite as used inside domesticradio sets; complex transmitting antennasmay be mounted on a mast 100 meters tall.An omnidirectional antenna transmits orreceives signals from all directions. A di-rectional antenna is designed to operatepreferentially in a single direction.

anthropic principle /an-throp-ik/ A the-ory in cosmology about the present state ofthe Universe. The weak anthropic principleconcerns intelligent life on Earth and statesthat the Universe is the way that it is be-cause if it were otherwise we would not behere to observe it. For example, if the valueof the gravitational constant were signifi-cantly different, the Universe would nothave evolved in a way that allowed intelli-gent life to form. The strong anthropicprinciple deals with ideas of other possibleuniverses and with other lifeforms. The an-thropic principle has been the subject ofmuch controversy among physicists.

anticlastic curvature /an-tee-klas-tik/The saddle-shaped curve on the upper sur-face of a horizontal bar that is being bentby a downward force at each end. The ef-fect is easily demonstrated by bending aneraser.

antiferromagnetism /an-tee-fe-roh-mag-nĕ-ti-zăm/ A kind of MAGNETISM found inmany solids at low temperatures. The mol-ecular magnets form two arrays, alignedantiparallel. At the lowest temperaturesthere are equal numbers with equal mag-netic moments in opposite directions, giv-ing zero resultant magnetization. As thetemperature is raised, the susceptibility in-creases up to the Néel temperature above

which the substance is paramagnetic. TheNéel temperature is named for the Frenchphysicist Louis Néel (1904–2000). See alsoferrimagnetism.

antimatter Matter formed of antiparti-cles. Nuclei of antimatter would consist ofantiprotons and antineutrons, and wouldbe surrounded by orbiting positrons. Whenmatter encounters antimatter annihilationoccurs. See annihilation.

antimony /an-tă-moh-nee/ A metalloid el-ement existing in three allotropic forms;the most stable is a brittle silvery metal. Itis used in alloys – small amounts of anti-mony can harden other metals. It is alsoused in semiconductor devices.

Symbol: Sb; m.p. 630.74°C; b.p.1635°C; r.d. 6.691; p.n. 51; r.a.m. 112.74.

antinode /an-tee-nohd/ See node.

antiparallel /an-tee-pa-ră-lel/ Having par-allel lines of action that are directed in op-posite directions.

antiparticle A particle of the same massand spin, but opposite charge (and otherproperties) to its corresponding particle.For example, a proton and antiproton bothhave mass 1836 times that of an electronand spin ½ unit, but the charge on the pro-ton is +1 unit, while that on the antiprotonis –1 unit. For unstable particles, such as anisolated neutron, the particle and antiparti-cle have the same half-life. For unchargedparticles the antiparticle is indicated by abar above the symbol, such as ³ for the an-tineutron. For charged particles the distinc-tion is indicated by the sign, for example,e+ is the positron, the antiparticle of anelectron. Antiparticles of fermions are sub-ject to a conservation law according towhich new particles can only be created inparticle–antiparticle pairs, while particlescan be destroyed only by annihilation withtheir antiparticles. This rule of numberconservation does not apply to BOSONS. Seealso fermion.

aperture A measure of the effective diam-eter (d) of a mirror or lens compared with

11

aperture

its focal distance (f): aperture = d/f. Thus a50-mm camera lens may be used with anaperture diameter of 12.5 mm. Then, aper-ture = 12.5/50. This is usually described asan f-number. In this case the aperture di-ameter is f/4, often written as f4.

The transmitted light intensity dependson aperture diameter, so that I is propor-tional to d2. However, large apertures leadto large aberrations although diffractioneffects are more serious at small apertures.In many optical instruments, iris di-aphragms vary the aperture to obtain theoptimum results.

aplanatic lens /ap-lă-nat-ik/ A lens de-signed so as to minimize both its astigmaticand coma aberration.

apochromatic lens /ap-ŏ-krŏ-mat-ik/ Alens designed to correct for chromaticaberration at three different wavelengths.Apochromatic lenses are constructed ofthree or more kinds of glass. They thushave better correction than achromaticlenses, which correct at two differentwavelengths (usually in the red and blue re-gions of the spectrum). See achromaticlens.

apparent depth Because radiation travelsat different speeds in different media, theapparent depth or thickness of a transpar-ent sample is not the same as its real depth

or thickness. The effect is very obviouswhen one looks down into a glass of wateror a clear pool. It is associated with the factthat a long object partly submerged inwater seems bent at the water surface.

The refractive constant of the substancecan be measured on this basis:

refractive index =real depth/apparent depth

The relation is used in a number ofmethods for finding the refractive constantof a transparent medium. It applies to allwave radiations, not just to visible radia-tion.

apparent expansion See expansivity.

Appleton layer /ap-ăl-tŏn/ (F-layer) Theupper of the main layers in the IONOSPHERE,at a height above about 150 km. It reflectsradio waves. The Appleton layer is namedfor the British physicist Sir Edward VictorAppleton (1892–1965). See Heavisidelayer.

aqueous humor The watery substancebetween the cornea and the lens in the EYE.

Arago’s spot See Poisson’s spot.

arc, electric See electric arc.

Archimedes’ principle /ar-kă-mee-deez/The upward force on an object totally orpartly submerged in a fluid is equal to theweight of fluid displaced by the object. Theupward force, often called upthrust, resultsfrom the fact that the pressure in a fluid(liquid or gas) increases with depth. If theobject displaces a volume V of fluid of den-sity ρ, then:

upthrust u = Vρgwhere g is the acceleration of free fall.

If the upthrust on the object equals theobject’s weight, the object will float. Theprinciple is named for the Greek mathe-matician Archimedes (287 BC–212 BC). Seeflotation; law of.

arc lamp An intense light source in whichthe light is produced by an electric arc be-tween two (usually carbon) electrodes. Arc

aplanatic lens

12

observer

medium 1

surface

medium 2

realrealrealdepthdepthdepth

apparentapparentapparentdepthdepthdepth

imageimageimage

objectobjectobject

Apparent depth

lamps are used in lighthouses and assearchlights and spotlights.

argon /ar-gon/ An inert colorless odorlessmonatomic element of the rare-gas group.It forms 0.93% by volume of air. Argon isused to provide an inert atmosphere inelectric and fluorescent lights, in welding,and in extracting titanium and silicon. Theelement forms no known compounds.

Symbol: Ar; m.p. –189.37°C; b.p.–185.86°C; d. 1.784 kg m–3 (0°C); p.n. 18;r.a.m. 39.95.

arithmetic series A series in which thedifference between two consecutive mem-bers is a constant number. If the first termof an arithmetic series is a and the commondifference between two consecutive termsis d then the nth term is given by [a +(n–1)d] and the sum of the first n terms isgiven by n[2a + (n–1)d]/2.

armature 1. The part of an electric motoror generator that carries the principal cur-rent. This is the rotating coil in a smallmotor but the stationary coil in a largemotor or generator. Torque acting on thearmature enables work to be done againstthe load. See also electric motor; rotor; sta-tor.2. The moving part of any electromechani-cal device, such as an electric bell or relay.

arsenic /ar-sĕ-nik, ars-nik; adj. ars-sen-ik/A toxic metalloid element existing in sev-eral allotropic forms; the most stable is abrittle gray metal. It is used in semiconduc-tor devices, alloys, and gun shot.

Symbol: As; m.p. 817°C (gray) at 3MPa pressure; sublimes at 616°C (gray);r.d. 5.78 (gray at 20°C); p.n. 33; r.a.m.74.92159.

artificial radioactivity Radioactivityproduced by nuclear reactions. Variousmethods are available.

Bombardment by neutrons, particularlyusing a nuclear reactor, can give very manyartificial radioactive substances, most ofwhich are beta active, emitting electrons.For example:

5927Co + 10n → 60

27Co + γ rays6027Co is a beta active material with half-life5.3 years and is very important as the betaemission is followed instantaneously bygamma rays of high quantum energy,which are used in radiography and cancertherapy.

Bombardment by light atomic nucleiaccelerated in a cyclotron or similar ma-chine often gives positron-emitting ra-dionuclides. For example

2412Mg + 21H → 22

11Na + 42He2211Na has half-life 2.6 years and emitspositrons and gamma rays. Transuranic el-ements can be produced in this way.

The products of nuclear fission areoften highly active; most emit electrons(beta rays) and several also emit gammarays.

asdic /az-dik/ See sonar.

Aspect experiment See Bell’s paradox.

astable circuit /ay-stay-băl/ (pulse genera-tor) A multivibrator circuit that switchescontinually and regularly from one state toanother. Unlike other forms of MULTIVIBRA-TOR, no trigger pulse is needed. It is used incomputers as a source of clock pulses forcounting, because the output is a rectangu-lar voltage waveform.

In the astable multivibrator, two tran-sistors are arranged with the base terminalof each connected to the collector terminalof the other through capacitors C1 and C2respectively. There is a steady voltage sup-ply. C1 charges and C2 discharges until thetransistors switch from one state to an-other and the charging direction reverses.The value of the capacitances and resis-tances determines the switching frequency.

astatic coils /ay-stat-ik/ Two identicalcoils connected together in series and sus-pended on the same axis. When a currentpasses through them, any external mag-netic field will result in the same turningforce on each, but in opposite directions.Thus neither the Earth’s magnetic field,nor any other external magnetic distur-bance, will affect the rotation of the axis.

13

astatic coils

astatic pair Two identical magnetic nee-dles suspended on the same vertical axiswith their N- and S-poles pointing in op-posite directions. The couples on the nee-dles from an external magnetic field, suchas the Earth’s, are equal and opposite.Astatic pairs are used in very sensitive gal-vanometers in which the current-carryingcoils are wound round each needle in op-posite directions. The current therefore ro-tates them both in the same direction andexternal magnetic effects are canceled out.

astatine /ass-tă-teen, -tin/ A radioactiveelement belonging to the halogen group. Itoccurs in minute quantities in uraniumores. Many short-lived radioisotopes areknown, all alpha-particle emitters.

Symbol: At; m.p. 302°C (est.); b.p.337°C (est.); p.n. 85; most stable isotope210At (half-life 8.1 hours).

asteroid Any of a number of small objectsthat orbit round the Sun in a narrow belt ofspace (the asteroid belt) located betweenthe orbit of Mars and the orbit of Jupiter.Asteroids have a range of sizes, with thelargest having a radius of approximately500 km. They are sometimes known asminor planets or planetoids.

astigmatism /ă-stig-nă-tiz-ăm/ 1. A com-mon eye defect in which the observer can-not focus clearly on objects at any distance.The cause is usually a non-sphericalcornea. Visual astigmatism may be cor-rected with a lens with a suitable degree ofcylindrical curvature. See anastigmaticlens.2. See aberration.

astronomical telescope See Kepleriantelescope; telescope.

astronomical unit (au; AU) The meandistance between the Sun and the Earth,used as a unit of distance in astronomy formeasurements within the solar system. It isapproximately 1.496 × 1011 meters.

astrophysics The science that deals withphysical and chemical processes in astro-

nomic phenomena, such as the formationand evolution of stars and galaxies.

atmolysis /at-mol-ă-sis/ The separation ofa mixture of gases by using their differentrates of diffusion.

atmosphere See standard pressure.

atmosphere of the Earth The layer ofgas that surrounds the Earth. It consistsmostly of nitrogen (about 78%) and oxy-gen (about 21%) with a little carbon diox-ide and inert (noble) gases. The gas is heldin place by the gravitational field of theEarth. The atmosphere does not have asharp cut-off but becomes thinner as thedistance from the surface of the Earth in-creases. See also pressure of the atmos-phere.

atmospheric pressure See pressure of theatmosphere.

atmospheric window A region in theelectromagnetic spectrum for which radia-tion of a particular range of wavelengthscan reach the Earth from space without ab-sorption by the atmosphere.

atom The smallest part of an element thatcan take part in a chemical reaction. Atomsconsist of a small dense positively chargednucleus, made up of neutrons and protons,with electrons in a cloud around this nu-cleus. The chemical reactions of an elementare determined by the number of electrons(which is equal to the number of protons inthe nucleus). All atoms of a given elementhave the same number of protons (the pro-ton number). A given element may havetwo or more isotopes, which differ in thenumber of neutrons in the nucleus.

The electrons surrounding the nucleusare grouped into shells – i.e. main orbitsaround the nucleus. Within these main or-bits there may be sub-shells. These corre-spond to atomic orbitals. An electron in anatom is specified by four quantum num-bers:1. The principal quantum number (n) canhave values 1, 2, etc. The correspondingshells are denoted by letters K, L, M, etc.,

astatic pair

14

the K shell (n = 1) being the nearest to thenucleus. The maximum number of elec-trons in a given shell is 2n2. This quantumnumber has the largest effect on the ener-gies of the states; high values of n corre-spond to weakly bound (higher energy)electrons.2. The orbital quantum number (l), whichspecifies the angular momentum. For agiven value of n, l can have possible valuesof n–1, n–2, … 2, 1, 0. For instance, the Mshell (n = 3) has three sub-shells with dif-ferent values of l (0, 1, and 2). Sub-shellswith angular momentum, 0, 1, 2, and 3 aredesignated by letters s, p, d, and f. Thisquantum number has the second largest ef-fect on the energies; higher values of l givemoderately higher energy electrons.3. The magnetic quantum number (m).This can have values –l, –(l – 1) … 0 … + (l+ 1), + l. It determines the orientation ofthe electron orbital in a magnetic field.States with the same values of n and l butdifferent values of m have the same energyin the absence of a magnetic field, but dif-fer slightly when a field is applied.4. The spin quantum number (ms), whichspecifies the intrinsic angular momentumof the electron. It can have values +½ and–½. Quantum states in which the spin isparallel to the orbital angular momentumare at slightly higher energy than ones inwhich it is antiparallel. This results, for ex-ample, in the fact that the yellow light froma sodium lamp has two very close lines inits spectrum.

Each electron in the atom has fourquantum numbers and, according to thePauli exclusion principle, no two electronscan have the same set of quantum num-bers. This explains the electronic structureof atoms. See also Bohr theory.

atom bomb A bomb in which the explo-sion is caused by a fast uncontrolled fissionreaction. See nuclear weapon.

atomic clock An apparatus for measur-ing time by the frequency of radiation emit-ted or absorbed in transitions of atoms. Seecesium clock.

atomic energy See nuclear energy.

atomic heat See Dulong and Petit’s law.

atomicity /at-ŏ-mis-ă-tee/ The number ofatoms per molecule of a compound.Methane, for instance has an atomicity offive (CH4).

atomic mass Another name for RELATIVE

ATOMIC MASS, often applied to isotopes.

atomic mass unit (amu) Symbol: u Aunit of mass used for atoms and molecules,equal to 1/12 of the mass of an atom of car-bon-12. It is equal to 1.660 54 × 10–27 kg.

atomic number See proton number.

atomic orbital See orbital.

atomic physics See nuclear physics.

atomic pile A nuclear reactor, particu-larly the early form constructed by pilingup graphite blocks (the moderator) anduranium rods (the fuel).

atomic radius An imprecise measure-ment usually expressed as a half of the dis-tance between neighboring atoms of thesame kind in a crystal or molecule. De-pending on the type of chemical bondingbetween the atoms, it may be qualified ascovalent radius, ionic radius, or metallicradius.

atomic theory The theory that matter ismade up of atoms that combine to formmolecules. Each chemical element has aparticular type of atom, which may joinwith like atoms to form molecules of the el-ement, or with atoms of other elements toform molecules of a compound. The atomconsists of a dense positively charged nu-cleus containing protons and neutrons,surrounded by electrons. The number ofprotons in the nucleus determines the num-ber and distribution of the electrons, whichare held by the positive charge of the nu-cleus. Because the outer electrons form thechemical bonds between atoms, the chemi-cal properties of an element depend on the

15

atomic theory

electronic structure of the atom, and there-fore also on the number of protons. Thenumber of neutrons in the nucleus mayvary, forming different isotopes of an ele-ment. These cannot usually be separatedby chemical means.

atomic volume The relative atomic massof an element divided by its density.

atomic weight See relative atomic mass.

attenuation /ă-ten-yoo-ay-shŏn/ 1. Thereduction of intensity of a radiation as itpasses through a medium. It includes re-ductions due to both absorption and scat-tering.2. Reduction in current, voltage, or powerof an electrical signal passing through a cir-cuit.

atto- Symbol: a A prefix denoting 10–18.For example, 1 attometer (am) = 10–18

meter (m).

attractor The point or set of points inphase space to which a changing systemmoves with time. The idea of an attractorfor a system comes from CHAOS THEORY.The attractor of a system may be a singlepoint (in which case the system reaches afixed state that is independent of time). Al-ternatively, it may be a closed curve,known as a limit cycle. This is the type ofbehavior found in oscillating systems. Insome systems, the attractor is a curve thatis not closed and does not repeat itself.This, known as a strange attractor, is char-acteristic of chaotic systems. See also phasespace.

AU (au) See astronomical unit.

audibility, limits of The frequencies be-yond which sound cannot be heard by thehuman ear. The lowest audible frequencyis about 20 hertz (a deep rumble), and thehighest 15–20 kilohertz (a very high-pitched whistle). Because hearing deterio-rates continuously with age, older peoplecannot detect sounds as high as childrencan. See also infrasound; ultrasonics.

audiofrequency /aw-dee-oh-free-kwĕn-see/ A frequency within the audible fre-quency range (about 20 hertz to about 20kilohertz). Sound vibrations in this rangecan be detected by the human ear. Au-diofrequency electrical signals are con-verted directly into sound in a loudspeaker.

audiometer /aw-dee-om-ĕ-ter/ A devicefor measuring the frequency range of thehuman ear and the minimum intensity ofsound that can be detected at the differentfrequencies. It consists of a signal genera-tor used to feed a tone of variable fre-quency and intensity through a set ofearphones.

Auger effect /oh-zhay/ The ejection of anelectron from an atom or ion without theemission of radiation (x-rays or gammarays). It results from the de-excitation of anexcited electron within the atom. It can beregarded as the internal conversion of thephoton that would otherwise have beenemitted. See internal conversion. TheAuger effect is named for the French physi-cist Pierre Auger (1899–1994).

aurora /ô-ror-ă, -roh-ră/ (polar lights) (pl.auroras or aurorae) An atmospheric phe-nomenon in which colored luminous arcsand streamers appear in the night sky. It iscaused by charged particles from the Suninteracting with atoms in the Earth’s upperatmosphere and the effect is strongest nearthe magnetic poles, giving rise to the au-rora borealis (northern lights) in the northand aurora australis (southern lights) in thesouth.

autoionization /aw-toh-ÿ-ŏ-ni-zay-shŏn/The spontaneous IONIZATION of excitedatoms, ions, or molecules, as in the AUGER

EFFECT.

avalanche A process such as that in whicha single ionization leads in stages to a largenumber of ions. The electrons and ionsproduced ionize more atoms, so that thenumber of ions multiplies quickly. SeeGeiger counter.

atomic volume

16

avalanche diode See Zener diode.

Avogadro constant /ah-vŏ-gah-droh/Symbol: NA The number of particles inone mole of a substance. Its value is6.002 142 × 1023. The constant is namedfor the Italian physicist and chemist CountAmedeo Avogadro (1776–1856).

Avogadro’s law Equal volumes of allgases at the same temperature and pressurecontain equal numbers of molecules. It isoften called Avogadro’s hypothesis. It isstrictly true only for ideal gases and is read-ily explained by the kinetic theory of gases.

avoirdupois /av-er-dŭ-poiz/ A system ofweights based on the pound, which is sub-divided into 16 ounces or 7000 grains. Inscientific use it has been superseded by SI

UNITS.

axis See principal axis.

azeotropic mixture (azeotrope) A mix-ture of two liquids that boils without anychange in composition. The proportions ofcomponents in vapor are the same as in theliquid. Azeotropic mixtures cannot be sep-arated by distillation.

17

azeotropic mixture

18

back e.m.f. An e.m.f. that opposes thenormal flow of electric charge in a circuitor circuit element. 1. In some electrolyticcells a back e.m.f. is caused by the layer ofhydrogen bubbles that build up on thecathode as hydrogen ions pick up electronsand form gas molecules. See also polariza-tion.2. See self-induction.

background radiation Ever-presentlow-intensity ionizing radiation from nat-ural sources, such as cosmic radiation fromouter space and radioactivity from naturalsources in the ground. In astronomy, theterm background radiation refers to a cos-mic background of microwave radiationthought to have originated with the bigbang at the formation of the Universe. Seebig-bang theory.

ballistic galvanometer /bă-lis-tik/ An in-strument that measures the total electriccharge passing through it in a sudden pulseof current. It is a moving-coil instrumentconstructed and calibrated so that themaximum deflection of the pointer is pro-portional to the total charge that haspassed. The coil suspension is lightlydamped in a ballistic galvanometer. Pro-vided that the discharge through it occursin a much shorter time than the suspen-sion’s natural period of oscillation, themaximum deflection is proportional to thetotal charge.

ballistic pendulum A device for measur-ing the velocity of a projectile (e.g. a bul-let). It consists of a heavy pendulum, whichis struck by the projectile. The velocity canbe calculated by measuring the displace-ment of the pendulum and using the law ofconservation of momentum.

ballistics The study of the motion of pro-jectiles.

Balmer series /bahl-mer/ A series of linesin the spectrum of radiation emitted by ex-cited hydrogen atoms. The lines corre-spond to the atomic electrons falling intothe second lowest energy level, emitting en-ergy as radiation. The wavelengths (λ) ofthe radiation in the Balmer series are givenby:

l/λ = R(1/22 – 1/n2)where n is an integer and R is the Rydbergconstant. See Bohr theory. See also spectralseries.

band, energy See energy bands.

band-pass filter An electrical or opticalfilter that transmits only frequencies withina single band.

band spectrum A spectrum that appearsas a number of bands of emitted or ab-sorbed radiation. Band spectra are charac-teristic of molecules. Often each band canbe resolved into a number of closely spacedlines. The bands correspond to changes ofelectron orbit in the molecules. The closelines seen under higher resolution are theresult of different vibrational states of themolecule. See also spectrum.

band theory (of solids) See energy bands.

band width An indication of the range offrequencies, or wavelengths (wave band)that:1. an antenna can receive efficiently;2. a radio receiver or amplifier can effi-ciently handle;3. exist in a radio transmission above andbelow the carrier-wave frequency. See also

B

carrier wave.Bandwidth is a measure of the amount

of information that can be transmitted.

bar A unit of pressure defined as 105 pas-cals. The millibar (mbar) is more common;it is used for measuring atmospheric pres-sure in meteorology.

barium /bair-ee-ŭm/ A dense, low-meltingreactive metal. The electronic configura-tion is that of xenon with two additionalouter 6s electrons. Barium metal is used asa ‘getter’, i.e., a compound added to a sys-tem to seek out the last traces of oxygen;and as an alloy constituent for certain bear-ing metals. Metallic barium has the body-centred cubic structure.

Symbol: Ba; m.p. 729°C; b.p. 1640°C;r.d. 3.594 (20°C); p.n. 56; r.a.m. 137.327.

Barkhausen effect /bark-how-zĕn/ Aphenomenon that demonstrates the do-main theory of magnetism. When a ferro-magnetic substance is being magnetized,changes of induction occur as domains re-verse direction. The effect is demonstratedas shown in the diagram; a series of clicksis heard when the current is switched onand off. The Barkhausen effect is namedfor the German physicist Heinrich GeorgBarkhausen (1881–1956).

barn Symbol: b A unit of area defined as10–28 square meter. The barn is sometimesused to express the effective cross-sectionsof atoms or nuclei in the scattering or ab-sorption of particles.

barometer A device that measures the

pressure of the atmosphere: the standardvalue is around 100 kPa.

The liquid barometer has a column ofliquid in a vertical tube. Various types ofmercury barometer are commonly used. Asthe external atmospheric pressure rises andfalls, the length of the liquid column risesand falls.

The aneroid (non-liquid) barometeremploys a thin-metal evacuated box.Changes in atmospheric pressure move thesides of the box, and levers communicatethis movement to a pointer. In general, it isnot as accurate as a liquid barometer, butit is much easier to transport and use, andis much cheaper. It can also be used as analtimeter (see altimeter).

The liquid barometer provides an ab-solute measure; aneroid barometers mustbe calibrated.

See also barometric height.

barometric height The ‘height’ of a col-umn in a liquid barometer. As the usualbarometer liquid is mercury (because of itsvery high density), barometric height hashistorically been measured in millimetersof mercury (mmHg); 1 mmHg is about133.322 pascals. The standard value of the

19

barometric height

pointer

spring

chain

pivot

box (low pressure inside)

An aneroid barometer (not to scale)

d.c.

magnetizing coil

audioamplifier

search coil

speaker

soft ferromagnetic sample

Barkhausen effect

pressure of the atmosphere is 760 mmHg,(101 325 Pa). See also STP.

baryon number /ba-ree-on/ A propertyof an elementary particle, equal to +1 for abaryon and -1 for an antibaryon. Gaugebosons, leptons, and mesons have a baryonnumber of 0. The baryon number is con-served in all observed types of particle–par-ticle interaction. It has been suggested thatbaryon number might not be conserved incertain types of theories such as GRAND

UNIFIED THEORIES. However, such baryonnumber violating processes have neverbeen observed. See baryons; elementaryparticle.

baryons A group of heavy ELEMENTARY

PARTICLES, which includes protons and neu-trons. The baryons form a subclass of thehadrons. They are further subdivided intonucleons and hyperons.

base See transistor.

base unit A unit within a system of mea-surement from which other units may bederived by combining it with one or moreother base units. With the exception of thekilogram, base SI UNITS are defined in termsof physical constants.

battery (pl. batteries) A number of similarunits, such as electric cells, working to-gether. Many dry ‘batteries’ used in radios,flashlights, etc., are in fact single cells. If a

number of identical cells are connected inseries, the total e.m.f. of the battery is thesum of the e.m.f.s of the individual cells. Ifthe cells are in parallel, the e.m.f. of thebattery is the same as that of one cell, butthe current drawn from each is less (thetotal current is split among the cells).

Baumé scale /boh-may/ A scale of relativedensities (specific gravities) of liquids,sometimes used on hydrometers, on which0° is the density of water and 10° is thedensity of a 10% sodium chloride solution(both at a temperature of 12.5°C). Thescale is named for the French chemist An-toine Baumé (1728–1805). See hydrome-ter.

beam A group of rays of light, or otherforms of radiation, moving in the same di-rection. Strictly, a beam is the entire set ofrays coming from a point or area of an ob-ject. A pencil is a narrow beam from a sin-gle point.

beat frequency See beats.

beats A regular increase and decrease inintensity of sound waves (or other waves)caused by two waves of slightly differentfrequencies being added together. Thewaves successively reinforce and canceleach other as they move in and out ofphase. Sometimes radiofrequency wavesproduce audiofrequency beats in soundequipment. The frequency of the resultingsignal (the beat frequency) is given by thedifference in frequencies of the two signals;i.e. f1 – f2. If two waves of equal amplitude(a) produce beats, the resulting amplitude(A) is given by:

A = 2acos[2π(f1 – f2)t – θ]/2where θ is the phase angle between theoriginal signals. See also heterodyne; inter-ference.

beauty See quark.

becquerel /bek-ĕ-rel/ Symbol: Bq The SIunit of activity of radioactive nuclides. Theactivity in becquerels of a sample at a giventime is the average number of disintegra-tions per second of its atoms at that time.

baryon number

20

Caution It is not wise to work with mercuryin this way.

‘vacuum’(includes vapor)

pressureair

mercury

barometricbarometricbarometricheightheightheight

A simple liquid barometer (not to scale)

The unit is named for the French physicistAntoine Henri Becquerel (1852–1908). Seealso curie.

Beer’s law The fraction of light of a givenwavelength absorbed by a solution variesexponentially with the concentration of theabsorbing substance and the thickness ofits absorbing layer. The law is named forthe German chemist, mathematician, andphysicist August Beer (1825–63).

bel See decibel.

Bell’s paradox A supposed paradox aris-ing from theoretical work on quantum me-chanics by the Irish physicist John Bell(1928–90). The work concerns the inter-pretation of quantum mechanics put for-ward by Niels Bohr, who argued thatquantum mechanics depended on proba-bilities and that particles had an indetermi-nate existence until they were observed.Einstein never accepted this idea – he be-lieved that there was some underlying de-terministic mechanism governed byso-called hidden variables.

As an attack on Bohr’s theories he (withothers) postulated a thought experimentknown as the Einstein-Podolsky-Rosen ex-periment (or EPR experiment). One simpleform of it is to think of a particle of zerospin decaying into two particles with spin,which fly apart. Because spin is conserved,the particles must have opposite values; ifone has a spin ‘up’ the other must have spin‘down’. In the experiment, one waits untilthe particles are several meters apart andthen measures the spin of one particle. Oneinstantly knows the spin of the other (be-cause it must be opposite). But accordingto Bohr, the spin is neither ‘up’ nor ‘down’until it is measured but is in an indetermi-nate state. Einstein argued that this couldnot be the case. Otherwise, one particlewould have to communicate instantlyacross space. In Einstein’s interpretation,the spins would be determined at the timeof decay of the original particle and wouldbe governed by hidden variables.

In the mid 1960s Bell proved a theorem,Bell’s theorem, concerning measurementsof spin in different directions for two par-

ticles. He showed that a certain set of in-equalities (Bell’s inequalities) would hold ifhidden variables operated and Einstein wascorrect. If Bohr was correct, they wouldnot hold.

The theorem opened the way for a realexperimental test of the theories. In theearly 1980s the French physicist Alain As-pect (1947– ) and his team did such an ex-periment in Paris, making simultaneousmeasurements on photons separated by 12meters. The results of the Aspect experi-ment supported Bohr’s interpretation ofquantum mechanics rather than Einstein’s.

The consequence of this is very mysteri-ous (hence the ‘paradox’). It seems thattwo particles can be a large distance apartand still be part of a single system with nei-ther one state nor another but a superposi-tion of both. This phenomenon is knownas quantum entanglement.

Bénard cell /bay-nard, bay-nar/ Any of anumber of small convection cells that canappear in a liquid when it is heated frombelow under certain circumstances. At acertain temperature convection of the liq-uid suddenly occurs. The convection cellsformed are an example of how a degree oforder can be produced in a system whenenergy is supplied. They were studied bythe French scientist Henri Bénard in about1900.

berkelium /ber-klee-ŭm, ber-kee-lee-ŭm/A silvery radioactive transuranic elementof the actinoid series of metals, not foundnaturally on Earth. Several radioisotopeshave been synthesized.

Symbol: Bk; m.p. 1050°C; p.n. 97; r.d.14.79 (20°C); most stable isotope 247Bk(half-life 1400 years).

Bernoulli effect /ber-noo-lee/ The rela-tion between the pressure in a steadilyflowing fluid, and its velocity. The pressureis less where the velocity is higher as, forexample, where water flows through a nar-rower section in a pipe. The pressure thatlifts an aircraft also depends on this effect.For horizontal flow, provided frictional re-sistance is negligible

21

Bernoulli effect

p1 – p2 = ½ρ(v22 – v1

2)where p1 is the pressure where the speed isv1, and p2 is the pressure where the speed isv2. ρ is the density of the fluid. The princi-ple is used in instruments for measuring thespeed of flow, such as the Pitot tube. TheBernoulli effect is named for the Swissmathematician Daniel Bernoulli (1700–82).

beryllium /bĕ-ril-ee-ŭm/ A light metallicelement, similar to aluminum but some-what harder. It has the electronic configu-ration of helium with two additional outer2s electrons. It is used as an antioxidantand hardener in some alloys, such as cop-per and phosphor bronzes. Beryllium is ex-tremely toxic.

Symbol: Be; m.p. 1278±5°C; b.p.2970°C; r.d. 1.85 (20°C); p.n. 4; r.a.m.9.012182.

beta decay /bay-tă, bee-tă/ A type of ra-dioactive decay in which a nucleus emits,for instance, an electron. The result is a nu-clide with the same mass number but a pro-ton number one greater (electron emission)than the original nuclide. An example ofbeta decay is:

13H → 2

3He + e– + ν_

The particles emitted in beta decay arebeta particles. Streams of beta particles arebeta rays or beta radiation. High-energyparticles may penetrate metal sheets ofmass/area a few gram/cm2, or tens of me-ters of air at STP. The lowest energy parti-cles may be absorbed in a few millimetersof air.

Beta particles may have a range of ener-gies up to a maximum value characteristicof the nucleus concerned. The total energyis constant; it is carried by the beta particleand an antineutrino emitted at the sametime. In another type of beta decay,positrons are emitted. In such cases the ex-cess energy is carried by a neutrino. An ex-ample is:

173N → 1

63C + e+ + ν

_

See also alpha decay.

beta transformation The transformationof a nucleus by beta decay. Also the decay

of a neutron to a proton, an electron, andan antineutrino:

n → p + e– + ν_

betatron /bay-tă-tron, bee-/ A device foraccelerating electrons to very high energies(300 MeV or more). Electrons producedfrom a source are injected into an evacu-ated donut-shaped ring between the polesof an electromagnet just as the magneticfield is being increased. As the magneticfield increases the electrons are accelerated,making as many as a quarter of a millioncircuits before the magnetic field reaches itsmaximum, at which time the orbit ischanged by passing a current through aux-iliary coils to deflect the electrons onto atarget. A betatron can be compared to atransformer in which a cloud of electronsin the toroid constitutes the secondary cir-cuit. Alternating current circulates in theprimary coil (the magnetizing coil) but theelectrons are extracted at the end of a quar-ter cycle before the decreasing primary cur-rent can cause deceleration.

BeV See GeV.

bevatron /bev-ă-tron/ The name given tothe proton synchrotron at the University ofCalifornia, which can accelerate protons toenergies of about 10–9 joule (6 GeV).

bias A potential applied to an electrode inan electronic device to produce the desiredcharacteristic.

biaxial crystal /bÿ-aks-ee-ăl/ A type ofbirefringent crystal having two axes, paral-lel to which the ordinary ray and the extra-ordinary ray travel at the same speed.

biconcave /bÿ-kong-kayv/ Describing aLENS with two concave faces. Compare bi-convex.

biconvex /bÿ-kon-veks/ Describing a LENS

with two convex faces. Compare bicon-cave.

big-bang theory The theory that the Uni-verse originated in a very small hot densestate from which it has expanded. Evidence

beryllium

22

for the big-bang theory comes from the ob-served expansion of the Universe, the cos-mic microwave background radiation, andthe abundances of the light elements in theUniverse.

bimetallic strip A strip of two metalsjoined side by side. When heated, the met-als expand by different amounts, causingthe strip to bend. Bimetallic strips are usedin thermostats and circuit breakers.

binary star A system of two stars orbitingabout their common center of mass. Abouthalf the stars in the Universe are thought tooccur as binary stars. A particular type ofbinary-star system in which one of the starsis a pulsar has been used to give very accu-rate checks for general relativity theory.

binding energy (of a nucleus) The energyequivalent to the difference between themass of the nucleus and the sum of themasses of its constituent nucleons. An ex-ample of calculating the binding energy of37Li, with 4 neutrons and 3 protons isshown.

A useful measure is binding energy pernucleon. In the example the binding energyper nucleon is 39.2501/7 = approximately5.6 MeV. For most nuclei, binding energylies between about 7 and about 9 MeV pernucleon, reaching a maximum of about 9MeV for nuclei of mass number about 60.The difference in mass in the example (i.e.the mass equivalent to the binding energy)is the mass defect.

binoculars An optical instrument provid-ing a telescope for each eye, thus giving dis-tance perception as well as magnification.

Prism binoculars use a pair of prismsinside each telescope. These reflect rays byinternal reflection. Their effect is to bringthe inverted image upright, reduce the tele-scope length, and allow the object lenses tobe farther apart than the eyes (thus im-proving stereoscopic vision). Binocularsare often described thus: 15 × 40. The firstfigure is the magnification; the second isthe aperture of each object lens in mm.

Opera glasses are a simpler low-powerdevice, consisting of two Galilean tele-

scopes side by side. The telescopes produceupright images without the need for extrainverting lenses or prisms.

binocular vision Vision using two eyes.The brain forms a single three-dimensionalview from the two separate images. Thistype of vision (stereoscopic vision) givesmore information about distance andshape than monocular vision could.

bioelectricity /bÿ-oh-i-lek-tris-ă-tee/ Elec-tricity generated in muscles, nerves, andother biological structures.

bioluminescence /bÿ-oh-loo-mă-ness-ĕns/See luminescence.

biophysics /bÿ-oh-fiz-iks/ The use ofphysics in the study of biological phenom-ena. A common example is the physical ex-planation of the working of the eye.

Biot–Savart law /bee-oh sah-var/ The el-emental field strength dB at a point distantr from a current element Idl in free space isgiven by:

dB = µ0Idlsinθ/4πr2

The Biot–Savart law is named for theFrench physicists Jean Baptiste Biot(1774–1862) and Félix Savart (1791–1841).

bipolar transistor /bÿ-poh-ler/ See field-effect transistor.

23

bipolar transistor

CALCULATION OF MASS DEFECTAND BINDING ENERGY

mass of neutrons (4 × 1.008 983 amu) 4.035 932 amu

mass of protons (3 × 1.008 144 amu) 3.024 432 amu

total mass of constituents 7.060 364 amumass of 7Li nucleus 7.018 222 amumass defect 0.042 142 amubinding energy (1 amu = 931.14 MeV) 39.240 MeV

biprism, Fresnel’s /bÿ-priz-ăm/ A glassprism with a large angle, used to producetwo coherent (virtual) sources for light in-terference experiments. As with Young’sdouble slit arrangement, the wavelength λof the incident monochromatic radiation isgiven by:

λ = yd/Dwhere y is the fringe separation, d is thesource separation, and D is the source-screen distance. The fringes obtained withthis arrangement are brighter than those inYoung’s experiment. The biprism is namedfor the French physicist Augustin JeanFresnel (1788–1827) and Young’s experi-ment for the British physicist, physician,and Egyptologist Thomas Young (1773–1829).

birefringent crystal /bÿ-ri-frin-jĕnt/ Acrystal that splits incident transmitted lightinto two beams, each polarized perpendic-ularly to the other. The effect (called bire-fringence or double refraction) isparticularly well-known in calcite (Icelandspar). It depends on the angle of incidencerelative to the crystal axes, along which thespeed of the light differs. The ordinary rayobeys the laws of refraction: it is polarizedperpendicularly to the crystal axis. The ex-traordinary ray does not obey the laws ofrefraction (in the usual sense); hence itsname. The study of the polarization prop-erties of crystals is of great significance ingeology, where it is used for the identifica-tion of minerals.

bismuth /biz-mŭth/ A brittle pinkishmetallic element. Bismuth is widely used inalloys, especially low-melting alloys. Theelement has the property of expandingwhen it solidifies.

Symbol: Bi; m.p. 271.35°C; b.p.1560±5°C; r.d. 9.747 (20°C); p.n. 83;r.a.m. 208.98037.

bistable circuit /bÿ-stay-băl/ (flip-flop)An electronic circuit, usually a MULTIVIBRA-TOR, that has two stable states and isswitched from one to the other by a triggerpulse. Bistable circuits are used in com-puter logic for counting and storing binarydigits (0 and 1). They form the basis of sev-eral different LOGIC GATES.

In a bistable multivibrator the inputpulse is fed to the base terminal of onetransistor (TR1) through a resistor R1 anddirectly to the collector of the other tran-sistor (TR2). The base of TR2 and the col-lector of TR1 are connected through aresistor R2. In logic circuits, bistable cir-cuits may have two or perhaps more in-puts. These are connected so that theoutput level (high or low) depends onwhether one or both inputs are high. Some-times a square-wave input is used as aclock or counter.

Bitter pattern A microscopic pattern ofdomain boundaries on a ferromagneticsurface, made visible by painting the sur-face with a colloidal suspension of verysmall iron particles. The production of Bit-ter patterns is similar to showing the shapeof a magnet under a sheet of paper by usingiron dust. Bitter patterns are named for theAmerican physicist Francis Bitter (1902–67).

black body A body that absorbs all theradiation falling on it. The absorptanceand emissivity of a black body are bothequal to 1. In practice, a small hole in auniform-temperature enclosure acts as ablack body.

The radiation from a black body coversthe whole wavelength range (sometimesthe alternative term full radiator is used).The distribution of power with wavelengthof this black-body radiation has a charac-

biprism, Fresnel’s

24

D

d

superposition regionvirtual source

biprism

screen

Biprism, Fresnel’s

teristic form. As the temperature increasesthe amount of radiation increases and themaximum in the curve moves to longerwavelengths. A black body radiates mainlyinfrared radiation below about 800 K. Vis-ible radiation does not predominate untilthe temperature is above about 6000 K.

black hole A region of space–time inwhich the gravitational field is so strongthat even light cannot escape from it. Thereis a considerable amount of observationalevidence for the existence of black holes inthe Universe. They are thought to arisefrom the gravitational collapse of verylarge stars that have exhausted their nu-clear fuel. It has been suggested that super-massive black holes power QUASARS.

blanket A layer of fertile material sur-rounding the core in a breeder reactor.

blind spot The area of the retina wherethe optic nerve leaves the EYE. It is not sen-sitive to light as in this region there is nolayer of rods and cones.

blink microscope A type of microscopeused to compare two very similar pho-tographs (such as particle tracks from abubble chamber). The photographs areseen side by side, one with each eye, andare rapidly exposed and concealed. Thebrain tries to superimpose the two images,thus revealing any slight difference be-

tween them. See also microscope (com-pound).

Bloch wall /blok/ The boundary of amagnetic domain, over the width of whichthe atomic magnetic moment directionschange. In iron, Bloch walls are around100 nm thick. The wall is named for theSwiss-born American physicist Felix Bloch(1905–83).

block and tackle See pulley.

blooming A method of coating lenses toreduce back-reflection from their surfaces.It involves destructive interference in thethin layer. Each such layer can completelyprevent reflection at only one wavelength(λ). λ is four times the layer thickness (t).For best effects the coating medium usedshould have a refractive constant n =√(n1n2), where n1 and n2 are the refractiveconstants of the media on each side. Single-layer blooming is normally used to preventreflection of yellow light; bloomed surfacesthus reflect reds and blues, and appear pur-ple. Multilayer blooming is sometimes em-ployed, but is very costly.

blue shift See red shift.

Board of Trade unit (BTU) A unit of en-ergy equivalent to the kilowatt-hour (3.6 ×106 joules). It was formerly used in the UKfor the sale of electricity.

bohrium /bor-ee-ŭm, boh-ree-/ A syntheticradioactive element first detected by bom-barding a bismuth target with chromiumnuclei. Only a small number of atoms haveever been produced.

Symbol: Bh; p.n. 107; most stable iso-tope 262Bh (half life 0.1s).

Bohr magneton Symbol: µB The unit ofatomic magnetic moment, the moment of asingle electron spin. It equals eh/4πmec,where e is the charge on an electron, h isthe Planck constant, me is the electron restmass, and c is the speed of light. Its value is9.274 009 49 x 10–24 joules per tesla(JT–1). The unit is named for the Danishphysicist Niels Bohr (1885–1962).

25

Bohr magneton

l λT2

T2 >T1

T1

λO

Black-body radiation

Bohr theory A pioneering attempt toapply quantum theory to the study ofatomic structure, by Niels Bohr (1913). Heassumed the newly introduced theory thatan atom consisted of a massive positivelycharged nucleus with orbital electrons, andfirst considered in detail the simplest atom,that of hydrogen, with only one electron.The electron was supposed to move in cir-cular orbits of radius r at speed v. By sim-ple mechanics the total energy of such anorbit (kinetic plus potential) is shown to be–e2/8πε0r, where e is the electron charge.Bohr assumed that only certain orbits werepossible, and tried to find a quantum ruleto determine which ones by making as-sumptions (soon seen to be false) concern-ing the frequencies of radiation emittedand absorbed by the atoms. His calcula-tions led however to the correct formulafor the energies of the allowed states of theatom, and showed that the angular mo-menta were quantized in units of h/2πwhere h is the Planck constant. For the nthquantum state the angular momentum isnh/2π and the energy En is given by

En = –me4/8ε20h2n2

Assuming that the frequency of emitted ra-diation was given by hν = En1 – En2, Bohrfound that transitions to the orbit with n =2 from higher values corresponded to thelines in the visible spectrum of hydrogen,while transitions to n = 3 gave lines in thenear infrared.

The theory was soon successfully ex-tended to the spectrum of singly-ionizedhelium and to the characteristic lines in thex-ray spectrum (see Moseley’s law). Overthe next twelve years the theory was devel-oped far enough to suggest that very manyfacts in physics and chemistry might be ex-plained in such terms, but innumerable dif-ficulties were encountered with thedetailed calculations. Various attempts toovercome these problems led to the mod-ern theory of quantum mechanics pio-neered by Heisenberg (1925), Schrödinger(1926), and Dirac (1928). Although Bohr’stheory has been superseded it is of out-standing historical and philosophicalinterest.

boiling A change from liquid to gas oc-curring at a characteristic temperature (theboiling point). Boiling occurs when the sat-urated vapor pressure of the liquid equalsthe external pressure. Bubbles of vapor canthen form in the liquid. The temperature atwhich this happens depends on externalpressure; boiling points are therefore usu-ally quoted at standard pressure. See alsochange of state; latent heat.

boiling-water reactor (BWR) A nuclearreactor in which water (in contact with thefuel elements) is used as both coolant andmoderator. The water boils inside the reac-tor core. Compare pressurized-water reac-tor.

bolometer /boh-lom-ĕ-ter/ An instrumentfor measuring small amounts of radiantheat or microwaves. It depends on thechange in resistance of a piece of metal foilor a superconductor when it absorbs radi-ant energy.

Boltzmann constant /bohlts-măn, -mahn/Symbol: k The fundamental constant1.380 650 5 × 10–23 J K–1, equal to the gasconstant (R) divided by the Avogadro con-stant (NA). The constant is named for theAustrian theoretical physicist Ludwig Ed-ward Boltzmann (1844–1906). See also de-grees of freedom.

bomb calorimeter A sealed insulatedcontainer, used for measuring energy re-leased during combustion of substances(e.g. foods and fuels). A known amount ofthe substance is ignited inside the calorime-ter in an atmosphere of pure oxygen, andundergoes complete combustion at con-stant volume. The resultant rise in temper-ature is related to the energy released bythe reaction. Such energy values (calorificvalues) are often quoted in joules per kilo-gram (J kg–1).

boron /bor-on, boh-ron/ A hard ratherbrittle metalloid element. It has the elec-tronic structure 1s22s22p1. Only smallquantities of elemental boron are neededcommercially; the vast majority of boronsupplied by the industry is in the form of

Bohr theory

26

borax or boric acid. Natural boron con-sists of two isotopes, 10B (18.83%) and 11B(81.17%). These percentages are suffi-ciently high for their detection by splittingof infrared absorption or by n.m.r. spec-troscopy.

Symbol: B; m.p. 2300°C; b.p. 2658°C;r.d. 2.34 (20°C); p.n. 5; r.a.m. 10.811.

boron chamber A device for detectinglow-energy neutrons, in which a com-pound of boron (usually the gas BF3) fillsan ionization chamber. The 10B nuclei,which constitute 18% of natural boron,absorb neutrons and emit alpha particles,which are detected by the ionization theycause.

Bose–Einstein condensation /bohz ÿn-shtÿn/ A phenomenon in which severalthousand atoms of certain elements areable to combine to form a single entity (asuperatom) at very low temperatures. Thephenomenon is important in the theory ofsuperfluids.

Bose–Einstein condensation was firstobserved for atoms which are bosons in thelate twentieth century. In the early twenty-first century it was observed for bosonsformed by the pairing of atoms, which arefermions. Bose–Einstein condensation isnamed for the Indian physicist SatyendraNath Bose (1894–1974) and the German-born physicist Albert Einstein(1879–1955), who discovered BOSE–EIN-STEIN STATISTICS in 1924. The phenomenonof Bose–Einstein condensation was pre-dicted by Einstein in 1924–5.

Bose–Einstein statistics The statisticalrules for studying systems of identicalbosons. It is assumed that (a) all identicalparticles are to be regarded as absolutelyindistinguishable; and (b) any number ofidentical bosons can have the same set ofquantum numbers in a given system. Theserules were first introduced by Bose (1924)in his proof of Planck’s radiation law,treating photons as quasi-particles. SeeFermi–Dirac statistics; Maxwell–Boltz-mann statistics.

boson /boh-zon/ A particle that obeysBOSE–EINSTEIN STATISTICS and has zero orintegral spin. Unlike fermions, bosons arenot conserved in number. That is bosonscan be generated or destroyed singly, not inparticle–antiparticle pairs, subject only tothe basic conservation laws of mass, en-ergy, momentum, charge, etc. See elemen-tary particles; fermion; meson.

boundary layer A thin layer of fluid,such as the one next to a solid surface pastwhich the fluid is moving. Friction with thesurface slows flow within the boundarylayer so that next to the surface the fluid isstationary. At the other edge of the bound-ary layer, the velocity approaches that ofthe main flow. Within it the effects of vis-cosity are significant, whereas in the mainstream they can often be neglected.

Bourdon gauge /boor-dŏn/ (Bourdontube) A type of fluid pressure gauge con-sisting of a coiled flattened tube. Pressureapplied by a fluid inside the tube makes ittend to straighten, and this movementworks a pointer that moves around a dial.

Boyle’s law At a constant temperature,the pressure of a fixed mass of a gas is in-versely proportional to its volume: i.e. pV= K, where K is a constant. (A graph of pagainst 1/V is a straight line.) The value ofK depends on the temperature and on thegas. The law holds strictly only for idealgases. Real gases follow Boyle’s law at lowpressures and high temperatures. Boyle’slaw is named for the Irish physicist RobertBoyle (1627–91). See gas laws.

Boyle temperature See gas laws.

Boys’ experiment (1895) A method ofdetermining the gravitational constant, G.A short beam (about 25 mm) with a goldsphere hanging from each end was sus-pended horizontally by a quartz torsionfiber. Measurements were made of the pe-riod of the torsional oscillations of thebeam and of its angular deflection whenlarge dense masses were placed near eachsphere. In this way, G could be calculated.The method was more accurate than

27

Boys’ experiment

Cavendish’s similar experiment for G. Theexperiment is named for the British inven-tor Sir Charles Vernon Boys (1855–1944).

Bragg’s law If a beam of x-rays of wave-length λ is directed at a crystal with paral-lel crystal planes that are distance d apart,then the reflected x-rays from each planeundergo interference. Constructive inter-ference occurs at angles θ where nλ =2dsinθ, n being an integer (1, 2, 3, etc.). θis the angle between the crystal plane andthe incident beam (called the Bragg angle).The equation is used in determining crystalstructure from interference patterns pro-duced by monochromatic x-rays. The lawis named for the British physicist SirLawrence Bragg (1890–1971).

breeder reactor A NUCLEAR REACTOR thatproduces additional nuclei at a rate greaterthan that at which fuel is consumed. Thecore fuel consists of a fissile element, forexample, uranium enriched to about 25%in the 235U isotope. The core is surroundedby a blanket of fertile material, mostly 238Uin the form of natural or depleted uranium.Some of the surplus neutrons from the fis-sion of 235U convert 238U into 239Pu, whichis fissile. A primary circuit of liquid sodiumcan be used through the core to carry heataway. The heat is transferred to a sec-ondary circuit of sodium that boils water,the steam then operating turbines and gen-erators as in a conventional power station.Such a reactor is also termed a fast breederreactor or fast reactor because the neutronsmoving through the core and blanket arefast moving, being of high energy (severalMeV) as compared to those in thermal re-actors (about 0.025 eV).

bremsstrahlung /brem-shtrah-lûng/ X-rays emitted when fast electrons are sloweddown violently, as when electrons strikethe target in an x-ray tube. The Germanword translates as ‘braking radiation’.Bremsstrahlung is caused when an electronpasses through the electric field of a nu-cleus and constitutes the continuous x-rayspectrum.

Brewster angle /broo-ster/ Symbol: iB Theangle of incidence, on a partially reflectingsurface, at which the reflected radiation isfully plane-polarized. It is also the angle ofincidence at which the reflected and re-fracted beams are perpendicular. Polariza-tion by reflection is a refractive property ofthe surface.

1n2 = taniBThe plane of polarization is parallel to

the surface. The refracted radiation ispartly polarized parallel to the normal.Formerly, the Brewster angle was calledthe angle of polarization or the polarizingangle. The Brewster angle is named for theScottish physicist Sir David Brewster(1781–1868).

bridge circuit An arrangement of fourelectrical components in a square with aninput across two opposite corners and anoutput across the other opposite corners.See Wheatstone bridge.

brightness A vague term describing theintensity of light. It can be applied to asource of light, to light itself, or to an illu-minated surface. The brightness or inten-sity of light, in any of these three cases,relates to the rate of supply of energy (i.e.the power). The relation is complicated asit must take account of the sensitivity of theeye (or other detector) at different frequen-cies. See also photometry.

Brinell test /bri-nel/ A way of measuringthe hardness of a material. A standard steelball of known hardness is pressed into thematerial’s surface with a known force. Thesize of the indentation indicates the hard-ness. The test is named for the Swedishmetallurgist Johan August Brinell(1849–1925).

British thermal unit (Btu) A unit of en-ergy. It was formerly defined by the heatneeded to raise the temperature of onepound of air-free water by one degreeFahrenheit at standard pressure. Slightlydifferent versions of the unit were in usedepending on the temperatures betweenwhich the degree rise was measured. At60.5°F it equals 1.054 615 kilojoules.

Bragg’s law

28

broken symmetry A situation in whichthe state of a system has a lower degree ofsymmetry than the symmetry of the equa-tion that describes the system. There aremany examples of broken symmetry inphysics, particularly in the theory of con-densed matter. Ferromagnetism and super-conductivity are examples of broken-symmetry phenomena. Broken symmetry isalso important in theories that attempt tounify different interactions and particlephysics.

bromine /broh-meen, -min/ A deep red,moderately reactive element belonging tothe halogens. Bromine is a liquid at roomtemperature (mercury is the only other ele-ment with this property).

Symbol: Br; m.p. –7.25°C; b.p.58.78°C; r.d. 3.12 (20°C); p.n. 35; r.a.m.79.904.

Brownian movement (Brownian mo-tion) The random motion of small particlesin a fluid – for example, smoke particles inair. The particles, which may be largeenough to be visible with a microscope, arecontinuously bombarded by the invisiblysmall molecules of the fluid. Brownianmovement is named for the Scottishbotanist Robert Brown (1773–1858). Seealso kinetic theory.

brush An electrical contact to a movingpart of an electric motor or generator.

brush discharge A form of bright gas dis-charge occurring near sharp points of highpotential. The potential difference causingsuch a discharge is lower than that neces-sary for a spark or arc. The discharge ischaracterized by luminous streamers,which take on a treelike form.

bubble chamber A container of a liquidkept slightly above its boiling temperatureby increased pressure and used to showtracks of ionizing radiation. The liquid isoften liquid hydrogen. Just before the pas-sage of a particle the pressure is momen-tarily reduced, and a photograph taken.Ions formed along the paths of chargedparticles or gamma-ray photons act as nu-

clei on which bubbles form. Magneticfields can be applied causing curvature ofthe paths of charged particles. Bubblechambers are more useful than CLOUD

CHAMBERS. The greater density of the liquidincreases the chance that a nuclear reactionwill occur.

bulk modulus See elastic modulus.

bumping When a gas-free liquid is heatedin a smooth container the temperature mayrise well above the boiling temperature atthe applied pressure without boiling; theliquid is superheated. Then if a bubbleforms the liquid will boil very violently andis said to bump. As this can be dangerous itis usual to place rough objects such as bro-ken porcelain in flasks used for boiling cer-tain liquids. Bubbles form readily on therough surfaces and insure smooth steadyboiling.

Bunsen burner /bun-sĕn/ A gas burnerconsisting of a vertical metal tube with anadjustable air-inlet hole at the bottom. Gasis allowed into the bottom of the tube andthe gas-air mixture is burnt at the top.With too little air the flame is yellow andsooty. Correctly adjusted, the burner givesa flame with a pale blue inner cone of in-completely burnt gas, and an almost invis-ible outer flame where the gas is fullyoxidized and reaches a temperature ofabout 1500°C. The Bunsen burner isnamed for the German chemist RobertWilhelm Bunsen (1811–99). He was notthe actual inventor of the Bunsen burner,but used it to great effect in pioneeringwork on spectroscopy.

Bunsen cell A type of primary cell inwhich the positive electrode is formed bycarbon plates in nitric acid solution and thenegative electrode consists of zinc plates insulfuric acid solution.

buoyancy The tendency of an object tofloat. The term is sometimes used for theupward force (upthrust) on a body. Seecenter of buoyancy.

29

buoyancy

butterfly effect Any effect in which asmall change to a system results in a dis-proportionately large disturbance.

The term originates in the idea that theEarth’s atmosphere is so sensitive to initialconditions that a butterfly flapping itswings in one part of the world may be thecause of a tornado happening in anotherpart of the world. See chaos theory.

buzzer A electrical device in which a vi-brating component, operated by an alter-

nating electric current, produces a continu-ous buzzing sound.

BWR See boiling-water reactor.

bypass capacitor A capacitor that allowsalternating currents to pass through itrather than through another componentconnected in parallel. The capacitance ofthe capacitor determines the frequencyrange of alternating current that can passmost easily.

butterfly effect

30

cable, coaxial An electrical cable consist-ing of a central wire in an insulating sheathsurrounded by a woven mesh of conduc-tor, all inside an outer insulating sheath.Coaxial cables are not affected by externalelectric or magnetic disturbances or sig-nals. They are used in transmitting high-frequency signals; for example, intelevision antenna connections. Normallythe outer conductor is earthed.

cadmium /kad-mee-ŭm/ A transitionmetal obtained as a by-product during theextraction of zinc. It is used to protectother metals from corrosion, as a neutronabsorber in nuclear reactors, in alkali bat-teries, and in certain pigments. It is highlytoxic.

Symbol: Cd; m.p. 320.95°C; b.p.765°C; r.d. 8.65 (20°C); p.n. 48; r.a.m.112.411.

cadmium cell See Weston cadmium cell.

calcite /kal-sÿt/ (Iceland spar) A naturallyoccurring form of calcium carbonate. It isthe best-known example of a mineral thatshows double refraction (birefringence).

calcium /kal-see-ŭm/ A moderately soft,low-melting reactive metal. The electronicconfiguration is that of argon with an ad-ditional pair of 4s electrons.

Calcium is widely distributed in theEarth’s crust and is the third most abun-dant element. At ordinary temperaturescalcium has the face-centred cubic struc-ture with a transition at 450°C to the close-packed hexagonal structure.

Symbol: Ca; m.p. 839°C; b.p. 1484°C;r.d. 1.55; p.n. 20; r.a.m. 40.0878.

calculus /kal-kyŭ-lŭs/ The branch of

mathematics that deals with the differenti-ation and integration of functions. Bytreating continuous changes as if they con-sisted of infinitely small step changes, dif-ferential calculus can, for example, be usedto find the rate at which the velocity of abody is changing with time (acceleration)at a particular instant.

Integral calculus is the reverse process,that is finding the end result of known con-tinuous change. For example, if a car’s ac-celeration a varies with time in a knownway between times t1 and t2, then the totalchange in velocity is calculated by the inte-gration of a over the time interval t1 to t2.See differentiation; integration.

calendar year See year.

californium /kal-ă-for-nee-ŭm/ A silveryradioactive transuranic element of the acti-noid series of metals, not found naturallyon Earth. Several radioisotopes have beensynthesized, including californium-252,which is used as an intense source of neu-trons in certain types of portable detectorand in the treatment of cancer.

Symbol: Cf; m.p. 900°C; p.n. 98; moststable isotope 251Cf (half-life 900 years).

Callendar and Barnes’ experiment/kal-ĕn-der barnz/ The method was firstused (1900) to determine Joule’s equiva-lent. It was extended to the measurementof the specific heat capacities of liquids andgases over a range of temperatures. Thevalues are determined very nearly underconstant pressure.

The method introduced high-precisionconstant-flow calorimetry, pioneering theuse of platinum-resistance thermometersand the measurement of electric currentand potential difference with potentiome-

31

c

calomel electrode

32

and potential difference with potentiome-ters for calorimetric measurements.

The fluid passes at a constant ratethrough a thermally insulated tube con-taining a spiral electrical heating wirealong the axis. When steady state isreached the input and output temperaturesare recorded. Then

VI = mcp(θ2 – θ1) + wwhere V and I are the p.d. across the heatercoil and the current in it respectively, m isthe mass of fluid passed per unit time, cp isthe specific heat capacity, θ1 and θ2 are theinput and output temperatures and w is the(small) rate of heat loss. The rate of fluidflow is then changed and the values of Vand I are adjusted until steady state isreached with the same values of θ2 and θ1.Assuming the rate of heat loss is the samethis can be eliminated; hence cp can befound. The experiment is named for theEnglish physicist and engineer Hugh Cal-lendar (1863–1930) and the Canadianphysicist Howard Barnes (1873–1950).

calomel electrode A half cell having amercury electrode coated with mercury(I)chloride, in an electrolyte consisting ofpotassium chloride and (saturated) mer-cury chloride solution. Its standard elec-trode potential against the hydrogenelectrode is accurately known and it is aconvenient secondary standard.

caloric theory /kă-lor-ik, -loh-rik/ An ob-solete theory that heat was a weightlessfluid. The theory was abandoned in the19th century.

calorie /kal-ŏ-ree/ 1. Symbol: cal Any ofvarious c.g.s. units of energy approxi-mately equal in SI derived units to 4.185joules (J). Originally the calorie was de-fined as the heat needed to raise the tem-perature of one gram of water by oneCelsius degree. Because the specific heatcapacity of water changes slightly withtemperature, the value determined for thiscalorie varied. Consequently new calorieswere defined whose values were fixed withreference to a specific temperature or to amean value. For example, the mean or

thermochemical calorie (calTH) was de-fined as one hundredth of the heat neededto raise one gram of water from zero de-grees Celsius (0°C) to 100°C, and the 15°Ccalorie as the heat needed to raise one gramof water from 14.5°C to 15.5°C. Today,the thermochemical calorie is defined as4.184 joules (J), the 15°C calorie used inNorth America as 4.1858J, and the inter-national table calorie (calIT) as 4.186 8joules. 2. Symbol: Cal A f.p.s. unit of energy equalto 1000 15° calories or the energy neededto raise the temperature of one kilogram ofwater at 14.5°C one Celsius degree. It isalso called the Calorie, kilocalorie, or di-etary calorie, the latter because it has beenused to describe the equivalent amount ofenergy derived during digestion from aspecified amount of food.

Calorie See calorie.

calorific value /kal-ŏ-rif-ik/ A measure-ment of the energy content of fuels. It is theamount of heat released when unit mass orvolume of a fuel burns completely. Seebomb calorimiter.

calorimeter /kal-ŏ-rim-ĕ-ter/ A device formeasuring thermal energy; for example indetermining thermal capacity, specific la-tent thermal capacity, energies of combus-tion, etc. See also bomb calorimeter.

camera An optical instrument able torecord an image formed by visible light (orby other electromagnetic radiation). Therecord may be in the form of chemicalchanges in a photographic emulsion, orelectrical signals as in a T.V. camera. A lensor system of lenses is used to focus the ra-diation onto the sensitive surface. Adjust-ment can be made for different objectdistances. The shutter allows light in for aset time (except in a video camera); the di-aphragm varies the aperture.

camera, pin-hole See pin-hole camera.

camera obscura /kam-ĕ-ră ŏb-skyoor-ă/A chamber or box in which an upside-down image of an external scene is formed

by a small aperture or lens in the oppositeside. It was the origin of the modern pho-tographic camera. See also camera; pin-hole camera.

Canada balsam /bawl-săm/ A transpar-ent adhesive with a refractive constant of1.53. As this constant is similar to that ofmany optical media, Canada balsam hasvarious uses in optical instrumentation.See; for example; Nicol prism.

canal rays Streams of positive ions ob-tained from a discharge tube by boringsmall holes in the cathode. The ions beingattracted to the cathode can thus passthrough it forming positive rays.

candela Symbol: cd The SI base unit of lu-minous intensity; the luminous intensity ina given direction of a source that emitsmonochromatic radiation of frequency540 × 1012 hertz and that has radiant in-tensity in that direction of 1/683 watt persteradian. Formerly, the unit was definedas the intensity (in the perpendicular direc-tion) of the black-body radiation from asurface of 1/600 000 square meter at thetemperature of freezing platinum and at apressure of 101 325 pascals.

candle The former unit of luminous in-tensity, now replaced by the SI unit thecandela. 1 candle = 1.02 cd. See candela.

candle-power An outdated measure ofluminous intensity. The unit until 1948was the international standard candle. Thiswas first defined, in the UK, in the 1860Gas Act; it was the brightness of a candlemade in a certain way and burning at a cer-tain rate.

capacitance /kă-pass-ă-tăns/ Symbol: CThe ability of a system of conductors andinsulators to store electric charge. If, in agiven case, a charge Q is maintained by apotential difference V, then the capacitanceis defined as the quotient Q/V. The unit ofcapacitance is the farad (F). See also capac-itor.

capacitor /kă-pass-ă-ter/ (formerly, con-denser) A device for storing electriccharge. It usually consists of two parallelconductors separated by some insulatingmaterial (the dielectric). The capacitance ofa capacitor increases:1. the greater the common area of the con-ductors;2. the smaller the distance between them;3. the higher the relative permittivity of the

dielectric.The charge in a capacitor is stored partlyby polarization of the particles of the di-electric. The capacitance (C) of a parallel-plate capacitor is given by

C = εA/dwhere ε is the permittivity of the materialbetween the plates, A their common area,and d their separation.

An isolated sphere has capacitance:C = 4πε1ε0r

where r is the radius of the sphere, and ε1ε0the permittivity of the medium.

capillary action The effect that occurswhen a fine tube, or capillary, is placed ver-tically with one end in a liquid. The heightof the liquid inside the tube will be aboveor below the level of the liquid by anamount depending on the cohesion (sur-face tension) of the liquid and the adhesionbetween liquid and tube. The narrower thecapillary is, the greater the difference inheight. Because water ‘sticks’ to glass – itsadhesion tends to be greater than its cohe-sion – it has a concave meniscus in a glasstube, and will be drawn up the tube by cap-illary action. Mercury, on the other hand,will be lowered inside a glass capillary, be-cause here the cohesion is greater than theadhesion.

The distance h that a liquid of density ρand surface tension γ will rise up a tube ofradius r is given by the equation

h = 2γ cosα/rgρwhere α is the contact angle between themeniscus and the tube. α is measuredbelow the meniscus, so that for a convexmeniscus, α is greater than 90° and h isnegative.

capillary tube A tube with a narrow bore(internal diameter). Capillary tubing usu-

33

capillary tube

ally has relatively thick walls. Glass capil-laries are used in mercury thermometersand experiments on surface tension. Seealso capillary action.

capture The absorption of one particle byanother. For instance, a positive ion maycapture an electron to form a neutral atom.In some nuclear reactions, an atomic nu-cleus may capture a neutron with emissionof one or more gamma-ray photons.

carbon /kar-bŏn/ A nonmetallic element;carbon is a universal constituent of livingmatter and the principal deposits of carboncompounds are derived from livingsources; i.e., carbonates (chalk and lime-stone) and fossil fuels (coal, oil, and gas). Italso occurs in the mineral dolomite.Minute quantities of elemental carbon alsooccur as the allotropes graphite and dia-mond. A third allotrope, buckminster-fullerene (C60), also exists. Naturallyoccuring carbon consists of three isotopes:12C (98.89%), 13C (1.11%) and 14C(minute traces in the upper atmosphereproduced by slow neutron capture by 14Natoms). 14C is used for radiocarbon datingbecause of its long half-life of 5730 years.

Symbol: C; m.p. 3550°C; b.p. 4830°C(sublimes); C60 sublimes at 530°C; r.d.3.51 (diamond), 2.26 (graphite), 1.65 (C60)(all at 20°C); p.n. 6; r.a.m. 12.011.

carbon black (soot) A form of amor-phous carbon produced by incompletecombustion of gas (or other organic mat-ter). It is used in experiments as a coatingfor surfaces that need to be good absorbersof radiation, for example in detectors ofthermal radiation, such as the thermopile.It is also used to increase the amount ofthermal radiation emitted by a surface.

carbon cycle (carbon-nitrogen cycle) Aseries of nuclear reactions postulated to ac-count for energy production in stars. In thisseries 16

2C is an intermediary in the processby which hydrogen nuclei fuze to form he-lium with release of energy. The first step isthe fusion of carbon and hydrogen nuclei:

162C + 11H → 1

73N + gamma radiation

173N → 1

63C + positron

163C + 11H → 1

74N + gamma radiation

174N + 11H → 1

85O + gamma radiation

185O → 1

75N + positron

175N + 11H → 1

62C + 24He

The net result is:41

1H → 24He

with a release of about 4.4 pJ of energy. Seealso proton-proton chain reaction.

carbon dating (radiocarbon dating) Amethod of dating – measuring the age of(usually archaeological) materials that con-tain matter of living origin. It is based onthe fact that 14C, a beta emitter of half-lifeapproximately 5730 years, is being formedcontinuously in the atmosphere as a resultof cosmic-ray action.

The 14C becomes incorporated into liv-ing organisms. After death of the organismthe amount of radioactive carbon de-creases exponentially by radioactive decay.The ratio of 12C to 14C is thus a measure ofthe time elapsed since the death of the or-ganic material.

Uncertainties arise because of uncer-tainty as to the past rate of production of14C, the possibility of exchange of carbonwith carbon of a different age during theelapsed time, the possibility of contamina-tion of the sample, and the effect of burn-ing of fossil fuels on the composition ofatmospheric carbon.

The method is most valuable for speci-mens of up to 20 000 years old, though ithas been modified to measure ages up to70 000 years. For ages of up to about 8000years the carbon time scale has been cali-brated by dendrochronology; i.e. by mea-suring the 12C:14C ratio in tree rings ofknown antiquity.

carbon microphone See microphone.

carbon–nitrogen cycle See carbon cycle.

Carnot cycle /kar-noh/ The idealized re-versible cycle of four operations occurringin a perfect heat engine. These are the suc-cessive adiabatic compression, isothermalexpansion, adiabatic expansion, andisothermal compression of the workingsubstance. Heat Q1 enters the workingsubstance from a furnace during the ex-

capture

34

pansion at the higher temperature T1 and asmaller quantity Q2 is discharged at thelower temperature T2. The net work doneby the engine in one cycle is W, which byconservation of energy is equal to Q1 – Q2.By definition, the efficiency η is equal toW/Q1. Hence, η = 1 – Q1/Q2. Kelvin de-fined temperature T on the thermodynamicscale such that T2/T1 = Q2/Q1 in this idealengine. Hence

η = 1 – (T1/T2)This is the highest efficiency possible inprinciple. In practice, all real heat engineshave lower efficiencies. The cycle is namedfor the French physicist Nicolas LeonardSadi Carnot (1796–1832). Compare Ottocycle. See also Carnot’s principle.

Carnot’s principle (Carnot theorem)The efficiency of any heat engine cannot begreater than that of a reversible heat engineoperating over the same temperaturerange.

Carnot (1824) derived this theorem bya fallacious argument before the formula-tion of the concept of energy. When theconcept of energy and its conservationwere established about 1849 Clausius andKelvin showed that Carnot’s principle wasconsistent with the new ideas provided oneadded a new principle, the second law ofthermodynamics. See reversible change.

carrier 1. See carrier wave.2. A charge carrier – either an electron or apositive hole.3. The agent that carries the electric chargein a current, e.g. an electron, positive hole,or ion.

carrier wave An electromagnetic wave,usually in the long-wave radio to radar fre-quency range, that is used to carry infor-mation in a radio transmission. Theinformation is superimposed on the carrierwave by MODULATION.

Cartesian coordinates /kar-tee-zhăn/ Amethod of defining the position of a pointby its distance from a fixed point (origin) inthe direction of two or more straight lines.On a flat surface, two straight lines, calledthe x-axis and the y-axis, form the basis ofa two-dimensional Cartesian coordinatesystem. The point at which they cross is theorigin (O). An imaginary grid is formed bylines parallel to the axes and one unitlength apart. The point (2,3), for example,is the point at which the line parallel to they-axis two units in the direction of the x-axis, crosses the line parallel to the x-axisthree units in the direction of the y-axis.Usually the x-axis is horizontal and the y-axis is perpendicular to it. These areknown as rectangular coordinates. If theaxs are not at right angles, they are obliquecoordinates

In three dimensions, a third axis, the z-axis, is added to define the height or depthof a point. The coordinates of a point arethen three numbers (x,y,z). A right-handedsystem is one for which if the thumb of theright hand points along the x-axis, the fin-gers of the hand fold in the direction inwhich the y-axis would have to rotate topoint in the same direction as the z-axis. Aleft-handed system is the mirror image ofthis. In a rectangular system, all three axsare mutually at right-angles. See also polarcoordinates.

cascade connection A method of electri-cal connection in which the output termi-nals of the first device or network areconnected to the input terminals of the sec-

35

cascade connection

T1

T2

volume (V)

pre

ssu

re(P

)

Carnot cycle

ond, those of the second to the third, andso on.

cascade liquefier A device for liquefyinga series of gases in stages. The critical tem-perature of each gas is different. A gas witha high critical temperature is liquefied bycompression and evaporated under a lowerpressure, cooling a second gas below itscritical temperature. The second gas canalso be liquefied and evaporated to pro-duce a still lower temperature, and so on.See also Linde process.

cascade process Any process that takesplace in a number of stages.

An example is the diffusion processused to enrich uranium. The gas uraniumhexafluoride diffuses through a long seriesof porous barriers. A very slight enrich-ment takes place at each, because of thevery slightly higher speed of diffusion of235UF6 compared with that of 238UF6. Thegas-centrifuge enrichment process is also acascade process.

Cassegrainian telescope /kass-ĕ-grayn-ee-ăn/ A type of reflecting telescope inwhich the converging mirror has a hole inits center. Light is reflected back onto a di-verging mirror, then forward through thehole into the eyepiece. The telescope isnamed for the French sculptor Sieur Guil-laume Cassegrain (c. 1650–1700). See alsoreflector.

catadioptric lens /kat-ă-dÿ-op-trik/ Acompound lens in which both a mirror(s)and lenses are used to form an image.

catapault field The magnetic field thatresults when a conductor of electricitythrough which an electric current is flow-ing is put in a uniform external magneticfield.

cathetometer /kath-ĕ-tom-ĕ-ter/ An opti-cal instrument for accurately measuringheight or lengths; a small telescope or mi-croscope mounted so that it can be slidalong a graduated scale.

cathode /kath-ohd/ In electrolysis, theelectrode that is at a negative potentialwith respect to the anode. In any electricalsystem, such as a discharge tube or a solid-state electronic device, the cathode is theterminal at which electrons enter the sys-tem.

cathode-ray oscilloscope (CRO) An in-strument for investigating electrical sig-nals. An electron beam is directed at theface of a cathode-ray tube, forming a smallspot. The beam can be deflected in the hor-izontal and vertical directions by an elec-trostatic field from two sets of plates. Thehorizontal deflection is often a constant re-peating sweep of the spot produced by aninternal time base. The signal to be investi-gated is amplified and applied to the verti-cal deflecting plates. Thus, a graph of thesignal is ‘drawn’ on the screen.

cathode rays Streams of electrons givenoff by the cathode of a gas-discharge tubeat low pressure. If there is sufficient resid-ual gas, the discharge occurs with a coldcathode. In this case, electrons are ejectedfrom the cathode by positive-ion bombard-ment. In a high vacuum, the cathode is anelectrically heated wire, which emits by thethermionic effect. See also secondary emis-sion; thermionic emission.

cathode-ray tube (CRT) An electrontube that converts electrical signals into apattern on a screen. The cathode-ray tubeforms the basis of the CATHODE-RAY OSCIL-LOSCOPE and the television receiver. It con-sists of an electron gun, which produces anelectron beam. The electrons are focusedonto and moved across a luminescent

cascade liquefier

36

to eye lensand observer

converging mirror

divergingmirror

Cassegrainian telescope

screen by magnetic and/or electric fields, togive a small moving spot of light.

cation /kat-ÿ-ŏn, -on/ A positivelycharged ion, formed by removal of elec-trons from atoms or molecules. In electrol-ysis, cations are attracted to the negativelycharged electrode (the cathode). Compareanion.

caustic The curve (surface in three dimen-stions) on which rays meeting a curved re-flector or lens meet after reflection orrefraction. See focal point.

Cavendish’s experiment /kav-ĕn-dish/(1798) This was the first experiment tomeasure the gravitational constant G in thelaboratory (rough measurements had al-ready been made by observing the attrac-tion of a pendulum by mountains, e.g.Bouger, 1749). Since this experiment bythe English physicist and chemist HenryCavendish (1731–1810), many investiga-tors have performed similar laboratory ex-periments with improved accuracy (seeBoys’ experiment). These have shown thatNewton’s law applies with high precisionon the laboratory scale, but, in recentyears, small departures from this law havebeen established. See also Newton’s law ofuniversal gravitation.

In the original apparatus, a beam withsmall lead spheres at each end was sus-pended horizontally by a torsion wire.Large spheres of lead were then placedclose to the smaller spheres on oppositesides of the beam in order to turn the beamthrough an angle. The lead spheres werethen moved to the opposite sides of thebeam, turning the beam in the opposite di-rection. G could be calculated from thetotal angular deflection. The method,which was the first attempt to measure G,was less accurate than Boys’ experiment.

cavitation /kav-ă-tay-shŏn/ The forma-tion of small cavities in a liquid, caused bya reduction in fluid pressure. The cavitiesmay collapse, generating a large impulsivepressure which may erode and damagenearby solid surfaces (such as pump im-pellers, turbine blades, and ships’ pro-

pellers). The phenomenon is exploited forcutting and drilling metals using ultrasonicwaves.

cavity resonator See klystron; mag-netron.

CD See compact disk.

celestial mechanics The study of the mo-tion of planets and their satellites. Celestialmechanics is largely dealt with using New-tonian mechanics, with small correctionsresulting from general relativity theory.

cell 1. A system having two plates (elec-trodes) in a conducting liquid (electrolyte).An electrolytic cell is used for producing achemical reaction by passing a currentthrough the electrolyte (i.e. by ELECTROLY-SIS). A voltaic (or galvanic) cell produces ane.m.f. by chemical reactions at each elec-trode. Electrons are transferred to or fromthe electrodes, giving each a net charge. Seealso accumulator; Clark cell; Daniell cell;Leclanché cell.2. See photocell; photoelectric cell.3. See Kerr effect.

Celsius scale A TEMPERATURE SCALE inwhich the temperature of melting pure iceis taken as 0° and the temperature of boil-ing water 100° (both at standard pressure).The degree Celsius (°C) is equal in magni-tude to the kelvin provided that the scalehas been calibrated so as to conform to theInternational Practical Temperature Scaleat all temperatures. Before 1948 the Cel-sius scale was known as the centigradescale. Celsius’ original scale of 1742 wasinverted (i.e. had 0° as the steam tempera-ture and 100° as the ice temperature). Thescale is named for the Swedish astronomerAnders Celsius (1701–44).

center of buoyancy (for an object in afluid) The center of mass of the displacedfluid volume. For a floating object to bestable, the center of mass of the object mustlie below the center of buoyancy; when theobject is in equilibrium, the two lie on avertical line. See also Archimedes’ princi-ple; flotation, law of.

37

center of buoyancy

center of curvature Each surface of asimple curved LENS or MIRROR is part of asphere. The center of curvature c of such asurface is the center of the sphere of whichthe surface is part.

center of gravity See center of mass.

center of mass A point in a body (or sys-tem) at which the whole mass of the bodymay be considered to act. Often the termcenter of gravity is used. This is, strictly,not the same, except if the body is in a con-stant gravitational field. The center ofgravity is the point at which the weightmay be considered to act.

The center of mass coincides with thecenter of symmetry if the body has a uni-form density throughout. In other cases theprinciple of moments may be used to locatethe point. The centroid of a plane or solidshape is the point at which the center ofmass would be if the shape or solid were ofuniform-density material.

center of oscillation The point on a sta-tionary compound PENDULUM located verti-cally below the pivot at a distance thatequals the length of the equivalent simplependulum.

center of pressure If a surface lies hori-zontally in a fluid, the pressure at all pointswill be the same. The resultant force willthen act through the centroid of the sur-face. If the surface is not horizontal, thepressure on it will vary with depth. The re-sultant force will now act through a differ-ent point; the center of pressure is not atthe centroid. The center of pressure of asubmerged surface is the point throughwhich the resultant of the pressure forcesacts.

centi- Symbol: c A prefix denoting 10–2.For example, 1 centimeter (cm) = 10–2

meter (m).

centigrade scale See Celsius scale.

centimetric waves /sen-tă-met-rik/ Elec-tromagnetic waves with wavelengths in therange 1–10 cm (i.e. part of the microwaveregion).

central bright image The image that oc-curs at the center of a diffraction patternproduced when light is diffracted at anopening. This image is brighter than all theother images produced by the diffraction.

center of curvature

38

surface A surface B

lens section

Cb Ca

Center of curvature

•

••

base of tankPb

Mb

Pb

Ps

side oftank

Pb = center of pressure of base

Mb = center of mass of base

Pb = Mb

Ps = center of pressure of side

Ms = center of mass of side in contact with liquid

Ms

Ps

Center of pressure

central force A force that acts on any af-fected object along a line to an origin. Elec-tric forces between charged particles arecentral; frictional forces are not.

centrifugal force A force supposed to actradially outward on a body moving in acurve. In fact there is no real force acting;centrifugal force is said to be a ‘fictitious’force, and the use of the term is bestavoided. The idea arises from the effect ofinertia on an object moving in a curve. If acar is moving around a bend, for instance,it is forced in a curved path by friction be-tween the wheels and the road. Withoutthis friction (directed toward the center ofthe curve) the car would continue in astraight line. The driver also moves in thecurve, constrained by friction with the seat,restraint from a seat belt, or a ‘push’ fromthe door. To the driver it appears that thereis a force radially outward pushing his orher body out – the centrifugal force. In factthis is not the case; if the driver fell out ofthe car he or she would move straight for-ward at a tangent to the curve. It is some-times said that the centrifugal force is‘reaction’ to the centripetal force – this isnot true. (The ‘reaction’ to the centripetalforce is an outward push on the road sur-face.) See also centripetal force.

centrifuge /sen-tră-fyooj/ A device forseparating the components of a suspensionby spinning. In simple types, the liquid con-taining suspended particles is placed in atube, which is whirled round in a horizon-

tal circle. Particles less dense than the liq-uid move toward the axis of rotation;denser particles accumulate at the otherend.

The device thus accelerates the processof separation that would result from grav-itational forces. The gravitational pressuregradient is replaced by a much strongerpressure gradient related to centripetalforces. An ultracentrifuge is a high-speedcentrifuge suitable for separating verysmall particles or even large molecules. Gascentrifuges are used in isotope separation.

centripetal force A force that causes anobject to move in a curved path rather thancontinuing in a straight line. The force isprovided by, for instance:– the tension of the string, for an objectwhirled on the end of a string;– gravity, for an object in orbit round aplanet;– electric force, for an electron in the shellof an atom.

The centripetal force for an object ofmass m with velocity v, and path radius r ismv2/r, or mω2r, where ω is angular veloc-ity. A body moving in a curved path with avelocity v has an acceleration because thedirection of the velocity changes, eventhough the magnitude of the velocity mayremain constant. This acceleration, whichis directed toward the center of the curve,is the centripetal acceleration. It is given byv2/r or ω2r.

centroid /sen-troid/ See center of mass.

Cerenkov radiation /chĕ-renk-off/ Abluish light that is emitted when chargedparticles travel through a transparentmedium at a speed that exceeds the speedof light in the medium. The radiation isnamed for the Russian physicist PavelAlekseyevich Cerenkov (1904–90).

cerium /seer-ee-ŭm/ A ductile malleablegray element of the lanthanoid series ofmetals. It occurs in association with otherlanthanoids in many minerals. It is used inseveral alloys (especially for lighter flints),as a catalyst, and in compound form in car-

39

cerium

• •center of arc

curved path

Centrifugal force

bon-arc searchlights, etc., and in the glassindustry.

Symbol: Ce; m.p. 799°C; b.p. 3426°C;r.d. 6.7 (hexagonal structure, 25°C); p.n.58; r.a.m. 140.15.

cesium /see-zee-ŭm, see-see-/ (caesium) Asoft golden highly reactive low-melting ele-ment. Cesium is used in photocells, as acatalyst, and in the cesium atomic clock.The radioactive isotopes 134Cs (half life2.065 years) and 137Cs (half life 30.3 years)are produced in nuclear reactors and po-tentially dangerous atmospheric pollu-tants.

Symbol: Cs; m.p. 28.4°C; b.p. 678.4°C;r.d. 1.873 (20°C); p.n. 55; r.a.m. 132.91.

cesium clock An apparatus used to pro-duce the steady frequency used in definingthe second. It depends on the fact that, in amagnetic field, cesium-133 atoms can havetwo different energy levels between whichtransitions occur by absorption of radio-frequency radiation of a frequency of9 192 631 770 hertz. In a cesium clock, thenumber of atoms in the higher state is de-tected, and the signal used to stabilize theoscillator producing the radiation.

c.g.s. system A system of units that usesthe centimeter, the gram, and the second asthe fundamental mechanical units. Muchearly scientific work was performed usingthis system, but it has now almost beenabandoned.

In the c.g.s. system there are two sets ofelectrical units: electrostatic units in whichthe permittivity of free space (ε0) is unity;and electromagnetic units in which the per-meability of free space (µ0) is unity.

chain reaction The progressive disinte-gration of fissile material (e.g. 235U) bybombardment with neutrons, which inturn results in the production of more neu-trons. These may, under suitable condi-tions, produce further fissions.

Fission of 235U yields a varying numberof neutrons depending on the energy of theincident neutrons. Neutrons may escapefrom the mass of uranium or be absorbedby nonfissile nuclei and so be ineffective in

promoting the chain reaction. If one fissionproduces neutrons which, in turn, causemore than one fission, there is a branchingchain reaction, which may be explosive.On the other hand, if insufficient neutronsare captured the chain reaction will die out.To sustain a controlled chain reaction innatural uranium, it is necessary to slowdown the neutrons in a moderator. Slowneutrons are more likely to cause fission in235U than to be captured by the moreabundant nonfissile isotope 238U. A chainreaction can only be sustained in uraniumwithout using a MODERATOR if the propor-tion of 235U is considerably increased (en-richment). The artificial fissile nuclides239Pu, 241Pu, and 233U can also sustainchain reactions. See nuclear reactor.

change of state A change from one stateof matter to another. See latent heat.

chaos theory The theory of systems thatexhibit apparently random unpredictablebehavior. The theory originated in studiesof the Earth’s atmosphere and the weather.In such a system there are a number of vari-ables involved and the equations describ-ing them are nonlinear. As a result, thestate of the system as it changes with timeis extremely sensitive to the original condi-tions. A small difference in starting condi-tions may be magnified and produce alarge variation in possible future states ofthe system. As a result, the system appearsto behave in an unpredictable way and mayexhibit seemingly random fluctuations(chaotic behavior). The study of such non-linear systems has been applied in a num-ber of fields, including studies of fluid

cesium

40

CHANGES OF STATE

solid–liquid melting (fusion)liquid–solid freezingliquid–gas evaporation

(boiling at boiling temperature)

gas–liquid condensationsolid–gas sublimationgas–solid condensation

dynamics and turbulence, random electri-cal oscillations, and certain types of chem-ical reaction. See also attractor; butterflyeffect.

characteristic In an electronic device,such as a diode or a transistor, a graph thatshows how a voltage or current betweentwo of the terminals varies with respect tovoltage or current at other terminals of thedevice.

charcoal An amorphous form of carbonmade by heating wood or other organicmaterial in the absence of air. Activatedcharcoal is charcoal heated to drive off ab-sorbed gas. It is used for absorbing gasesand for removing impurities from liquids.

charge (electric charge) Symbol: Q Abasic property of some elementary parti-cles of matter. Charge has no definition;rather it is taken as a basic experimentalquantity. There are two types of chargeconventionally called positive and nega-tive. Like charges repel each other and un-like charges attract each other. The unit ofcharge is the coulomb (C). The charge on abody arises from an excess or deficit ofnegative electrons with respect to positiveprotons.

charge density The electric charge perunit volume of a material or per unit areaof a surface or per unit length of a line.Volume charge density (symbol: ρ) is mea-sured in coulombs per cubic meter (C m–3).Surface charge density (symbol: σ) is mea-sured in coulombs per square meter(C m–2). The unit of linear charge density,λ, is the coulomb per meter (C m–1). For aconductor, excess charge is distributedover the surface; the surface charge densityincreases with curvature.

Charles’ law /sharlz, charl-ziz/ (law ofCharles and Gay-Lussac) This was origi-nally an experimental law relating the be-havior of real gases to an arbitrarytemperature scale (mercury-in-glass). For agiven mass of gas at constant pressure, thevolume increases by a constant fraction ofthe volume at 0°C for each Celsius degree

rise in temperature. The constant fraction(α) has almost the same value for all gases– about 1/273 – and Charles’ law can bewritten in the form

V = V0(1 + αvθ)where V is the volume at temperature θ andV0 the volume at 0°C. The constant αv isthe thermal expansivity of the gas.

A similar relationship exists for thepressure of a gas heated at constant vol-ume:

p = p0(1 + αpθ)Here, αp is the pressure coefficient. Verynearly, αp = αv for all gases. From the idealgas equation pVm = RT, we deduce thatVm ∝ T at constant pp ∝ T at constant Vm.These equations are sometimes said to ex-press Charles’ law, although they are justconsequences of the definition of T andcannot be derived from his experimentalresults. The law is named for the Frenchphysicist and physical chemist JacquesAlexandre César Charles (1746–1823),and for the French physicist and chemistJoseph-Louis Gay-Lussac (1778–1850).See also gas laws.

charm See quark.

chemical hygrometer See hygrometer.

chemiluminescence /kem-ă-loo-mă-nes-ĕns/ See luminescence.

chemisorption /kem-ă-sorp-shŏn, -zorp-/See adsorption.

chirality /kÿr-al-ă-tee/ See optical activity.

Chladni figures /klahd-nee/ Patterns thatreveal the modes of vibration of a glass ormetal plate. They are made by sprinkling afine powder on the plate. The powder ac-cumulates along the nodes of the vibration,where the plate does not vibrate. The fig-ures are named for the German physicistErnst Florens Friedrich Chladni (1756–1827).

chlorine /klor-een, -in, kloh-reen, -rin/ Agreen reactive gaseous element belonging

41

chlorine

choke

42

diode

tunnel diode

n-p-n transistorB

C

E

B

C

E

p-n-p transistor

amplifier

loudspeaker

microphone

chassis connection

aerial

ground

resistor fixed

resistor(variable)

capacitor (fixed)

+ capacitor(electrolytic)

inductor (fixed)

inductor (withmagnetic core)

inductor variable

switch (simple)

+ –

cell

A.C. source~

A ammeter

transformer

transformer(magnetic core)

V = voltmeterG = galvanometer

Circuit elements

to the halogens. It accounts for about0.055% of the Earth’s crust.

Symbol: Cl; m.p. –100.38°C; b.p.–33.97°C; d. 3.214 kg m–3 (0°C); p.n. 17;r.a.m. 35.4527.

choke An inductor used to reduce thehigh-frequency components of an alternat-ing signal by presenting a higher imped-ance for them. Chokes are also used forsmoothing fluctuations in the output cur-rent of a rectifier circuit.

choroid /kor-oid, koh-roid/ The middle ofthe three layers of the EYE.

chromatic aberration /krŏ-mat-ik/ Seeaberration.

chromium /kroh-mee-ŭm/ A transitionmetal; chromium is used in strong alloysteels and stainless steel and for plating ar-

ticles. It is a hard silvery metal that resistscorrosion at normal temperatures.

Symbol: Cr; m.p. 1860±20°C; b.p.2672°C; r.d. 7.19 (20°C); p.n. 24; r.a.m.51.9961.

chromosphere /kroh-mŏ-sfeer/ The partof the atmosphere of the Sun that is directlyabove the photosphere and below thecorona. It is roughly 10 000 kilometersthick.

circuit, electrical A combination of elec-trical components that form a conductingpath. When the path is broken, for exam-ple by a switch, the circuit is said to beopen. When a complete loop is formed al-lowing current to flow as a result of a po-tential difference in the circuit, it is said tobe closed. A short circuit is one in whichthere is a low resistance path throughwhich the current can flow. See also inte-grated circuit.

circuit breaker A safety device in an elec-tric circuit that interrupts the flow of cur-rent in the event of a short circuit or otherfault. See also fuse.

circuit element A resistor, capacitor, in-ductor, transistor, or other device used inmaking up electric circuits.

circular measure Measurement of anglesin radians.

circular motion A form of periodic (orcyclic) motion, that of an object moving atconstant speed v in a circle of constant ra-dius r. For this to be possible, a positivecentral force must act. The terms used todescribe circular motion are shown in thetable overleaf. See also centripetal force;rotational motion.

circular polarization A type of polariza-tion of electromagnetic radiation in whichthe plane of polarization rotates uniformlyround the axis as the ray progresses. Circu-larly polarized light is equivalent to (and isproduced by) the combination of twoequal plane-polarized rays moving to-

43

circular polarization

plane angle = s /r

r

s

2π radians

area A

Ω

rtotal 4πsteradians

solid angleΩ = A /r

Circular measure

gether but out of phase by 90°. See alsoplane polarization; polarization.

Clark cell A type of cell formerly used asa standard source of e.m.f. It consists of amercury cathode coated with mercury sul-fate, and a zinc anode. The electrolyte iszinc sulfate solution. The e.m.f. producedis 1.434 5 volts at 15°C. The Clark cell hasbeen superseded as a standard by the Wes-ton cadmium cell. The cell is named for theEnglish engineer Josiah Clark (1822–98).

classical physics The part of physics thatwas developed before (and so does not in-clude) quantum theory. For instance, New-ton’s laws of motion belong to classicalmechanics; they are a special case of quan-tum mechanics in the case of a body havinga small quantum mechanical wavelength.

cleavage The splitting of a crystal alongplanes of atoms, to form smooth surfaces.

clinical thermometer A thermometer de-signed for taking body (‘blood’) tempera-ture; a mercury thermometer with a kink inthe thread just above the bulb, and cali-brated in the range 35–46°C (95–115°F).The mercury reaches a maximum value but

does not then return to the bulb untilshaken down past the kink.

closed circuit See circuit; electrical.

closed pipe A pipe with one end closedand the other end open. If air is blown intothe pipe a stationary sound wave may beformed, with a node at the closed end andan antinode at the open end.

closed shell An ELECTRON SHELL in anatom or molecule that is completely filledwith electrons. Closed shells of nucleons innuclei also exist.

closed system (isolated system) A set ofone or more objects that may interact witheach other, but do not interact with theworld outside the system. This means thatthere is no net force from outside or energytransfer. Because of this the system’s angu-lar momentum, energy, mass, and linearmomentum remain constant.

close packing A type of packing of atomsin crystals, in which the atoms are regardedas spheres that have exactly the same sizeand fill space in the most efficient way. Ina single layer each sphere is surrounded bysix other spheres, arranged at the cornersof a hexagon. A second layer fills as manyof the hollows as possible. There are twoways in which a third layer can be placed.If it is directly above the first layer thenthere is hexagonal close packing, with thelayer sequence being denoted ABABAB ....If the third layer is above the hollows of thefirst layer that have not been filled by thesecond layer, then there is cubic close pack-

Clark cell

44

B (magnetic vector)

E (electric vector)

Circular polarization

QUANTITIES USED IN DESCRIBING CIRCULAR MOTION

Quantity Symbol Formulaangular displacement θ –angular velocity ω ω = v/rcentripetal acceleration a a = v2/r = ω2rcentripetal force F F = mv2/r = mω2rfrequency f f = ω/2πperiod T T = 1/f

ing, with the layer sequence being denotedABCABC....

cloud chamber A chamber used to showthe tracks of ionizing radiation, especiallyalpha and beta particles.

A diffusion cloud chamber has feltstrips near the top soaked in water andethanol. The bottom of the chamber is heldat a low temperature, and there is continu-ous diffusion of vapor down the chamber.At one particular level, water droplets con-dense only along the tracks of ionizing ra-diation. The expansion cloud chambercontains moist air, sometimes with ethanolvapor, which is cooled by a sudden adia-batic expansion, causing the air to becomesupersaturated with water vapor. Waterdroplets condense out preferentially onions formed along the tracks.

It can be arranged that passage of anionizing particle through the chamber isdetected by a counter and the resultingpulse can be used to operate the pump, sothat the expansion takes place just after theion pairs have been formed. A camera mayalso be triggered to take a photograph ofthe tracks just as they become visible. Mag-netic fields can be applied and the resultingcurvature of the tracks provides informa-tion about the charge and energy of theparticles.

See also bubble chamber.

coaxial /koh-aks-ee-ăl/ Denoting bodiesor shapes that have a common axis of ro-tation or radial symmetry. See also cable;coaxial.

cobalt /koh-bawlt/ A lustrous silvery-bluehard ferromagnetic transition metal. It isused in alloys for magnets, cutting tools,and electrical heating elements and in cata-lysts and some paints.

Symbol: Co; m.p. 1495°C; b.p.2870°C; r.d. 8.9 (20°C); p.n. 27; r.a.m.58.93320.

Cockcroft–Walton accelerator /kok-roft wawl-tŏn/ The first particle accelerator(1932), used to achieve the first artificialnuclear disintegration by bombarding alithium target with protons (to produce

alpha particles). The device was a simpleform of linear accelerator; potential differ-ences up to 800 kV were achieved by avoltage multiplier device. The Cock-croft–Walton accelerator is named for theBritish physicist Sir John Cockcroft(1897–1967) and the Irish physicist ErnestThomas Sinton Walton (1903–95).

coefficient of expansion See expansiv-ity.

coefficient of friction See friction.

coercive force The magnetizing field in-tensity required to reduce the flux densityin a material to zero. If the material is mag-netically saturated the coercive force is amaximum; it is then referred to as the co-ercivity. See also hysteresis cycle.

coercivity /koh-er-siv-ă-tee/ See hysteresiscycle.

coherent Two sources of waves are saidto be coherent if there is a constant rela-tionship between the phases of the wavesemitted by them. For most sources of lightor similar electromagnetic radiations(other than radio waves) it is usually neces-sary to derive the radiations of the twosources from one original source, as inYoung’s interference experiment.

Radiation is said to be coherent if thereis a regular phase relationship betweenwidely different parts of a wavefront, or ifsuch regularity is maintained for a consid-erable time. Radiation from a laser is ex-ceptionally coherent.

coherent units A system or sub-set ofUNITS (e.g. SI units) in which the derivedunits are obtained by multiplying or divid-ing together base units, with no numericalfactor involved other than one.

cohesion See surface tension.

coincidence circuit A device that detectsthe occurrence of two events that either co-incide or occur within a specified time in-terval of each other. Signals recording thetwo events are fed into the device, which

45

coincidence circuit

produces an output only if the two im-pulses occur within the specified time. Sucha device is the basis of a coincidencecounter.

cold emission Emission of electrons froma solid by a process other than thermionicemission. The term is usually used to de-scribe either field emission or secondaryemission.

cold rolling The reduction in the thick-ness of a metal by applying pressure to it.This process usually strengthens the metalby introducing dislocations.

collector See transistor.

colligative properties /kŏ-lig-ă-tiv/ Theproperties of a solution that depend onlyon the number of solute particles (such asions or molecules) present in the solutionbut not on the type of particles present. Ex-amples of colligative properties include de-pression of the freezing point, elevation ofthe boiling point, reduction in vapor den-sity, and osmotic pressure.

collimator /kol-ă-may-ter/ An arrange-ment for producing a parallel beam of ra-diation for use in a spectrometer or otherinstrument. A system of lenses and slits isutilized.

collision An interaction between objectsin which they approach each other nearenough to exert a mutual influence, al-though they do not necessarily come intoactual contact. The objects may be sub-atomic particles, groups of particles, orrigid bodies and the interaction may in-volve an exchange of charge, energy, ormomentum, which is usually conservedafter the collision.

colloid /kol-oid/ A substance containingvery small particles (sizes in the range10–9–10–5 m). Sols, gels, and emulsions areexamples of colloids.

color A physiological sensation producedin the eye-brain system relating to thewavelength of visible radiation. Tradition-

ally the visible spectrum is divided intoseven color regions, although many peoplecannot distinguish the color ‘indigo’ be-tween violet and blue. Individual eyes dif-fer in their sensitivities to differentwavelengths and the spectral colors alsomerge gradually into each other. In theretina of the eye, certain cells (cones) areresponsible for color vision; they cannotoperate at low light levels, which is whycolor vision is not so effective at night.

Monochromatic radiations of differentwavelengths are called hues; the normalhuman eye can distinguish yellow huesonly 1 nm apart. If a hue is mixed withwhite light, it is an ‘unsaturated’ hue, nowcalled a tint. Different saturated hues mixtogether, either to produce the effect ofother hues, or of nonspectral colors. Thestudy of color mixing by addition of col-ored lights (hues) shows that any color sen-sation can be produced by mixing threeprimary hues. It is normal to choose a red,a green, and a blue for this purpose. Col-ored television pictures are produced onthis basis.

While ‘white’ light is defined as the nor-mal mixture of all visible radiation, thesame sensation can be obtained by mixingcomplementary pairs of lights (hues).

The apparent colors of surfaces in whitelight depends on the wavelengths that arereflected. Thus yellow paint (pigment) re-flects mainly yellow wavelengths (with per-haps some orange and green); the rest areabsorbed. When two paints of differentcolors are mixed, the color reflected will bethe sum of the wavelengths absorbed byneither pigment. This is ‘color mixing bysubtraction’. The three usual primary col-ors are the greenish-blue ‘cyan’ (white lightwith red absorbed); the crimson magenta(green absorbed), and yellow (blue ab-sorbed).

color (in particle physics) A quality anal-ogous to electric charge that characterizesthe strong interactions of QUARKS. Theword color in this context has nothing todo with the physiological sensation ofcolor. However, some of the properties ofcolor for strongly interacting particles areanalogous to ordinary color. There are

cold emission

46

three ‘primary’ colors for quarks, denotedred, blue, and green.

color blindness See color vision.

colorimeter /kul-ŏ-rim-ĕ-ter/ An instru-ment able to give readings for any color interms of the intensity of each of the threeprimary colors.

color vision The ability of the eye to dis-tinguish different COLORS. The mechanismis not fully understood. It is thought thatthere may be three types of cone cell in theretina, able to react to red, green, and bluelight. Nerve signals corresponding to theintensities of each of these give color im-pressions in the brain.

About 5% of males and 0.5% of fe-males have inherited defects of color vi-sion. In many cases, there is a reducedability to distinguish colors, particularlyred and green and especially in dim light. Inmore extreme cases there is very little dis-crimination in the whole range from red togreen. The popular term color blindness isto be avoided as the lack of any color vi-sion is extremely rare. A few individualshave exceptionally good color vision, espe-cially in the blue and violet. These peoplecan see a distinct color ‘indigo’.

coma See aberration.

comet A small body that moves aroundthe Sun with a highly eccentric orbit. Theperiods of the orbits of comets vary be-tween about 150 years (short-periodcomets) and hundreds of thousands ofyears (long-period comets). A comet con-sists of a nucleus made of ice and dust sur-rounded by a coma, which consists of gasand dust. If the comet is near the Sun radi-ation pressure drives gas and dust awayfrom the coma to form a ‘tail’, which al-ways points away from the Sun.

common emitter See transistor.

communication satellite A man-madesatellite that is put into a PARKING ORBIT

and designed to allow television and tele-

phone communication between differentplaces.

commutator /kom-yŭ-tay-ter/ The part ofa direct-current ELECTRIC MOTOR or gener-ator that connects the coil(s) to the outsidecircuit, changing the connections round asthe coil rotates.

compact disk (CD) A storage system inwhich data is recorded in the form of tinypits or patches in a spiral track on the disk.The data is read by directing a low-powerlaser onto the track and detecting the re-flected radiation. CDs are commonly usedto store music, and also as computer stor-age devices. Some types are re-writable.

comparator /kom-pă-ray-ter, kŏm-pa-ră-/An apparatus used in measurements of theexpansivity of solids. A horizontal bar ofthe material is used with a fine scratch neareach end. The bar is surrounded by a waterbath and two vertical microscopes areused, focused on the scratches on each end.Changes of length, produced by changes intemperature, are measured by the micro-scopes; a standard bar at constant temper-ature is used for comparison.

compass A device used to show magneticforce field direction. It consists of a smallmagnet pivoted so that it is free to move ina horizontal plane. In the Earth’s magneticfield a compass points along the magneticmeridian. A scale, graduated in degrees,may be placed underneath the magnet toassist in navigation. See also magnetome-ter.

complementary colors Two coloredlights (hues) that mix to produce the sensa-tion of white. There is an infinite numberof pairs of complementary colors. Thespectral hues can be plotted around aroughly triangular ‘chromaticity curve’that has white at the center. The membersof each pair of complementary colors lie atopposite sides of white on this curve. Seealso color.

complexity theory The study of highlycomplex physical systems. Key ingredients

47

complexity theory

in complexity theory include chaos theoryand the concepts of broken symmetry andself-organization. Computers are used ex-tensively in analyzing such systems.

complex number A number z that can bewritten in the form z = x + iy, where x andy are real numbers and i is the square rootof –1 (i.e. i2 = –1), with x and iy beingcalled the real part and the imaginary partrespectively of the complex number. Com-plex numbers are used extensively in thephysical sciences and in engineering.

component forces See component vec-tors.

component vectors The components ofa given vector (such as a force or velocity)are two or more vectors with the same ef-fect as the given vector. In other words thegiven vector is the resultant of the compo-nents. Any vector has an infinite number ofsets of components. Some sets are more usethan others in a given case, especially pairsat 90°.

component velocities See componentvectors.

composite material A material that iscomposed of two or more materials. Forexample, reinforced concrete is concretethat is set round steel wires. Other exam-ples are various plastics reinforced withglass or carbon fiber. Composite materialsare frequently produced so as to have bet-ter mechanical properties than single mat-

erials. For example, reinforced concreteimproves the tensile properties of concrete.

compound lens Two or more lenses usedtogether as a unit. For instance, the eye-piece of a telescope and the lens of a cam-era are both normally compound lenses;each has a number of elements (the singlelenses) along the same optical axis. Insectcompound eyes are not compound lensesin this sense – the elements are not on a sin-gle axis.

The elements of a compound lens mayor may not touch. The function of com-pound (rather than single) lenses is usuallyto minimize aberrations.

See also doublet.

compound microscope See microscope,compound.

compound pendulum See pendulum.

compressibility /kŏm-pres-ă-bil-ă-tee/The reciprocal of the bulk modulus of amaterial.

Compton effect /komp-tŏn/ An increasein the wavelength of x-rays or gamma rayswhen scattered by loosely bound electronsin substances, the electrons being ejected.Theoretically the phenomenon is treated asa collision between a photon and an elec-tron, the latter being regarded as a free par-ticle initially at rest. The photon transfersenergy and momentum to the electron,hence the wavelength increases. TheCompton effect is named for the Americanphysicist Arthur Holly Compton (1892–1962). See also duality.

Compton wavelength The length-scaleassociated with a particle at which the de-scription of the particle is dominated byrelativistic quantum mechanics. It is de-fined by h/mc, where h is the Planck con-stant, m is the rest mass of the particle, andc is the speed of light in a vacuum. TheCompton wavelength of an electron is2.4263 × 10–12 m. It is named for ArthurCompton.

complex number

48

B

FA

A = F sin B = F cos

Component vectors

concave /kong-kayv, kong-kayv/ Curvinginward, away from the viewpoint. A con-cave mirror is one with a concave reflectingsurface. A concave lens is either a bicon-cave or a plano-concave lens. See also con-vex; lens; mirror.

concavo-convex /kong-kay-voh-kon-veks/ Describes a LENS with one concavesurface and one convex surface. Most spec-tacle lenses have this shape. Concavo-con-vex lenses can be converging or diverging.Lenses of this type are sometimes calledmeniscus lenses.

condensation /kon-den-say-shŏn/ Achange from vapor to liquid – the reverseof evaporation. See also dew; relative hu-midity.

condensation pump See diffusion pump.

condenser 1. An early term for capacitor.2. A lens, set of lenses, or mirror in an op-tical instrument used to concentrate lightonto the object to be viewed. See micro-scope; compound; projectors.

condenser microphone A type of micro-phone in which the diaphragm is one plateof a charged capacitor (‘condenser’).Sound waves move the diaphragm, thus al-tering the capacitance. The correspondingchanges in potential difference generate thesignal.

conductance /kŏn-duk-tăns/ Symbol G.The ratio I/V in an electrical conductor,where I is the current and V is the potentialdifference. The conductance is the recipro-cal of the resistance. The SI unit is thesiemens (symbol: S).

conduction /kŏn-duk-shŏn/ 1. A processof heat transfer through a substance with-out movement of the substance itself. Therate of transfer depends on the samplelength and cross-sectional area, the tem-perature difference, and the nature of thematerial.

Good conductors, such as copper andsilver, are often metals that have free elec-trons. The energy is transmitted by move-ment of these. In poor solid conductors(insulators) there are no conduction elec-trons and the transfer is only by vibrationsof atoms or molecules in the crystal struc-ture. See also conductivity; thermal.2. Passage of charge through a sampleunder the influence of an electric field. Thecharge may be carried by electrons (e.g. inmetals), by electrons and positive holes (inelectrolytes and semiconductors), or byions (in electrolytes and gases). See also en-ergy bands.

conduction band See energy bands.

conductivity, electrical /kon-duk-tiv-ă-tee/ Symbol: σ The ability of a material toconduct electric current; the reciprocal ofthe resistivity. Conductivity does not de-pend on the dimensions of the conductor.

49

conductivity, electrical

concave convex

Concave and convex surfaces

a convergingconcavo-convex lens

a divergingconcavo-convex lens

Types of concavo-convex lens

It is also the ratio of current density toelectric field strength. The unit is thesiemen per meter (S m–1).

conductivity, thermal Symbol: λ, k Ameasure of the ability of a material to con-duct energy. It is defined as the energytransfer per unit time per unit cross-sec-tional area of the conductor, per unit tem-perature gradient along the conductor. Theunit of thermal conductivity is the watt permetre kelvin (W m–1 K–1). For a parallel-sided block of material with no lossthrough the sides:

E/t = λA(θ2 – θ1)/lwhere E is the amount of energy trans-ferred in a time t, A the cross-sectionalarea, l the length, and θ2 and θ1 the tem-peratures of the faces. In general:

dE/dt = –λAdθ/dtSee also Lees’ disk; Searle’s bar.

conductor, electrical All metals are goodconductors of electricity, as is graphite.These are called electrical conductors.Most nonmetals are very poor conductors,and good insulators may have electricalconductivities of the order of 10–20 of thoseof metals at ordinary temperatures. Theelectrical conductivity of nonmetals usu-ally increases rapidly with temperature sosome become fairly good conductors athigh temperatures. See also energy bands;semiconductor.

conductor, thermal A substance that hasa relatively high thermal conductivity. Ingeneral, many metals are good conductorsof energy – copper and silver are notableexamples. Many non-metallic solids arepoor conductors (i.e. they are thermal in-sulators). Gases are particularly poor con-ductors (or good insulators).

cones The cells in the retina of the EYE thatare important for vision in normal light.They are also responsible for color vision.Their mechanism of action is not fully un-derstood. See also color.

configuration /kŏn-fig-yŭ-ray-shŏn/ Thearrangement of electrons in shells aroundthe nucleus of an atom. The electron con-

figuration largely determines the chemicalbehavior of an element as well as somephysical properties, such as electrical con-ductivity. See electron shell.

conic /kon-ik/ A type of plane curve de-fined so that for all points on the curve thedistance from a fixed point (the focus) hasa constant ratio to the perpendicular dis-tance from a fixed straight line (the direc-trix). The ratio is the eccentricity of theconic, e; i.e. the eccentricity is the distancefrom curve to focus divided by distancefrom curve to directrix.

The type of conic depends on the valueof e: when e is less than 1 it is an ellipse;when e equals 1 it is parabola; when e isgreater than 1 it is hyperbola. A circle is aspecial case of an ellipse with eccentricity0.

The original definition of conics was asplane sections of a conical surface – hencethe name conic section. In a conical surfacehaving an apex angle of 2θ, the cross-sec-tion on a plane that makes an angle θ withthe axis of the cone, (i.e. a plane parallel tothe slanting edge of the cone) is a parabola.A cross-section in a plane that makes anangle greater than θ with the axis is an el-lipse. A cross-section in a plane making anangle less than θ with the axis is a hyper-bola and because this plane cuts bothhalves (nappes) of the cone, the hyperbolahas two arms.

There are various ways of writing theequation of a conic. In Cartesian coordi-nates:

(1 – e2)x2 + 2e2qx + y2 = e2qwhere the focus is at the origin and the di-rectrix is the line x = q (a line parallel to they-axis a distance q from the origin). Thegeneral equation of a conic (i.e. the generalconic) is:

ax2 + bxy + cy2 + dx + ey + f = 0where a, b, c, d, e, and f are constants (heree is not the eccentricity). This includes de-generate cases (degenerate conics), such asa point, a straight line, and a pair of inter-secting straight lines. A point, for example,is a section through the vertex of the coni-cal surface. A pair of intersecting straightlines is a section down the axis of thesurface.

conductivity, thermal

50

See also ellipse; hyperbola; parabola.

conjugate points Any pair of points rel-ative to a lens, reflector, or other opticalsystem such that either is imaged at theother. Compare the symmetry in objectdistance u and image distance v in theequation:

l/v + l/u = l/f

conservation law A physical law thatsome property of a system remains con-stant throughout a series of changes. Ex-amples are the laws of conservation ofmass, energy, momentum, and charge.

conservation of angular momentum,law of See constant angular momentum;law of.

conservation of charge The principlethat the total net charge of any closed sys-tem is constant.

conservation of energy, law of See con-stant energy; law of.

conservation of linear momentum,law of See constant linear momentum,law of.

conservation of mass, law of See con-stant mass; law of.

conservation of mass and energy Thelaw that the total energy (rest mass energy+ kinetic energy + potential energy) of aclosed system is constant. In most chemicaland physical interactions the mass changeis undetectably small, so that the measur-able rest-mass energy does not change (it isregarded as ‘passive’). The law then be-comes the classical law of conservation ofenergy; the inclusion of mass in the calcu-lation is necessary only in the case of nu-clear changes or systems involving veryhigh velocities. See also mass-energy equa-tion; rest mass.

conservative field A field of force suchthat the work done on or by a body that isdisplaced in the field is independent of thepath. Hence if a body is moved in a closed

path (back to the starting point) the network done is zero. Gravity and an electro-static field in a vacuum are conservative.Any form of friction prevents the field frombeing conservative, although the total en-ergy of any isolated system is conserved inall cases.

constant A quantity or factor that re-mains at the same value when others arechanging. See also fundamental constants.

constantan /kon-stăn-tan/ An alloy ofcopper (50–60%) and nickel used in ther-mocouples and precision resistors. Its elec-trical resistance varies very little withchanges in temperature.

constant angular momentum, law of(law of conservation of angular momen-tum) The total angular momentum of asystem cannot change unless a net outsidetorque acts. See also constant (linear) mo-mentum, law of.

constant energy, law of (law of conser-vation of energy) The total energy of a sys-tem cannot change unless energy is takenfrom or given to the outside. The law isequivalent to the first law of thermody-namics. See also mass-energy equation.

constant linear momentum, law of(law of conservation of linear momentum)The total linear momentum of a systemcannot change unless a net outside forceacts.

constant mass, law of (law of conserva-tion of mass) The total mass of a systemcannot change unless mass is taken from orgiven to the outside. See also mass-energyequation.

constant momentum, law of See con-stant (linear) momentum, law of.

constant pressure gas thermometer Seegas thermometer.

constant volume gas thermometer Seegas thermometer.

51

constant volume gas thermometer

constructive interference See interfer-ence.

contact angle An angle formed betweensolid and liquid surfaces. For example,when a drop of mercury rests (in air) ontop of a horizontal glass surface, the con-tact angle measured inside the drop fromthe glass to the mercury-air interface, isgreater than 90°. This is because the mer-cury does not wet the glass – its cohesion isgreater than the adhesion to glass. Waterdoes wet the surface of clean glass and thecontact angle is less than 90°. See also cap-illary action; meniscus.

contact potential A potential differenceacross the space between the free surfacesof two solids that are in contact.

containment /kŏn-tayn-mĕnt/ 1. Theprocess of containing radioactive materialwithin a shield for safety reasons.2. The process of containing the plasma ina fusion reactor so that it does not come incontact with the walls of the vessel. Mag-netic fields are used.

continuous spectrum A SPECTRUM com-posed of a continuous range of emitted orabsorbed radiation. Continuous spectraare produced in the infrared and visible re-gions by hot solids. See black body.

continuous wave An electromagneticwave that is transmitted continuously overa period of time, as in radio communica-tion. It is distinguished from a pulsed or in-termittent wave as used in radar. See alsoradar.

control grid See grid.

control rods Rods of neutron-absorbingmaterial that can be moved into or out ofthe core of a nuclear reactor to control thechain reaction. Control rods are made ofboron, cadmium, or other substance thatabsorbs neutrons.

convection /kŏn-vek-shŏn/ The transferof energy by flow of a liquid or gas. In nat-ural convection the fluid flow is caused by

temperature differences between one partof the fluid and another. For example, inan electric kettle the heating element raisesthe temperature of the water next to it,which expands and rises. Colder waterthen flows in beneath it, setting up a con-vection current. In forced convection, en-ergy is carried away from the source byflow produced by a pump or fan.

In natural convection the rate of loss ofenergy from a body to the surroundings isproportional to θ5/4 where θ is the excesstemperature over the surroundings. Inforced convection it is proportional to θ.See also Newton’s law of cooling.

conventional current An electric currentconsidered to flow from points at positivepotential to points at negative potential. Intypical conductors, charge is carried byelectrons, which flow in the opposite direc-tion. In semiconductors, the charge may becarried by positive holes, flowing in thesame direction as the conventional current.

convergent Coming together. A conver-gent beam becomes narrower as it travels.Its narrowest point is called the focus; afterpassing through the focus, the beam will beDIVERGENT (moving apart).

converging lens A LENS that can refract aparallel beam into a convergent beam.Converging lenses used in air are thicker inthe middle than at the edge. They may bebiconvex, plano-convex, or concavo-con-vex in shape. As these lenses have positivepower, they are sometimes called positivelenses. Compare diverging lens.

converging mirror (converging reflector)

constructive interference

52

convergent beam divergent beam

focus

Convergent and divergent beams

A MIRROR that can reflect a parallel beaminto a convergent beam. Converging reflec-tors always have concave surfaces. The sec-tion shape is the arc of a circle in simplecases; the arc of a parabola is needed formore precise work. As these mirrors havepositive power, they are sometimes calledpositive mirrors. Compare diverging mir-ror.

converter A device for converting alter-nating current to direct current or viceversa.

converter reactor See nuclear reactor.

convex /kon-veks, kon-veks/ A convexmirror is one with a convex reflecting sur-face. A convex lens is either a biconvexLENS or a plano-convex lens. See also con-cave; mirror.

coolant /koo-lănt/ A fluid that removesenergy from a source (e.g. a hot motor) byconvection.

cooling correction A method of correct-ing for errors due to energy loss in experi-ments that involve temperature changes. Inthe method of mixtures, for instance, thefinal temperature reached by the mixturemay be slightly less than the theoretical oneas a result of cooling during the change. Agraph of temperature against timethroughout the course of the experiment(i.e. a cooling curve) allows a correction tobe made based on Newton’s law of cool-ing.

coordinates Numbers that define the po-sition of a point, or set of points. See alsoCartesian coordinates; polar coordinates.

coplanar forces Forces in a single plane.If only two forces act through a point, theymust be coplanar. So too are two parallelforces. However, nonparallel forces thatdo not act through a point cannot becoplanar. Three or more nonparallel forcesacting through a point may not be copla-nar.

copper /kopp-er/ A transition metal; cop-per is used in electrical wires and in such al-loys as brass and bronze. The metal itself isgolden-red in color.

Symbol: Cu; m.p. 1083.5°C; b.p.2567°C; r.d. 8.96 (20°C); p.n. 29; r.a.m.63.546.

core 1. A piece of iron or other magneticmaterial used to concentrate the magneticlines of force in a transformer, electromag-net, or similar device.2. The central part of a nuclear reactor inwhich the chain reaction occurs.

Coriolis force /kor-ee-oh-lis, ko-ree-/(Coriolis effect) A ‘fictitious’ force used todescribe the motion of an object in a rotat-ing system. For instance, air moving fromnorth to south over the surface of the Earthwould, to an observer outside the Earth, bemoving in a straight line. To an observeron the Earth the path would appear to becurved, as the Earth rotates. Such systemscan be described by introducing a tangen-tial Coriolis ‘force’. The force is named forthe French physicist Gustave-GaspardCoriolis (1792–1843).

corkscrew rule See Maxwell corkscrewrule.

cornea /kor-nee-ă/ (pl. corneas orcorneae) The transparent part of the EYE.

corona /kŏ-roh-nă/ The outer section ofthe atmosphere of the Sun. The innercorona (K-corona) has a temperature ofabout 2× 10–6K and extends to a height ofabout 75 000 km. The outer corona (F-corona) extends for millions of kilometers,and is much cooler.

corona discharge Small regions of glow-ing air around a charged conductor at acritical potential. It is often accompaniedby hissing sounds and is caused by the ion-ization of the air around the conductor.Corona discharges are produced at sharppoints, where the surface charge densityand electric field, are high.

53

corona discharge

corpuscular theory /kor-pus-kyŭ-ler/Until the early nineteenth century it wasmost usually believed that light consists ofparticles (‘corpuscles’). Rectilinear propa-gation, reflection, and refraction could beexplained by assuming Newton’s laws ofmotion. Phenomena such as diffractionand Newton’s rings, which are now be-lieved to require wave theory, were too lit-tle understood to ‘discredit’ thecorpuscular theory. The theory was aban-doned following the thorough investiga-tion of interference, diffraction andpolarization, which demand a wave the-ory. Also Foucault (1850) showed that thespeed of light in water is less than in air, inagreement with wave theory but not withcorpuscular theory. The concept of thephoton is sometimes regarded as a modernform of corpuscular theory. See also dual-ity; wave theory of light.

cosmic radiation High-energy radiationreaching the Earth. The primary cosmic ra-diation mostly enters the solar system fromremote regions in space, but part may bederived from the Sun. It consists mainly ofatomic nuclei (particularly protons, somealpha particles, and small numbers ofheavier nuclei) and there are some elec-trons and gamma rays. The nuclei thatreach the atmosphere of the Earth have en-ergies from 1010eV up to 1019eV. Theseparticles collide with atomic nuclei in theupper atmosphere and give rise to the sec-ondary radiation. This includes lower en-ergy protons and neutrons, and manyunstable particles, particularly pions.

Most of the secondary radiations eitherinteract or decay in the atmosphere. Thecharged pions decay to give muons, whichare very penetrating so that many reachsea-level and even penetrate deeply into theground. At all levels the penetrating radia-tions are accompanied by a (relatively) lesspenetrating soft component. This consistsof electrons, positrons, and gamma radia-tion.

cosmic string A hypothetical entity; along one-dimensional defect in the fabricof space-time with an intense gravitationalfield. They have been postulated by cos-

mologists to explain various phenomena incosmology but there is no evidence fortheir existence.

cosmological constant Symbol: λ. Aconstant that can be added to Einstein’sfield equations for general relativity the-ory, originally introduced by Einstein toaccount for a possible static Universe. In anexpanding Universe the cosmological con-stant is not necessary, but it is believed thatthis constant may have a small nonzerovalue, with the physical consequence thatthe expansion of the Universe is accelerat-ing. It is not known how to calculate thevalue of λ, although many attempts havebeen made.

cosmology /koz-mol-ŏ-jee/ The study ofthe Universe as a whole. Cosmology in-cludes such questions as the evolution ofthe Universe and the formation of large-scale structures such as galaxies and clus-ters of galaxies. Cosmology is mostlydictated by general relativity theory butconsideration of the EARLY UNIVERSE re-quires contributions from nuclear physicsand the theory of elementary particles.

coudé telescope /koo-day/ A type of re-flecting telescope. Light from the concavemirror is reflected back onto a convex mir-ror, then onto a plane mirror at an angle tothe axis, and into the eyepiece. See also re-flector.

corpuscular theory

54

light fromdistant object

to eyepiece

coudé telescope

coulomb /koo-lom/ Symbol: C The SI unitof electric charge, equal to the chargetransported by an electric current of oneampere flowing for one second. 1 C =1 A s. It is named for the French physicistAugustin de Coulomb (1736–1806).

coulombmeter /koo-lom-mee-ter/ Seevoltameter.

Coulomb’s law The electric force be-tween two charges is inversely propor-tional to the square of their distance apart.The full law giving the mutual force be-tween two charges Q1 and Q2 is

F = Q1Q2/4εrε0r2

where r is the distance apart and εrε0 thepermittivity of the medium between thecharges.

counter A device for detecting and count-ing particles and photons. See Geigercounter; proportional counter; scaler; scin-tillation counter; semiconductor counter;spark.

couple A pair of equal parallel forces inopposite directions and not acting througha single point. Their linear resultant is zero,but there is a net turning-effect (moment).The resultant turning effect T (torque) isgiven by

T = d1F1 + d2F2T = (d1 – d2)F

T = dF

creep A slow deformation of a solid as aresult of a continuous applied stress. Seealso slip.

critical angle See total internal reflection.

critical damping See damping.

critical density See critical state.

critical mass The minimum mass of ma-terial that can sustain a nuclear CHAIN RE-ACTION. An explosive chain reaction (as ina nuclear fission weapon) results whensubcritical masses are brought together toform a mass greater than the critical mass.In a nuclear reactor, the chain reaction iscontrolled by a moderator.

The critical mass depends on the purityof the material used, the geometry of thearrangement, and the presence or absenceof reflectors of neutrons around the fissilematerial.

critical point See critical state.

critical pressure See critical state.

critical reaction A nuclear chain reactioninitiated by a neutron in which, on average,one neutron is released from each nuclearreaction, thus enabling the chain reactionto be sustained. If less than one neutron isreleased on average then the reaction issaid to be subcritical and the chain reactionfizzles out. If more than one neutron is re-leased on average then the reaction is saidto be supercritical and the chain reactionproliferates very rapidly, resulting in a nu-clear explosion.

critical specific volume See critical state.

critical speed In fluid flow, the speed atwhich the behavior of the fluid switchesfrom that of laminar flow to that of turbu-lent flow or vice versa. See also Reynoldsnumber.

critical state (critical point) The state of afluid under conditions in which the liquidand gas phases have the same density. Thetemperature, pressure, and density con-cerned are the critical temperature, criticalpressure, and critical density respectively.The specific volume is the critical specificvolume. Above its critical temperature a

55

critical state

F1 = Fd

d1d1d1

d2d2d2 F2 = FO

(O is any convenient point)

Couple

gas cannot be liquefied by increasing thepressure. The critical point corresponds toa point of inflection on an isothermal forthe gas.

See also Andrews’ experiments.

critical temperature See critical state.

critical volume See critical state.

CRO /see-ar-oh/ See cathode-ray oscillo-scope.

cross produce See vector product.

cross-section In a collision process – forexample, the bombardment of nuclei byneutrons – the apparent area that particlespresent to the bombarding particles. This isnot its ‘true’ cross-sectional area, but de-pends on the probability of a reaction oc-curring. In particular, it varies with theenergy of the incident particles. The mea-surement is used for other types of collisionreactions besides neutron absorption, in-cluding reactions of atoms, ions, mole-cules, electrons, etc. The unit is the squaremeter (m2).

crown glass See optical glass.

CRT /see-ar-tee/ See cathode-ray tube.

cryogenics /krÿ-ŏ-jen-iks/ The physics ofvery low temperatures, including tech-niques for producing low temperatures andthe study of how materials behave whencooled.

cryometer /krÿ-om-ĕ-ter/ A thermometerdesigned to measure very low tempera-tures.

cryoscopy /krÿ-os-kŏ-pee/ The determi-nation of freezing points.

cryostat /krÿ-ŏ-stat/ A container for keep-ing samples at a constant low temperature.

crystal A solid with a regular geometricshape. In crystals the particles (atoms, ions,or molecules) have a regular three-dimen-sional repeating arrangement in space.

This is called the crystal structure. Thecrystal lattice is the arrangement of pointsin space at which the particles are posi-tioned. The external appearance of thecrystal is the crystal habit. The externalshape of the crystal depends on the internalarrangement of the lattice. It also dependson the way in which the crystal is formed.See also crystalline.

crystal habit See crystal.

crystal lattice See crystal.

crystalline /kris-tă-lin, -lÿn/ Describing asolid that has a crystal structure; i.e. a reg-ular internal arrangement of atoms, ions,or molecules. Note that a substance can becrystalline without necessarily having ageometrical external shape.

crystallography /kris-tă-log-ră-fee/ Thestudy of the formation, structure, andproperties of crystals. See also x-ray crys-tallography.

crystalloid /kris-tă-loid/ A substance thatis not a COLLOID. It can pass through asemipermeable membrane. See colloid.

crystal microphone See microphone.

crystal oscillator A fixed-frequency OS-CILLATOR in which the output is derivedfrom a crystal of Rochelle salt or quartzspecially cut so that its natural frequency ofmechanical vibration is the desired value.This is usually in the range of about onekilohertz to several megahertz.

The action of crystal oscillators is basedon the piezoelectric effect. A potential dif-ference is applied to two electrodes at-tached to two parallel cut faces of thecrystal. The electric field sets up a mechan-ical stress which causes the crystal to res-onate at its natural frequency. This in turngenerates an alternating potential differ-ence across the crystal.

crystal rectifier A semiconductor diode.See diode; rectifier; semiconductor.

critical temperature

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crystal structure See crystal.

crystal system A category of crystal clas-sification based on the symmetry of its ex-ternal form, which in turn reflects itsinternal structure. There are seven maincrystal systems: cubic, hexagonal, mono-clinic, orthorhombic, tetragonal, triclinic,and trigonal.

cubic expansivity See expansivity.

curie /kyoo-ree, kyoo-ree/ Symbol: Ci Aunit of radioactivity, equivalent to theamount of disintegrations per second fromthe decay of one gram of radium. It is equalto 37 gigabecquerels. It is named for theFrench physicist Pierre Curie (1859–1906).

Curie point See Curie temperature.

Curie’s law The susceptibility, χ, of someparamagnetic substances is inversely pro-portional to the thermodynamic tempera-ture, T:

χ = c/Twhere c is a constant. More generally, therelationship is that of the Curie–Weiss law:

χ = c/(T – θ)where θ is the Weiss constant, a fixed tem-perature characteristic of the material. Theconstant is named for the French physicistPierre Weiss (1865–1940).

Curie temperature (Curie point) Thetemperature above which a ferromagneticsubstance loses its ferromagnetism. It thenshows paramagnetism only; the alignmentof magnetic moments in domains is over-come by thermal vibrations. The Curietemperature for iron is 760°C; that fornickel is 356°C. Metals that are paramag-netic at room temperatures could becomeferromagnetic if cooled. For example, theCurie temperature of dysprosium is–188°C.

Curie–Weiss law /vÿss/ See Curie’s law.

curium /kyoo-ree-ŭm/ A highly toxic ra-dioactive silvery element of the actinoid se-ries of metals. A transuranic element, it isnot found naturally on Earth but is synthe-

sized from plutonium. Curium-244 andcurium-242 have been used in thermoelec-tric power generators.

Symbol: Cm; m.p. 1340±40°C; b.p. ≅ 3550°C; r.d. 13.3 (20°C); p.n. 96; moststable isotope 247Cm (half-life 1.56 × 107

years).

curl See vector calculus.

current Symbol: I A flow of electriccharge. Current is the result of motion ofelectrons or ions under the influence of ane.m.f. It is measured in amperes (A).

current balance (ampere balance) A de-vice for measuring electric current to a highdegree of accuracy, by measuring the elec-tromagnetic force produced between twoconductors carrying the current.

current density Symbol: j The electriccurrent per unit area of conductor cross-section. It is measured in amperes persquare meter (A m–2). In a conductor it isequal to nvQ, where n is the number of freecharges per unit volume, v is their averagedrift velocity, and Q is their charge.

cybernetics /sÿ-ber-net-iks/ The sciencethat deals with communication and con-trol, particularly with regard to machines.It includes details about the input and out-put of information, FEEDBACK, and so on.

cycle A series of events that is regularly re-peated (e.g. a single orbit, rotation, vibra-tion, oscillation, or wave). A cycle is acomplete single set of changes, startingfrom one point and returning to the samepoint in the same way.

cyclic accelerator /sÿ-klik, sik-lik/ See ac-celerator.

cyclotron /sÿ-klŏ-tron/ A device for accel-erating charged particles to high energies.Protons can be given energies of over10 MeV, deuterons over 20 MeV, andalpha particles about 40 MeV. Particles areinjected near the center of an evacuatedspace between two D-shaped boxes placedbetween the poles of a strong permanent

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cyclotron

magnet. Within each ‘dee’ the particles de-scribe a semicircular orbit. An alternatingvoltage is applied to the dees at such a fre-quency that the particles are accelerated bythe potential difference each time theyreach the gap, causing them to increasetheir path radii and speeds in steps. Even-tually, after several thousand revolutions,they reach the perimeter of the dees at highspeed, where a deflecting electric field di-rects them onto the target.

The energies that can be achieved arelimited by the relativistic increase in massof the particles. As their velocity ap-proaches that of light, the increase in masscauses the period of rotation to increase sothat they no longer reach the gaps in phasewith the potential difference. See also syn-chrocyclotron.

cylindrical polar coordinates A methodof defining the position of a point in spaceby its horizontal radius r from a fixed ver-tical axis, the angular direction θ of the ra-dius from an axis, and the height z above afixed horizontal reference plane. Startingat the origin O of the coordinate system,the point P(r,θ,z) is reached by moving outalong a fixed horizontal axis to a distancer, following the circumference of the hori-zontal circle radius r centred at O throughan angle θ, and then moving vertically up-ward by a distance z. For a point P(r,θ,z),the corresponding rectangular Cartesiancoordinates (x,y,z) are:

x = rcosθy = rsinθ

z = zCompare spherical polar coordinates.

cylindrical polar coordinates

58

Dalton’s law (of partial pressures) Thepressure of a mixture of gases is the sum ofthe partial pressures of each individualconstituent. (The partial pressure of a gasin a mixture is the pressure that it wouldexert if it alone were present in the con-tainer.) Dalton’s law is strictly true only forideal gases. The law is named for the Eng-lish scientist John Dalton (1766–1844).

damped oscillation An oscillation withan amplitude that progressively decreaseswith time. See damping.

damping The reduction in amplitude of avibration with time by some form of resis-tance. A swinging pendulum will at lastcome to rest; a plucked string will not vi-brate for long – in both cases internaland/or external resistive forces progres-sively reduce the amplitude and bring thesystem to equilibrium.

In most cases the damping force(s) willbe proportional to the object’s speed. Inany event, energy must be transferred fromthe vibrating system to overcome the resis-tance.

Where damping is an asset (as in bring-ing a meter pointer to rest), the optimumsituation occurs when the motion comes tozero in the shortest time possible, withoutvibration. This is critical damping. If theresistive force is such that the time taken islonger than this, overdamping occurs,without vibrations. Conversely, under-damping involves a longer time with sev-eral vibrations of decreasing amplitude.

Daniell cell /dan-yĕl/ A type of primarycell consisting of two electrodes in differentelectrolytes separated by a porous parti-tion. The positive electrode is copper im-mersed in copper(II) sulfate solution. The

negative electrode is zinc-mercury amal-gam in either dilute sulfuric acid or zincsulfate solution. With sulfuric acid thee.m.f. is about 1.08 volts; with zinc sulfateit is about 1.11 volts. The porous partitionallows ions to move through while the re-action is taking place, and the cell must bedismantled when not in use.

At the copper electrode copper ions insolution gain electrons from the metal andare deposited as copper atoms:

Cu2+ + 2e– → CuThe copper electrode thus gains a posi-

tive charge. At the zinc electrode, zincatoms from the electrode lose electrons anddissolve into solution as zinc ions, leavinga net negative charge on the electrode:

Zn → 2e– + Zn2+

The cell is named for the British chemistJohn Frederic Daniell (1790–1845).

dark energy The energy associated withthe acceleration of the expansion of theUniverse. About three-quarters of the en-ergy of the Universe exists in the form ofdark energy. The existence of dark energycan be taken into account using a nonzerovalue for the cosmological constant but thenature of this energy is not understood atthe present time.

dark matter Invisible matter in the Uni-verse that has been postulated in order toexplain observations that cannot be ac-counted for in terms of detectable matter.The nature of dark matter is not known atthe present time but it has been suggestedthat it consists of a mixture of neutrinoswith nonzero masses (hot dark matter) andparticles postulated to exist in SUPERSYM-METRY (cold dark matter).

dating Methods of determining the age of

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D

daughter

60

archaeological or geological specimens, theEarth, meteorites, etc. The main methodsof special interest in physics involve mea-surements of radioactivity. It is assumedthat some radioactive nuclide is disappear-ing by decay and a product is formed. Mea-surements of the amount of parent nuclide,or product nuclide, or the ratio parent toproduct can give an estimate of the age incertain circumstances. See carbon dating;fission-track dating; potassium-argon dat-ing; rubidium-strontium dating; thermolu-minescent dating; uranium-lead dating.

daughter A given nuclide produced by ra-dioactive decay from another nuclide (theparent).

day The time taken for the Earth to makeone complete rotation on its axis. There arevarious methods of measuring this. Thesolar day is the time between two succes-sive transits of the Sun across the meridian.Its value is not constant owing to theEarth’s elliptical orbit. The mean solar dayis the average of these values over one year.Its value is 86.4 kiloseconds. The siderealday is measured with reference to a star. Itsvalue is 86.164 09 kiloseconds.

d.c. /dee-see/ See direct current.

deadbeat Describing an instrument (e.g. agalvanometer) that is damped so that itsoscillations die away very quickly. Seedamping.

dead room See anechoic chamber.

de Broglie wave /dĕ-broh-lyee/ See dual-ity.

debye /dĕ-bay-ĕ/ Symbol: D A unit of elec-tric dipole moment equal to 3.335 64 ×10–30 coulomb meter. It is used in express-ing the dipole moments of molecules. Theunit is named for the Dutch-born Ameri-can physicist and chemist Peter Debye(1884–1966).

Debye model A model for the specificheat of solids that was proposed by PeterDebye in 1912. Debye was able to give a

good description of the specific heat ofsolids, particularly at low temperatures, interms of the lattice vibrations of a solidhaving a distribution of frequencies up to amaximum cut-off frequency.

deca- Symbol: da A prefix denoting 10.For example, 1 decameter (dam) = 10 me-ters (m).

decay The spontaneous disintegration ofunstable (radioactive) nuclei to give othernuclei, accompanied by the emission ofparticles and/or photons. The product of agiven decay may be stable or may itself beradioactive. In a sample of radioactive ma-terial the radioactivity falls with time; theactivity is proportional to the amount ofsubstance present.

Decay follows an exponential law. Atany time t the number (N) of original nu-clei present is given by:

N = N0exp –γtwhere N0 is the original number and γ is aconstant (the decay constant or disintegra-tion constant) for a given nuclide. γ is re-lated to the half-life by:

T = 0.693 15 γ

decay constant See decay.

deci- Symbol: d A prefix denoting 10–1.For example, 1 decimeter (dm) = 10–1

meter (m).

decibel /des-ă-bel/ Symbol: dB A unit ofrelative difference in power or intensitylevel, usually of a sound wave or electricalsignal, measured on a logarithmic scale.The threshold of hearing is taken as 0 dB insound measurement. Ten times this powerlevel is 10 dB. The fundamental unit is thebel, but the decibel is almost exclusivelyused (1 db = 0.1 bel).

A power P has a power level in decibelsgiven by:

10 log10(P/P0)where P0 is the reference power.

declination Symbol: ε The angle betweenthe geographic and magnetic meridians ata given point on the Earth’s surface. Al-lowance must be made for this when using

a compass to find geographical direction.At any point on the Earth’s surface the dec-lination changes slowly with time.

See also Earth’s magnetism; magneticvariation.

defect An irregularity in the orderedarrangement of particles in a crystal lattice.There are two main types of defect in crys-tals. Point defects occur at single latticepoints. A vacancy is a missing atom; i.e. avacant lattice point. Vacancies are some-times called Schottky defects (named forthe Swiss–German physicist Walter Schot-tky (1886–1976)). An interstitial is anatom that is in a position that is not a nor-mal lattice point. If an atom moves off itslattice point to an interstitial position theresult (vacancy plus interstitial) is a Frenkeldefect (named for the Russian mathemati-cal physicist Jacov Ill’ich Frenkel(1894–1952)). All solids above absolutezero have a number of point defects, theconcentration of defects depending on thetemperature. Point defects can also be pro-duced by strain or by irradiation. Disloca-tions (or line defects) are also produced bystrain in solids. They are irregularities ex-tending over a number of lattice pointsalong a line of atoms.

definition The sharpness of focus of animage. No image can be perfectly sharp be-cause of diffraction, even with a perfect op-tical system. See also resolving power.

deflection magnetometer See magne-tometer.

degaussing /dee-gow-sing/ The neutral-ization of an object’s magnetic field by theuse of an equal and opposite field. It is usedin color television sets to neutralize theEarth’s magnetic field – current-carryingcoils prevent the formation of color fringeson the image. A similar system is used toneutralize the magnetization of ships toprevent them from detonating magneticmines.

degeneracy pressure The pressure thatoccurs in systems with degenerate fermionsbecause of a combination of the Heisen-

berg uncertainty principle and the Pauli ex-clusion principle. It is degeneracy pressurethat prevents the gravitational collapse ofwhite dwarf stars or neutron stars to formblack holes. The degenerate fermions areelectrons in the case of a white dwarf andneutrons in the case of a neutron star.

degenerate Describing different quantumstates that have the same energy. For in-stance, the three p orbitals in an atom allhave the same energy but different valuesof the magnetic quantum number m. Dif-ferences in energy occur if a magnetic fieldis applied – the degeneracy is then said tobe ‘lifted’. The degeneracy of a system isclosely related to the symmetry of that sys-tem.

degradation The irreversible loss of en-ergy available to do work, with a conse-quent increase in entropy (in an isolatedsystem). For example, consecutive colli-sions can lead to loss of energy of motion.

degree 1. An interval on a scale of mea-surement, such as a temperature scale.2. A unit of plane angle; 1/360 of a com-plete turn.

degrees of freedom The independentways in which particles can take up energy.In a monatomic gas, such as helium orargon, the atoms have three translationaldegrees of freedom (corresponding to mo-tion in three mutually perpendicular direc-tions). The mean energy per atom for eachdegree of freedom is kT/2, where k is theBoltzmann constant; the mean energy peratom is thus 3kT/2.

A diatomic gas also has two rotationaldegrees of freedom (about two axes per-pendicular to the bond) and one vibra-tional degree. The rotations also eachcontribute kT/2 to the average energy. Thevibration contributes kT (kT/2 for kineticenergy and kT/2 for potential energy).Thus, the average energy per molecule fora diatomic molecule is 3kT/2 (translation)+ 2kT/2 (rotation) + kT (vibration) =7kT/2.

Linear triatomic molecules also havetwo significant rotational degrees of free-

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degrees of freedom

dom; non-linear molecules have three. Fornon-linear polyatomic molecules, the num-ber of vibrational degrees of freedom is 3N– 6, where N is the number of atoms in themolecule.

The molar energy of a gas is the averageenergy per molecule multiplied by the Avo-gadro constant. For a monatomic gas it is3RT/2, etc. See also phase space; specificthermal capacity.

demagnetization /dee-mag-nĕ-ti-zay-shŏn/ The removal of the magnetic field ofa magnet. In demagnetization, the domainsare disordered so that they lie in a randompattern. This can occur as a result of roughtreatment, or by raising the tempeature ofthe specimen and allowing it to cool whilelying in an East-West direction. The mostefficient method is to place the specimen ina coil through which is passed an alternat-ing current. The current is then reduced tozero, removing the magnetism. A similareffect is obtained by taking the specimenout of a coil carrying an alternating cur-rent.

demodulation /dee-moj-ŭ-lay-shŏn/ (de-tection) The process in which the originalmodulating signal is reproduced in its orig-inal form from a modulated carrier waveby a radio circuit. See also detector; modu-lation.

dendrite /den-drÿt/ A branching crystalwith a tree-like structure.

densitometer /den-să-tom-ĕ-ter/ An in-strument for measuring the density of ex-posure of a photographic emulsion.Densitometers have a light source and pho-tocell to measure the transmission (or re-flection) of the sample. They are used inobtaining quantitative measurements fromphotographic records of spectra, diffrac-tion experiments, etc.

density 1. Symbol: ρ The mass of a sub-stance per unit volume. This is also knownas mass density. The units are kg m–3.2. Symbol: ρL The mass of a material perunit length. It is known as linear density.

3. Symbol: ρA The mass of a material perunit area. It is known as area density.4. See relative density.5. See charge density.

depletion layer A region near the p–njunction of a semiconductor diode inwhich the density of electric charge carriersis lower than in the bulk of the p and nparts of the semiconductor. A depletionlayer is about 10–3 mm thick.

depolarizer A substance used in a voltaiccell to prevent polarization. Hydrogenbubbles forming on the electrode can be re-moved by an oxidizing agent, such as man-ganese(IV) oxide. See also polarization(electrolytic).

depression of freezing point The reduc-tion in the freezing point of a liquid (sol-vent) when a substance (solute) is dissolvedin it. The depression of freezing point isproportional to the concentration of thesolute, for dilute solutions and non-volatilesolvents at constant pressure.

depth of field (depth of focus) The objectdistance range of an optical system (e.g. acamera) that gives acceptably sharp im-ages. The smaller the aperture, the greaterthe depth of field.

depth of focus See depth of field.

derivative See differentiation.

derived unit A unit defined in terms ofBASE UNITS, and not directly from a stan-dard value of the quantity it measures. Forexample, the newton is a unit of force de-fined as a kilogram meter second–2

(kg m s–2). See also SI units

desorption /di-sorp-shŏn, -zorp-/ The re-verse of adsorption. See adsorption.

destructive interference See interfer-ence.

detector 1. (demodulator) An electroniccircuit for extracting the original modulat-

demagnetization

62

ing signal from a carrier wave. See alsomodulation.2. A device that responds to any physicaleffect, used to indicate the presence of asignal or to measure it. An example is anantenna inducing a voltage at the fre-quency of a received radio wave.

determinism The idea that knowing theexact state of a system and the law govern-ing its change enables the state of that sys-tem to be calculated exactly for any futuretime. In principle, Newtonian mechanics isa deterministic system but in practice thesensitivity to initial conditions characteris-tic of chaotic systems undermines the pre-dictability of most systems described byNewtonian mechanics. In addition, deter-minism is also undermined by the Heisen-berg uncertainty principle of quantummechanics.

deuterated /dew-ter-ay-tid/ See deu-terium.

deuterium /dew-teer-ee-ŭm/ Symbol: D,2H A naturally occurring stable isotope ofhydrogen in which the nucleus containsone proton and one neutron. The atomicmass is thus approximately twice that of1H; deuterium is known as ‘heavy hydro-gen’. Chemically it behaves almost identi-cally to hydrogen, forming analogouscompounds, although reactions of deu-terium compounds are often slower thanthose of the corresponding 1H compounds.Its physical properties differ slightly fromthe properties of 1H. Deuterium oxide,D2O, is called ‘heavy water’; it is used as amoderator and coolant in some types ofnuclear reactor. Chemical compounds inwhich deuterium atoms replace the usual1H atoms are said to be deuterated.

The natural abundance of deuterium issomewhat below 0.015% but this variesslightly with source.

deuteron /dew-ter-on/ A nucleus of a deu-terium atom; i.e. a combination of a protonand a neutron.

deviation The turning of a ray during re-flection or refraction. The angle of devia-

tion is the angle through which the ray’s di-rection changes – an undeviated ray haszero angle of deviation. In the case of a re-flecting surface, the angle of deviation (d)can vary between almost zero and 180°. Arefracting surface can produce values of dbetween zero and the complement of thecritical angle (180° – c), where c is the crit-ical angle. The angle of deviation producedby a prism varies with the angle of inci-dence and has a minimum value (D) whenthe ray passes symmetrically through theprism. D is related to the prism’s refractiveconstant (n) and its angle (A):

n = sin[(A + D)/2]/sin(A/2)This equation can be used for finding

the refractive constant of the material ofthe prism using a spectrometer to measureD.

dew Water droplets that condense fromair onto a cooler surface, such as may hap-pen outdoors at night. After dark, a leaf,for example, will radiate and becomecooler. If it is surrounded by calm warmmoist air, condensation will occur, just asit does on a cold window pane in a rela-tively warm humid room. If the surfacetemperature is below the freezing tempera-ture of water, the condensation will be ashoarfrost. See also relative humidity.

Dewar flask /dew-er/ (vacuum flask) Adouble-walled container of thin glass withthe space between the walls evacuated andsealed to stop conduction and convectionof energy through it. The glass is often sil-vered to reduce radiation. The flask isnamed for the Scottish scientist Sir JamesDewar (1842–1923).

dew temperature (point) See relativehumidity.

dextrorotatory /deks-troh-roh-tă-tor-ee, -toh-ree/ See optical activity.

dialysis /dÿ-al-ă-sis/ (pl. dialyses) Amethod of separating a COLLOID from aCRYSTALLOID using a semipermeable mem-brane. The membrane allows the passageof small crystalloid molecules but does not

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allow large colloid molecules to diffusethrough. See electrodialysis.

diamagnetism /dÿ-ă-mag-nĕ-tiz-ăm/ Themagnetic behavior of substances (e.g. bis-muth and lead) with a negative susceptibil-ity. The relative permeability is less thanone. Usually the value of susceptibility issmall for diamagnetic substances and rela-tive permeability is slightly less than one.Diamagnetism results from the motion ofelectrons in atoms; under the influence ofan applied field these change so as to op-pose the field. The magnetization of a dia-magnetic material is thus opposite to thatof a paramagnetic or ferromagnetic mater-ial. If a bar of a diamagnetic substance isplaced in a non-uniform field it settles withits axis perpendicular to the field.

Diamagnetism is a weaker effect thanparamagnetism or ferromagnetism. It isshown by all substances and is independentof temperature, although in some materialsit is masked by other types of magnetic be-havior. See also magnetism.

diaphragm /dÿ-ă-fram/ 1. A device usedin optical instruments to reduce or controlthe aperture of the system. An iris di-aphragm is a variable aperture made up ofa number of movable overlapping plates.Diaphragms (or stops) are used to controlthe light admitted. They are also employedto reduce aberration in lens and mirror sys-tems by restricting the light to the regionclose to the axis of the system. See alsoaberration.2. A thin sheet of metal or plastic that vi-brates to produce, or is vibrated by, soundwaves, as in a loudspeaker or some types ofmicrophone.

diascope /dÿ-ă-skohp/ An optical projec-tor for translucent objects (e.g. slides). Thename is rather old-fashioned.

diatomic /dÿ-ă-tom-ik/ Describing a mol-ecule that consists of two atoms. Hydrogen(H2), oxygen (O2), nitrogen (N2), and car-bon monoxide (CO) are examples of di-atomic gases.

diatonic scale /dÿ-ă-tonn-ik/ A musicalscale in which notes are arranged ingroups, with notes in a group lying be-tween two limits that differ in pitch by anoctave, where an octave is defined as beingan interval between two correspondingnotes in successive groups in which the fre-quencies of the notes have the ratio 2:1.The diatonic scale is used extensively in Eu-ropean music.

dichroic medium /dÿ-kroh-ik/ A birefrin-gent material in which radiation polarizedin one plane is freely transmitted, but radi-ation polarized perpendicular to this is ab-sorbed. Tourmaline is a natural mineralwith this property; Polaroid is a syntheticdichroic substance.

dielectric /dÿ-i-lek-trik/ A nonconductorof electricity. The name is usually usedwhere electric fields are possible, as withthe insulating material between the platesof a capacitor. See also relative permittiv-ity.

dielectric constant An early term for rel-ative permittivity.

dielectric heating The heating effectcaused by the rapid alternation of the elec-tric field across an insulator (dielectric) (aswith the material between the plates of acapacitor in an a.c. circuit). The effect isused as a heating technique for certain ma-terials. The loss of useful energy that re-sults is dielectric loss.

dielectric loss See dielectric heating.

dielectric strength The maximum elec-tric field strength that a dielectric can with-stand without causing it to break downand pass a spark discharge. It is usuallymeasured in kilovolts per meter.

differential equation An equation thatcontains derivatives. An example of a sim-ple differential equation is:

dy/dx + 4x + 6 = 0To solve such equations it is necessary touse integration. The equation above can berearranged to give:

diamagnetism

64

dy = –(4x + 6)dxintegrating both sides:

∫dy = ∫–(4x + 6)dxwhich gives:

y = –2x2 – 6x + Cwhere C is a constant of integration. Thevalue of C can be found if particular valuesof x and y are known: for example, if y = 1when x = 0 then C = 1, and the full solutionis

y = –2x2 – 6x + 1Note that the solution to a differentialequation is itself an equation. Differentiat-ing the solution gives the original equation.Equations like that above, which containonly first derivatives (dy/dx) are said to befirst order, if they contain second deriva-tives they are second order; in general, theorder of a differential equation is the high-est derivative in the equation. The degreeof a differential equation is the highestpower of the highest order derivative.

The differential equation in the exam-ple given is a first order and first degreeequation. Differential equations are usedextensively in all branches of physics.

differentiation /dif-ĕ-ren-shee-ay-shŏn/ Aprocess for finding the rate at which onevariable quantity changes with respect toanother. For example, a car might travelalong a road from position x1 to positionx2 in a time interval t1 to t2. Its averagespeed is (x2 – x1)/(t2 – t1), which can bewritten ∆x/∆t, where ∆x represents thechange in x in the time ∆t. However, thecar might accelerate or decelerate in this in-terval and it may be necessary to know thespeed at a particular instant, say t1. In thiscase the time interval ∆t is made infinitelysmall, i.e. t2 can be as close as necessary tot1. The limit of ∆x/∆t as ∆t approaches zerois the instantaneous velocity at t1. The re-sult of differentiation (i.e. the derivative) ofa function y = f(x) is written dy/dx or f′(x).On a graph of f(x), dy/dx at any point is theslope of the tangent to the curve y = f(x) atthat point. See also integration.

diffraction /di-frak-shŏn/ The effects ofan obstacle on passing radiation, makingthe shadow edge less sharp than expected.Some radiation bends round the obstacle

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diffraction

geometricshadow region

screen ‘shadow’on screen

inci

den

tra

dia

tio

n

Diffraction at a straight edge

inci

den

tra

dia

tio

nin

cid

ent

rad

iati

on

inci

den

tra

dia

tio

n

geometricshadow region

geometricshadow region

geometricshadow region

screen ‘shadow’on screen

screen ‘shadow’on screen

screen ‘shadow’on screen

Diffraction at a wide slit(width 5λ).

Diffraction at a narrow slit(width λ).

Diffraction at a slit(width 2½λ).

Diffraction at a slit (width 2½λ)

into the shadow region; in some parts ofthe non-shadow region the radiation is re-duced in intensity. Diffraction is observedwith all waves, particularly if the obstacleis comparable in size to the wavelength.Under these conditions, fringes (diffractionpatterns) are formed. See also Fraunhoferdiffraction; Fresnel diffraction.

diffraction grating The best gratings aremade of glass (for transmitted radiation) ormetal (for reflected radiation) with manythousand fine parallel grooves (lines) ruledon the surface with a diamond point. Forsome purposes cheap plastic casts of suchgratings are suitable. Interference betweenthe waves diffracted by the grooves causesmaxima of intensity in directions deter-mined by the wavelength, hence spectra areproduced.

Transmission gratings are used mainlyfor visible light. Generally reflection grat-ings are necessary for ultraviolet and in-frared. Using normal incidence on atransmission grating there is an undeviatedtransmitted beam (zero order) with spectraon each side. If d is the distance betweenthe centers of adjacent lines and λ is thewavelength, spectra are produced at angles±θ where

d sinθ = mλ (m = 1, 2, 3, etc.)The value of m is called the order of thespectrum. As sinθ cannot exceed 1 thenumber of orders of spectra is limited.

diffuse reflection See reflection.

diffuse refraction See refraction.

diffusion /di-fyoo-zhŏn/ 1. Movement ofa gas, liquid, or solid as a result of the ran-dom thermal motion of its particles (atomsor molecules). A drop of ink in water, forexample, will slowly spread throughoutthe liquid. Diffusion in solids occurs veryslowly at normal temperatures. See alsoGraham’s law.2. The random spreading out of a beam ofradiation on REFLECTION or transmission.Diffusion occurs when a beam of lightpasses through a translucent medium (e.g.wax or frosted glass) or is reflected by a

rough surface (e.g. paper or matt paint).See also refraction.

diffusion cloud chamber See cloudchamber.

diffusion pump (condensation pump;vacuum pump) A type of pump that canproduce a high vacuum. Mercury or oil atlow pressure diffuses through a small ori-fice and carries along in its flow moleculesof gas (air) from region already at low pres-sure (produced by a backing pump). Thediffused vapor and gas molecules condenseout on the cooled walls of the pump.

digital recording A technique for record-ing sound that does not actually recordsound directly but samples the pressure ofthe sound wave thousands of times per sec-ond and converts the values of the pres-sures found in this way into numbers.These numbers can be recorded, transmit-ted, and then turned back into sound.

dihedral /dÿ-hee-drăl/ Formed by or hav-ing two intersecting planes or sides. For ex-ample, the angle between two intersectingplane faces of a crystal is a dihedral angle.

dilatometer /dil-ă-tom-ĕ-ter/ An instru-ment for measuring thermal expansion.Depending on the type, it may measure lin-ear or cubic expansivity of a gas, liquid, orsolid. See also comparator; Regnault’s ap-paratus.

dimensional analysis A technique forchecking the validity of a solution to aproblem, a unit, or an equation in physics.

diffraction grating

66

source

rough surface

Diffusion of radiation

It depends on the fact that, once a unit sys-tem has been defined fully (as in SI), eachquantity can be expressed in terms of thebase quantities in only one way. Here thosebase quantities are called dimensions. Thetable shows, first, the three dimensionsused in mechanics, and, second, someother quantities in terms of these. For in-stance, the relationship between pressure,force, and area can be checked. Force di-vided by area has dimensions MLT–2/L2,i.e. dimensions ML–1T–2, as for pressure.

dimensions See dimensional analysis.

diode /dÿ-ohd/ An electronic device withtwo electrodes that exhibits rectifying ac-tion when a potential difference is applied.Current flows for one direction of the po-tential (the forward direction), but whenthe potential is reversed the current is nor-mally zero or very small. There are twoprincipal types of diode: 1. The semicon-ductor diode consists of a single p-n junc-tion. The current across the junctionincreases exponentially with voltage in theforward direction; in the reverse directionthere is only a very small (leakage) currentuntil breakdown occurs.2. The thermionic tube diode consists of aheated negative cathode emitting electrons(by thermionic tube emission) in a vacuumwith a positive anode, which accepts elec-trons when a positive potential is appliedto it. The emitted electrons form a ‘cloud’around the cathode, called the spacecharge. Since electrons repel each other

owing to their like charges, the spacecharge limits the current as the voltage isincreased. When the voltage is high enoughthe current reaches a maximum saturationvalue.

Some other types of SEMICONDUCTOR

diode are the light-emitting diode (LED),the tunnel diode, and the Zener diode. Seealso rectifier; thermionic tube.

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diode

DIMENSIONS AND UNITS OF SOME PHYSICAL QUANTITIES

Quantity Dimension Unit Normal unitmass [M] kg kglength [L] m mtime [T] s sarea [L2] m2 m2

volume [L3] m3 m3

density [ML–3] kg m–3 kg m–3

acceleration [LT–2] ms–2 ms–2

force [MLT–2] kg ms–2 Npressure [ML–1T–2] kg ms–2m–2 Pamomentum [MLT–1] kg ms–1 (N s)pulsatance [T–1] s–1 Hz

currentsaturation

space-chargelimitation

voltage

thermionic diode

Current-voltage characteristics of diodes

p n+ –

forward direction

voltage

+ forward direction

breakdown

current

– reverse direction

semiconductor diode

diopter /dÿ-op-ter/ Symbol: D The unit ofpower of a lens or mirror, equal to the rec-iprocal of the focal distance in meters. A 5D lens has a focal distance of 0.2 m; a di-verging mirror of focal distance 1250 mmhas a power of –0.8 D.

Power measures the ability of a reflec-tor, refracting surface, or lens to convergea parallel beam.

dip, angle of See inclination.

dip circle See inclinometer.

dipole /dÿ-pohl/ A pair of opposite electriccharges.

dipole antenna See half-wave antenna.

dipole moment Symbol: µ The productof the positive charge of a dipole and itsdistance from the negative charge (see di-pole). It is measured in coulomb meters (SIunits), though often expressed in debyes (1debye = 3.336 x 10–30 coulomb meter).

direct current (d.c.) Electric current inone direction only. Compare alternatingcurrent.

direct current electric motor An electricmotor that is run by direct current. Theelectric current flows round an armaturecoil which is connected to the source of thed.c. power, such as a battery, by a split-ringcommutator. Since the armature is in anexternal magnetic field, the field exerts acouple on the armature when currentflows. The commutator reverses the cur-rent direction when the motion of the sidesof the coil changes from up to down. Thismeans that the force in the armature is al-ways in the same direction, thus ensuringconstant rotation.

disappearing-filament pyrometer Seeoptical pyrometer.

discharge, electrical The passage of anelectric current through a gas at low pres-sure or a dielectric. It is usually accompa-nied by luminous effects. The gasmolecules become ionized and the recom-

bination of oppositely charged ions givesrise to the luminous effects.

See also canal rays; corona discharge;electric arc; electric spark; glow discharge;positive column.

discharge of a capacitor A process inwhich the electric charge in a capacitor isdischarged by forming a circuit consistingof the capacitor connected to a resistor.The mathematical description of thisprocess is analogous to that of radioactivedecay, with the decay of the charge beingexponential with time. See also time con-stant.

discharge tube A gas-filled or evacuatedglass tube with a pair of sealed-in elec-trodes. A high voltage causes an electricdischarge between the electrodes. An ex-ample is the familiar neon tube used foradvertising signs. See also Geissler tube.

discriminator /dis-krim-ă-nay-ter/ A cir-cuit that selects certain electrical signalsand rejects others, according to a particu-lar property of the signal, such as ampli-tude, frequency, or phase. For example, apulse-height analyzer selects signals havinga particular amplitude range, and a fre-quency discriminator picks out differentfrequencies.

disintegration The breaking up of unsta-ble nuclei into two or more fragments, ei-ther spontaneously or as a result ofbombardment by fast-moving particles.The disintegration of 7Li by proton bom-bardment in Cockcroft and Walton’s ex-periment is an example of the latter type;two 4He nuclei (alpha particles) are pro-duced.

disintegration constant See decay.

dislocation See defect.

disordered solid A solid that does nothave the order of a perfect crystal (or acrystal with a very small concentration ofimpurities or defects). There are severaltypes of disordered solids. In a randomalloy made up of two metals A and B the

diopter

68

pattern in which A and B occur is random.In a solid in which a crystal has a high con-centration of impurities, the random distri-bution of impurities in the solid givesanother type of disordered solid. In anamorphous solid (e.g. a glass) the atoms ofthe solid form a random network ratherthan a regular array.

dispersion During refraction, rays can bedeviated (changed in direction) by anglesrelated to the refractive index of themedium. However, the refractive constantof any medium varies with the wavelengthof the transmitted radiation. Thus, if a nar-row beam of radiation of mixed wave-lengths is deviated by refraction, the angleof deviation will vary with wavelength.This is called dispersion; the radiation isspread out. It can be used to produce thecolor spectrum of white light using a prism.It can also be a problem, causing chromaticaberration in lenses.

Dispersion is actually an effect in whichradiations having different wavelengthstravel at different speeds in the medium.Normally the refractive index increases asthe wavelength decreases, but there are re-gions, where the radiation is partially ab-sorbed, in which refractive index decreaseswith decreasing wavelength. See anom-alous dispersion.

dispersion forces See van der Waals’forces.

dispersive power Symbol: ω A measureof the variation for a medium of refractiveconstant n with wavelength λ. It is given bythe ratio:

ω = (nb – nr)/(ny – 1)Here, nb, nr, and ny are absolute refrac-

tive constants for blue, red, and yellowlight. More accurate values are obtained byusing three monochromatic spectral linesof known wavelength: F (blue), C (red),and D (yellow).

displacement Symbol: s The vector formof distance, measured in meters (m) and in-volving direction as well as magnitude.

dissipation The removal of energy from asystem to overcome some form of resistiveforce (mechanical or electrical). Withoutresistance (as in motion in a vacuum andthe current in a superconductor) there canbe no dissipation. Dissipated energy nor-mally appears as thermal energy.

distance Symbol: d The length of the pathbetween two points. The SI unit is themeter (m). Distance may or may not bemeasured in a straight line. It is a scalar;the vector form is displacement.

distance ratio (velocity ratio) For a MA-CHINE, the ratio of the distance moved bythe effort in a given time to the distancemoved by the load in the same time.

distillation A method of separating mix-tures of liquids or purifying liquids by heat-ing them to the boiling point, condensingthe vapor produced, and collecting the liq-uid or liquids that form.

distortion See aberration.

div See vector calculus.

divergent Moving apart. See convergent.

diverging lens A LENS that can refract aparallel beam into a divergent beam. Di-verging lenses used in air are thinner in themiddle than at the edge. They may be bi-concave, plano-concave, or concavo-con-vex in shape. As these lenses have negativepower, they are sometimes called negativelenses. Compare converging lens.

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diverging lens

N

4 m

7 m3 m

2 m

B

distance from A to B is 9 mdisplacement is 7 m ata bearing of N 73oE (073o)

A

Displacement and distance

diverging mirror (diverging reflector) AMIRROR that can reflect a parallel beaminto a divergent beam. Diverging reflectorsalways have convex surfaces. As these re-flectors have negative power, they aresometimes called negative mirrors. Com-pare converging mirror.

diverging reflector See diverging mirror.

D-layer See ionosphere.

domain A region inside a ferromagneticmaterial in which all the atomic magneticfields point the same way. When the mate-rial is unmagnetized, the directions of theseparate domains are random; when astrong external magnetic field is applied,the domains line up in the same direction.The domains with magnetic axes nearlyparallel to that of the magnetizing fieldgrow at the expense of those perpendicularto the field. The substance now has a resul-tant magnetic moment. The domains cangrow until the magnetic axes are in linewith the external field if this is strongenough. The material is then magneticallysaturated. The presence of magnetic do-mains can be shown by Bitter patterns, theBarkhausen effect, and by various othertechniques.

donor See semiconductor.

dopant /doh-pănt/ See semiconductor.

doping See semiconductor.

Doppler broadening /dop-ler/ The in-crease in the width of a spectral line as a re-sult of the motion of the particles emittingor absorbing the radiation. It is named forthe Austrian physicist Christian JohannDoppler (1803–53). See monochromaticradiation.

Doppler effect 1. An apparent change inthe frequency of a wave motion, caused byrelative motion between the source and theobserver. It is found with sound waves: asthe source and observer move together theapparent frequency of the sound is higherthan that produced; as they move apart it is

lower. An example is that of an approach-ing motorbike – the pitch of the enginesound appears to drop suddenly as itpasses.

The apparent frequency (f′) of sound asa result of relative motion between sourceand observer in a direct line is given by:

f′ = (V + Uo)f/(V – Us)where V is the speed of sound, Uo the ob-server’s velocity, Us the source velocity,and f the source frequency.2. A similar effect for electromagnetic radi-ation. The radiation emitted by a sourcewith a motion component towards the ob-server will have increased frequency: if thesource is moving away from the observer,the observed frequency is reduced. This hasgreat significance in astronomy. Thus theDoppler effect on radar pulses reflected bythe planets gives information on their rota-tion. The displacement of lines in the spec-tra of stars and galaxies (i.e. the red shift orthe blue shift) can tell the astronomer howthese bodies are moving.

For electromagnetic radiation the the-ory of the effect is not the same as forsound. This is because there is no fixedmedium to give a frame of reference. Rela-tivity theory gives the following result:

v = v0√[(1 – v/c)/(1 + v/c)]Here v is the observed frequency, v0 is

the emitted frequency; v is the speed of sep-aration of source and observer, related tothe speed of light c. If v is small comparedto c the expression simplifies to:

v = v0(1 – v/c)

Doppler shift See red shift.

dose The amount of energy from ionizingradiation absorbed by unit mass of mater-ial. The SI unit of absorbed dose is thegray. When considering effects on livingorganisms, the dose in grays is multipliedby a factor expressing the relative effective-ness of the radiation to obtain the doseequivalent which in SI units is expressed insieverts. For example, alpha rays causeabout twenty times as much biologicaldamage as do beta rays of the same energy.

All persons are exposed to ionizing ra-diation derived mostly from naturalcauses, such as cosmic rays, radioactivity

diverging mirror

70

in the environment, and radioactivity inthe body itself. Additional radioactivity iscaused by nuclear explosions and accidentsand by the use of luminous paints. Some in-dividuals receive additional doses in med-ical examination or treatment, or fromworking with x-radiation or radioactivesubstances. Persons employed in the nu-clear industry or as radiologists or radiog-raphers are protected by a statutory codethat defines working conditions and setslegal limits to the dose equivalent allow-able. National codes are based on the rul-ings of the International Commission onRadiological Protection. Exposure to ion-izing radiation can cause harm (particu-larly cancer) to the exposed persons andgenetic changes, which may affect their de-scendants.

dosimeter /doh-sim-ĕ-ter/ An instrumentthat measures the amount of ionizing radi-ation received by a person or a region. Asimple type is the film badge, which isworn by personnel and developed daily(radiation fogs the film) to check on ab-sorbed dose.

dot product See scalar product.

double refraction See birefringent crys-tal.

double slit experiment See Young’sdouble slit.

doublet A compound lens with two ele-ments, often in contact. The purpose isusually to reduce aberrations. If the lensesare in contact, the power of the doublet isthe sum of the powers of the elements.Thus, P = P1 + P2or, 1/f = 1/f1 + 1/f2 (f is focal distance).A 5 diopter (D) lens combined with a –2.5D lens forms a doublet of power 2.5 D, orfocal distance 400 mm.

drag A force exerted by a fluid (gas or liq-uid) on an object in its flow. It acts in thedirection of the flow and therefore tends toresist the motion of the object through thefluid.

drain See field-effect transistor.

drift velocity The average velocity of anelectron through a conductor when a cur-rent is flowing. If there are n electrons perunit volume, the cross-sectional area of thewire is A, V is the average speed of an elec-tron passing through a conductor, and e isthe charge of an electron, then the currentI is given by I = nAVe.

dry cell A voltaic cell in which the elec-trolyte is in the form of a jelly or paste. Drycells are used for flashlights and otherportable appliances. See also Leclanchécell.

duality Wave-particle duality: the conceptthat some entities show both wave and par-ticle properties. There are two cases. 1.Electromagnetic radiation. Einstein (1905)argued that, whereas the propagation ofthese radiations is fully described by thetheory of electromagnetic waves, interac-tion with matter occurs as if the radiationtravels in packets (photons) each with aquantum of energy hν, where h is thePlanck constant and ν is the frequency ofthe wave. His examples were the Planck ra-diation law, photoelectric emission, andphotoionization of gases. The principle hasbeen verified for radiations of all wave-lengths from microwaves to gamma rays,in many different phenomena involvingemission, absorption or scattering.Whereas such wave properties as fre-quency, phase speed, and electric and mag-netic fields are measurable quantities,photons are only observable when beingcreated or destroyed.2. Particle waves. In 1923 de Broglie sug-gested that atomic particles might havewave-like properties and that the wave-length (λ) would have the same relation-ship to the momentum (p) as applies toelectromagnetic radiation: λ = h/p. Thisconcept has been used very successfully inthe form of quantum theory called wavemechanics. Beams of particles includingelectrons, neutrons, and gas molecules inci-dent on crystals form diffraction patternsanalogous to those given by x-rays. Thewavelength formula is fully verified.

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duality

See also wave theory of light.

dubnium /dub-nee-ŭm/ A radioactive syn-thetic element made by bombarding 249Cfnuclei with 15N atoms. It was first reportedby workers at Dubna, a town nearMoscow.

Symbol: Db; p.n. 105; most stable iso-tope 262Db (half-life 34 s).

ductility /duk-til-ă-tee/ The property of ametal that allows it to be drawn out intowire. Compare malleability.

Dulong and Petit’s law /doo-long ănd pĕ-teez / The molar thermal capacity of a solidelement is approximately equal to 3R,where R is the gas constant (25 J k–1

mol–1). The law applies only to elementswith simple crystal structures at normaltemperatures. At lower temperatures themolar heat capacity falls with decreasingtemperature (it is proportional to T3).Molar thermal capacity was formerlycalled atomic heat – the product of theatomic weight (relative atomic mass) andspecific thermal capacity. The law isnamed for the French physicists Pierre-Louis Dulong (1785–1838) and Alexis-Thérèse Petit (1791–1820).

dynamic equilibrium See equilibrium.

dynamics The study of how objects moveunder the action of forces. This includesthe relation between force and motion and

the description of motion itself. See equa-tions of motion; Newton’s laws of motion.

dynamo A small device for convertingmechanical energy into electrical energy.The motion of a coil rotating in a magneticfield induces an alternating current in thewindings. This current itself causes a turn-ing force opposing the initial motion. Tokeep the dynamo turning, an energy inputis required from an external source, such asa gasoline or diesel motor. Many bicycleshave a small dynamo built into the hub ofthe wheel (or driven by the tire) to powerthe cycle lamps.

See also generator.

dynamometer /dÿ-nă-mom-ĕ-ter/ An ap-paratus for measuring force, usually theoutput power (brake horsepower) of an en-gine or motor.

dyne /dÿn/ Symbol: dyn The former unitof force used in the c.g.s system. It is equalto 10–5 N.

dysprosium /dis-proh-see-ŭm, -shee-ŭm/A soft malleable silvery element of the lan-thanoid series of metals. It occurs in asso-ciation with other lanthanoids. One of itsfew uses is as a neutron absorber in nuclearreactors; it is also a constituent of certainmagnetic alloys.

Symbol: Dy; m.p. 1412°C; b.p.22562°C; r.d. 8.55 (20°C); p.n. 66; r.a.m.162.50.

dubnium

72

ear The organ used to hear sounds. It is di-vided into three parts: the outer ear, themiddle ear, and the inner ear. Sound wavescause the ear-drum, in the outer ear, to vi-brate. The middle ear transfers the energyof sound waves into the inner ear. The re-ceptors for hearing are in the inner ear.

early Universe The era in the evolutionof the Universe soon after the BIG BANG

when it was very hot and dense. As theUniverse expanded it cooled, giving rise toa sequence of phase transitions associatedwith broken symmetries. The light ele-ments such as helium were mostly formedin the early Universe. It has been suggestedthat in the early Universe inflation, i.e. veryrapid expansion, occurred. The very earlyUniverse, occurring immediately after thebig bang, requires a fundamentally newphysics involving the combination of quan-tum mechanics and general relativity the-ory before it will be understood.

Earnshaw’s theorem /ern-shaw/ Theprinciple that in a system of bodies inwhich the interactions between the bodiesare described by an inverse square law,such as Newton’s law of gravitation orCoulomb’s law of electrostatics, the bodiescannot be in a stable static equilibriumstate. This result means that the planets ina planetary system such as the Solar Systemand the electrons in an atom cannot be sta-tionary. The law was found by the Rev-erend Samuel Earnshaw (1805–88) in1842.

Earth inductor A type of fluxmeter formeasuring large uniform fields (normallythat of the Earth). A large coil of knownarea and number of turns is flipped

through 180° and the induced e.m.f. ismeasured using a ballistic galvanometer.

earthing See grounding.

Earth’s magnetism (geomagnetism) Amagnetic field can be observed at any pointon or near the Earth’s surface. This field israther like that which would be obtained ifa giant bar magnet were present inside theplanet; it is closer to the field of a magne-tized steel sphere. A magnetic compass canbe used to show the direction of the field –of great importance in navigation. TheEarth’s north magnetic pole is currently offthe northern coast of Canada; the southmagnetic pole is on the edge of Antarctica.The strength and direction of the Earth’sfield at any point are defined in terms ofthree magnetic elements – the inclination,the declination, and the horizontal compo-nent of the field strength. These elementsare not constant. The source of the Earth’sfield is thought to be due to electric cur-rents circulating in the molten nickel-ironcore. See magnetic variation.

echelon /esh-ĕ-lon/ A type of diffractiongrating consisting of a number of equalthin glass sheets stacked on a slant. In usethe light is reflected from the stepped sideof the stack; d in the grating equation isvery large, so that very high spectral ordersare possible.

echo The result of reflection of soundwaves (or other waves), usually by a hardsurface. This causes an observer to detecttwo signals; the first a direct signal and thesecond a fainter reflected signal. The delaybetween the two indicates the distance ofthe reflector.

73

E

echolocation

74

echolocation /ek-oh-loh-kay-shŏn/ Amethod of finding the range and bearing ofsomething (the ‘target’) by transmittinghigh-frequency sounds and detecting theirechoes on their return. See sonar.

echo sounder See sonar.

eclipse The ‘hiding’ of one heavenly bodybehind another. The eclipsed object, theeclipsing object, and the observer are in astraight line.

In a solar eclipse, the Moon appears topass across the Sun, so that the Moon’sshadow sweeps over the Earth’s surface. Ifthe Moon appears to cover the Sun com-pletely, there is a total eclipse of the Sun –the observer is in the umbra of the Moon’sshadow. If the Moon only partly covers theSun, there is a partial eclipse – the observeris in the penumbra of the shadow. Solareclipses can happen only at New Moon;the Moon’s shadow is narrow, so totaleclipses of the Sun are rare at any one placeon the Earth. It is a coincidence that Sunand Moon appear to be of similar size fromthe Earth. However as neither theEarth–Moon distance nor the Sun–Earthdistance is constant, the sizes of Sun andMoon seen from the Earth do vary. Some-times there is an annular eclipse, when theMoon is not ‘big’ enough to cover the Sun’sdisk. Then the vertex of the lunar umbradoes not reach the Earth’s surface.

As the Earth’s shadow is larger than theMoon’s, lunar eclipses are more commonlyseeen than solar eclipses. Lunar eclipsescan occur only at Full Moon, when theEarth’s shadow sweeps the Moon’s sur-face. They also last longer than solareclipses, as Earth and Moon are now mov-ing in the same direction through space.Another big difference is that lunar eclipsesdo not clearly show umbra and penumbra.This is because sunlight is refracted into theumbra cone by the Earth’s atmosphere,acting as a ring-shaped lens. This refrac-tion also explains the reddish color of theMoon during eclipse.

eddy-current heating See inductionheating.

eddy currents Induced currents set up ina conductor by a changing magnetic field.They occur in transformers and other elec-trical devices. The currents produce a heat-ing effect corresponding to a loss of usefulenergy (eddy-current loss). Metal cores inelectrical machines are usually laminated(built of thin sheets) to reduce such losses;the surface layers between the laminationshave high electrical resistance.

One useful application of eddy currentsis in damping moving-coil instruments –the coil is wound on a piece of soft iron.When the coil moves in the instrument’smagnetic field, eddy currents are inducedin the iron so as to oppose the motion,causing the coil to settle quickly. As Lenz’slaw would predict, eddy currents alwaysflow so as to oppose the effect producingthem.

Edison cell See nickel-iron accumulator.

effective resistance The resistance ofpart of an electric circuit in which there isan alternating current. It is the power dissi-pated divided by the square of the current.If power is in watts and current in amperes,the units are then ohms. Effective resis-tance expresses a combination of two ef-fects: the resistance from scattering ofelectrons by lattice atoms (as for d.c.) andthe resistance from the magnetic effects ofthe changing current.

effective value See root-mean-squarevalue.

efficiency Symbol: η The ratio of thework done by a system or device to the en-ergy input. Similarly, the efficiency is equalto the useful power output divided by thepower input. There is no unit; however ef-ficiency is often quoted as a percentage.There are several branches of physics inwhich efficiency is used.1. For MACHINES the efficiency is the forceratio divided by the distance ratio.2. For an electric cell delivering currentthrough a load resistance (R), the efficiencyis given by η = R/(R + r), where r is the in-ternal resistance of the cell. Note that the

higher the value of R, the higher the effi-ciency.3. For an electric motor, the efficiency isthe mechanical power developed dividedby the electrical power input.4. For a heat engine, the efficiency is thework done divided by the heat input. SeeCarnot cycle.

effort The force that moves a load in asimple machine such as a lever or pulley.The ratio of the load to the effort is theforce ratio.

effusion The flow of gas moleculesthrough relatively large holes.

EHF See extremely high frequency.

einsteinium /ÿn-stÿ-nee-ŭm/ A radioac-tive transuranic element of the actinoid se-ries, not found naturally on Earth. It can beproduced in milligram quantities by bom-barding 239Pu with neutrons to give 253Es(half-life 20.47 days). Several other short-lived isotopes have been synthesized.

Symbol: Es; m.p. 860 ± 30°C; p.n. 99;most stable isotope 254Es (half-life 276days). The element is named for the Ger-man–Swiss–American theoretical physicistAlbert Einstein (1879–1955).

Einstein model A model for the specificheat of solids that was proposed by AlbertEinstein in 1907, in which it was assumedthat the specific heat is due to the vibra-tions of the atoms of the solid, with thesevibrations all having the same frequency.This model gives rough qualitative agree-ment with experiment, but not quantitativeagreement at low temperatures. An im-provement that gives much better agree-ment with experiment is the DEBYE MODEL.

Einstein–Podolsky–Rosen experiment/ÿn-stÿn pŏ-dol-skee roh-zĕn/ See Bell’sparadox.

Einstein’s equation See photoelectric ef-fect.

Einstein’s field equation An equationput forward by Albert Einstein

(1879–1955) in 1915 as the fundamentalequation of general RELATIVITY theory. Itgeneralizes Newton’s theory of gravity byrelating mass (energy) to the curvature ofspace–time.

Einstein shift See red shift.

elastance /i-las-tăns/ The reciprocal of ca-pacitance. It is measured in reciprocalfarads (F–1).

elastic collision A collision for which therestitution coefficient is equal to one. Ki-netic energy is conserved during an elasticcollision. See also restitution; coefficientof.

elasticity /i-las-tis-ă-tee/ The tendency ofa material to return to its original dimen-sions after a deforming stress has been re-moved. Up to a certain point (theproportional limit) the material obeysHooke’s law. The strain produced is pro-portional to the stress and the sample re-turns to its original dimensions if the stressis removed. Above the proportional limitthe material no longer obeys Hooke’s law,i.e. stress is not directly proportional tostrain. At slightly higher stresses the elasticlimit is reached. Above this the sample nolonger returns to its original dimensionsafter the stress is removed; i.e. a permanentdeformation occurs. The yield point is thepoint at which the material begins to ‘flow’– i.e. the strain increases with time (up tothe breaking point) without further in-crease in the stress.

elastic limit See elasticity.

elastic modulus The ratio of the stress ona body to the STRAIN produced. There arevarious moduli of elasticity depending onthe type of STRESS applied. The Youngmodulus (symbol: E) refers to tensile orcompressive stress when the cross-sectionis free to change. It is the force per unitcross-sectional area divided by the frac-tional elongation of the sample. The axialmodulus refers to tensile or compressivestress when constraints prevent change inthe cross-section. The bulk modulus (sym-

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elastic modulus

bol: K) is used for a bulk stress – i.e. pres-sure changes on the body. It is minus thepressure change divided by the fractionalchange in volume. The shear modulus (orrigidity modulus) (symbol: G) refers to ashearing (or twisting) stress. It is the tan-gential force per unit area divided by theangular deformation. Elastic moduli havethe same units as stress (newtons persquare meter). See also elasticity; Poissonratio.

elastomer /i-las-tom-ĕ-ter/ A substancethat is elastic – that is, it returns to its orig-inal shape when a deforming stress is re-moved. See elasticity.

E-layer See Heaviside layer.

electret /i-lek-trit/ A piece of permanentlyelectrified material, having a positivecharge at one end and a negative charge atthe other.

electrical energy Energy resulting fromthe position of an electric charge in an elec-tric field.

electrical storm A storm associated withthe separation of electric charge in clouds.When the resulting electric field is strongenough a flash of lightning occurs, fol-lowed by thunder.

electric arc A luminous continuous elec-trical discharge between two electrodes ina gas, having high current density and lowpotential difference. The electrodes areraised to high temperatures causingthermionic emission, which maintains thecurrent. Often there is sufficient evapora-tion of electrode material for its emissionspectrum to be prominent in the light. Thisarc spectrum does not include some of thelines produced by high-voltage discharges.Arcs can be used as sources in spectro-graphic studies. The heating effect of arcs isused in arc welding. Arcs, particularly be-tween carbon electrodes, are also used ashigh-intensity light sources called arclamps, which are used for example insearchlights.

electric bell A device in which a bell isstruck by a hammer whose movement isproduced by an electromagnet. In a direct-current (battery-operated) bell, the electro-magnet consists of two coils wound on twocores connected by an iron yoke. When thebutton is pressed to close the circuit, thecoils are energized and attract an iron bar(armature). The armature movementbreaks the circuit, the coil de-energizesagain, and the armature moves back (by aspring) and closes (‘makes’) the circuitagain, and so on, as long as the switch isclosed. An alternating-current bell does nothave this type of make-and-break contact.The armature is a permanent magnet,which is alternately attracted and repelledby the reversing poles of an electromagnetthrough which the alternating currentpasses.

electric charge See charge.

electric constant See permittivity.

electric current See current.

electric displacement Symbol: D Theelectric flux density in a dielectric material:

D = εrε0Ewhere E is the electric field strength in freespace and εrε0 the permittivity of the mat-erial.

electric field A region in which a forcewould be exerted on an electric charge.Like magnetic fields, electric fields can berepresented by lines of force. The electricfield is completely defined in magnitudeand direction at any point by the forceupon a unit positive charge situated at thatpoint. Electric fields can be produced byelectric charges or by changing magneticfields.

electric field strength (electric intensity)Symbol: E A measure of the strength of anelectric field at a point, defined as the forceper unit charge on an electric charge placedat that point: i.e. E = F/Q. The electric fieldstrength is the gradient of the electrical po-tential at a point (–dV/dr); the unit used isthe volt per meter (V m–1).

elastomer

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electric flux Symbol: Ψ A measure of anelectric field in a vacuum or in a dielectric.The flux in a field can be represented by thenumber of lines of electric force through agiven perpendicular area. The electric fluxdensity at a point is the number per unitarea at that point. Electric flux density isrelated to electric displacement.

electric image A method of solving elec-trostatic problems. A charge +Q a certaindistance from a conducting surface acts asif there were an ‘image’ of the charge ofmagnitude –Q positioned on the oppositeside of the surface. For a plane conductorthe image is as far behind the surface as thecharge is in front.

electric intensity See electric fieldstrength.

electricity The nature and effects of mov-ing or stationary electric charges, and thebranch of physics that studies them.

electric meter (watt-hour meter) An in-strument that measures electrical energyconsumption in watt-hours.

electric motor An electrical machine suchthat an electric current drives the motor en-abling it to do work mechanically. Currentpassed through a coil forms an electromag-net, which causes the coil (or rotor) to ro-tate in the magnetic field of a permanentmagnet or another electromagnet. The ro-tation causes a back e.m.f. in the coil,which restricts the amount of electricalwork done. When the motor is doing ex-ternal mechanical work the magnitude andphase of the back e.m.f. changes corre-spondingly, affecting the work done by theelectric power source. Electric motors canbe designed to work with direct-currentsupply, or, more commonly, with alternat-ing current. See also induction motor; syn-chronous motor.

electric polarization See polarization.

electric potential Symbol: V The poten-tial at a point in an electric field is the en-ergy required to bring unit electric charge

from infinity to the point. The unit of elec-tric potential is the volt, V. See also poten-tial difference.

electric power See power.

electric spark A discharge of electricity ina gas accompanied by light and sound. Thedischarge occurs between two points of op-posite high electric potentials.

The spark can only occur when the po-tential difference exceeds a certain value,called the sparking potential. The suddenexpansion and then contraction of the gasafter it has been heated by the spark givesrise to the characteristic clicking sound.

electrochemical equivalent /i-lek-trŏ-kem-ă-kăl/ Symbol: z The mass of an ele-ment released from a solution of its ionswhen a current of one ampere flows forone second during electrolysis.

electrochemical series See electromotiveseries.

electrochemistry /i-lek-trŏ-kem-iss-tree/The study of the formation and behavior ofions in solutions. It includes electrolysisand the generation of electricity by chemi-cal reactions in cells.

electrode Any part of an electrical deviceor system that emits or collects electrons orother charge carriers. An electrode mayalso be used to deflect charged particles bythe action of the electrostatic field that itproduces.

electrodeless deposition A method ofcoating objects with a thin layer of metal(similar to electrodeposition) withoutusing an electric current. An example is thedeposition of a layer of silver on glass orplastic to make mirrors. The method relieson the choice of electrolyte and the chem-istry involved.

electrodeposition /i-lek-troh-dep-ŏ-zish-ŏn/ (electroplating) The process of de-positing a layer of solid (metal) on anelectrode by electrolysis. Positive ions insolution gain electrons at the cathode and

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electrodeposition

are deposited as atoms. Copper, for in-stance, can be deposited on a metal cath-ode from an acidified copper sulfatesolution.

electrode potential A measure of the ten-dency of a metal to lose electrons to a sur-rounding solution. It is the potentialdifference, at equilibrium, between themetal and a solution of its ions.

The electrode potential cannot be mea-sured directly and is usually comparedagainst that of a hydrogen electrode. Met-als that have a greater tendency than hy-drogen to form positive ions have apositive electrode potential. Electrode po-tentials are quoted as measured under stan-dard conditions. See also half cell.

electrodialysis /i-lek-troh-dÿ-al-ă-sis/ (pl.electrodialyses) A method of removingsalts (crystalloids) from a colloidal solutionusing two semipermeable membranes. Thesolution is placed between the membranes,which have on their other sides pure sol-vent containing electrodes with a voltageapplied between them. See colloid; dialysis.

electrodynamics /i-lek-troh-dÿ-nam-iks/The study of the relationship between me-chanical forces and magnetic and electricforces. Such effects are the basis of, for ex-ample, the electrical generator and the elec-tric motor. In contrast to ELECTROSTATICS,electrodynamics deals with moving electriccharges and the associated magnetic fields.

electroforming /i-lek-trŏ-for-ming/ Amethod of using ELECTRODEPOSITION tomake metal objects. A non-conductingmold of the object to be made (called amandrel) is made conducting by coating itwith graphite or by silvering, and the man-drel is used as the cathode in an electro-plating bath. Metal builds up on the moldand when it is thick enough, the mold is re-moved by melting it (if wax) or dissolvingit (if plastic).

electroluminescence /i-lek-troh-loo-mă-ness-ĕns/ See luminescence.

electrolysis /i-lek-trol-ă-sis/ The produc-tion of chemical change by passing chargethrough certain conducting liquids (elec-trolytes). The current is conducted by mi-gration of ions – positive ones (cations) tothe cathode (negative electrode), and nega-tive ones (anions) to the anode (positiveelectrode). Reactions take place at the elec-trodes by transfer of electrons to or fromthem.

In the electrolysis of water (containing asmall amount of acid to make it conductadequately) hydrogen gas is given off at thecathode and oxygen is evolved at theanode. At the cathode the reaction is:

H+ + e– → H2H → H2

At the anode:OH– → e– + OH

2OH → H2O + O2O → O2

In certain cases the electrode material maydissolve. For instance in the electrolysis ofcopper(II) sulfate solution with copperelectrodes, copper atoms of the anode dis-solve as copper ions

Cu → 2e– + Cu2+

See also Faraday’s laws (of electrolysis).

electrolyte /i-lek-trŏ-lÿt/ A liquid contain-ing positive and negative ions, that con-ducts electricity by the flow of thosecharges. Electrolytes can be solutions ofacids or metal salts (‘ionic compounds’),usually in water. Alternatively they may bemolten ionic compounds – again the ionscan move freely through the substance.Liquid metals (in which conduction is byfree electrons) are not classified as elec-trolytes. See also electrolysis.

electrolytic capacitor A type of capaci-tor consisting of two metal plates, one witha very thin oxide layer, immersed in a suit-able electrolyte. Electrolytic capacitorsprovide a high capacitance for a small size.It is important that they are always chargedup with the correct plates positive and neg-ative, otherwise the oxide film may breakdown.

electrode potential

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electrolytic cell See cell; electrolysis.

electrolytic separation The separationof isotopes by electrolysis. See isotope sep-aration.

electromagnet /i-lek-troh-mag-nĕt/ A coilof insulated wire wrapped around a core ofsoft iron. When there is a current in thewire, a magnetic field results; the core be-comes magnetized. The core loses its mag-netism when the current is switched off.Electromagnets are used in telephones,electric bells, relays, and many other de-vices. See also solenoid.

electromagnetic induction /i-lek-troh-mag-net-ik/ The induction of an electro-motive force (e.m.f.) between the ends of aconductor by change in relation to an ex-ternal magnetic field. The ‘laws of electro-magnetic induction’ follow:1. (Faraday) An electromotive force is in-duced in a conductor when there is achange in the magnetic field around it.2. (Faraday) The electromotive force in-duced is proportional to the rate of changeof the field.3. (Lenz) The direction of the induced elec-tromotive force tends to oppose thechange.Electromagnetic induction is used in gener-ators, transformers, microphones, andmany other devices. The effect can alsocause problems, as in the formation ofeddy currents.

The magnitude of the induced e.m.f. isproportional to the rate of change of totalflux linkage, Φ. This is called Neumann’s

law, named for the German physicist FranzNeumann (1798–1895). Thus,

E = –dΦ/dtwhere E is the e.m.f. in volts, Φ the fluxlinkage in webers, and t the time in sec-onds. The minus sign expresses Lenz’s law.

See also mutual induction; self-induc-tion.

electromagnetic interaction See interac-tion.

electromagnetic moment See magneticmoment.

electromagnetic pump A pump with nomoving parts, used for circulating electri-cally conducting fluids. A direct current ispassed between two electrodes inserted inthe fluid circuit and a constant magneticfield is directed perpendicular to this cur-rent. There is a force on the fluid mutuallyperpendicular to these two directions, andtherefore parallel to the direction of flow,thus propelling the fluid. One of its appli-cations is in pumping liquid sodiumcoolant through nuclear reactors.

electromagnetic radiation Energywaves propagated by electric and magneticfields that oscillate at right angles to oneanother as they travel through space. Radi-ations of all frequencies (ν) travel in freespace with the same speed c = 2.997 925 ×108 m s–1. The wavelength (λ) in free spaceis given by λν = c. The spectrum includesradio waves, microwaves, infrared, light,ultraviolet, x- and gamma-radiation. See

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electromagnetic radiation

ELECTROMAGNETIC SPECTRUM(note: the figures are only approximate)

Radiation Wavelength (m) Frequency (Hz)gamma radiation –10–10 1019–

x-rays 10–12 –10–9 1017 –1020

ultraviolet radiation 10–9 –10–7 1015 –1017

visible radiation 10–7 –10–6 1014 –1015

infrared radiation 10–6 –10–4 1012 –1014

microwaves 10–4 –1 109 –1013

radio waves 1 – –109

duality; Poynting vector; wave theory oflight.

electromagnetic spectrum As electro-magnetic radiation has wave properties, itmust be possible to have a whole series thatvaries in frequency. This is in fact the case.Visible light is only a small part of thatspectrum. The other radiations behave inthe same way as light – showing reflection,refraction, absorption, diffraction, inter-ference, and polarization in the right cir-cumstances. All travel at the same speedthrough a vacuum – 2.997 925 × 108 m s–1

(about 300 000 km s–1).The table outlines the spectrum, with

indication of the frequencies and wave-lengths of each sector. Note that this is aspectrum – there are no sharp boundariesbetween the types, but a gradual change inbehavior as the frequency changes.

electromagnetic units See c.g.s. system.

electromagnetic waves See electromag-netic radiation.

electromagnetism /i-lek-troh-mag-nĕ-tiz-ăm/ 1. The various phenomena resultingfrom the interplay of electric and magneticfields.2. The magnetism produced by an ELEC-TROMAGNET.

electrometer /i-lek-trom-ĕ-ter/ An elec-tronic instrument for measuring low po-tential differences and currents, whiledrawing very little current from the circuit.Electrometers are d.c. amplifiers with veryhigh input impedances. Early types (valvevoltmeters) used special valve circuits foramplifying steady signals. In vibrating-reedelectrometers a capacitor is used with oneplate mechanically vibrated at constant fre-quency. A steady low potential differencecan thus be converted into an alternatingone, which can then be amplified. Moremodern types of electrometer use transistorcircuits. Electrometers are often used formeasuring very low currents (less than10–9 A) by passing the current through astandard high resistance. Ionization cur-rents are measured in this way.

electromotive force /i-lek-trŏ-moh-tiv/(e.m.f.) Symbol: E When a component ofan electric circuit (e.g. a cell) does work Win driving a charge Q round the circuit it issaid to have an electromotive force E givenby E = W/Q = P/I where P is the power andI is the current. As for potential difference,the SI unit is the volt. In some cases the sys-tem may work in reverse. For example,work may be done in recharging an accu-mulator by driving the current backwardthrough it. Then, ideally, the energy storedin the component is equal to EQ. Hencee.m.f. is to be distinguished from potentialdifference, which in current electricity al-ways refers to energy dissipation. If thecurrent through a resistance is reversed thepotential difference is reversed, but energyis dissipated just as before.

Electromotive forces can be generatedin a circuit also by electromagnetic induc-tion and by the thermoelectric effects, as inthe thermocouple.

If a cell with internal resistance r is con-nected across an external resistance R thecurrent I is given by

I = E/(R + r)The potential difference between the termi-nals V is IR, hence V = E – Ir. If R is in-creased to infinity, I becomes zero, hencethe value of E is equal to the value of V onopen circuit. As explained above, althoughtheir values may be equal, E and V are dis-tinct in character.

electromotive series (electrochemical se-ries) The arrangement of chemical ele-ments in order of their standard electrodepotentials. Elements that tend to lose elec-trons from their atoms and acquire a posi-tive charge are electropositive. Those thatgain electrons are below hydrogen in thetable and are electronegative.

A standard hydrogen electrode, atwhich the reaction H+ + e → ½H2 takesplace, is taken as having zero electrode po-tential. Elements higher in the series ac-quire positive charge more easily thanthose lower down, and tend to displacelower elements from solution. For exam-ple, if a strip of zinc is placed in a solutionof copper sulfate, copper will be depositedand the zinc will dissolve as ions.

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electron /i-lek-tron/ An elementary parti-cle of negative charge (–1.602 177 33 ×10–19 C) and rest mass 9.109 389 7 × 10–31

kg. Electrons are present in all atoms inshells around the nucleus. They are emittedfrom the nucleus in a type of beta decay.They are classified as leptons.

See also elementary particles.

electron affinity 1. The work needed toremove an electron from a negative ion andmove it to infinity.2. A measure of the electronegativity of anatom (i.e. its tendency to acquire elec-trons). An element’s position in the ELEC-TROMOTIVE SERIES gives an indication of itselectron affinity.

electron-beam welding A technique inwhich welding is carried out in a vacuumchamber using a narrow beam of high-en-ergy electrons. These electrons are emittedfrom a cathode, then accelerated and fo-cused using a magnetic field. Electron-beam welding has many specializedindustrial applications.

electron capture 1. The transformationof a proton into a neutron in an atomic nu-cleus, accompanied by the emission of x-rays. It occurs when the nucleus ‘captures’an orbital electron.2. The capture of an electron by an atom ormolecule to form a negative ion. See ion-ization; neutron capture.

electron charge The charge on an elec-tron, a fundamental constant equal to–1.602 177 33 x 10–19 coulombs.

electron configuration The arrangementof electrons (in shells) around the nucleusof an atom. Configurations are representedby a number (the principal quantum num-ber), a letter (representing the azimuthalquantum number) and a numerical super-script (indicating the number of electronsin that set). For example, 2p6 represents afull third shell (principal quantum number2 and azimuthal quantum number 1), con-taining six electrons.

electron diffraction The diffraction of abeam of electrons by matter. Since diffrac-tion is a characteristic property of wavesthe occurrence of electron diffractionshows the wave nature of electrons, in ac-cord with the expectations of quantum me-chanics. Electron diffraction is used toinvestigate molecules in the gas phase andcan be used to establish molecular geome-try and bond lengths. It is also an impor-tant technique for studying the structure ofsurfaces and reactions at surfaces. In thiscase the electrons used have a low energyso as not to penetrate the bulk of the mat-erial. The technique is called low-energyelectron diffraction or LEED.

electron gun A device that generates astream of electrons. In a cathode-ray tube,an electron gun produces the moving spotof light on the screen. An electron gun gen-erally consists of a heated cathode in a vac-uum tube. The electrons are emitted bythermionic emission and are acceleratedtowards a positive electrode (anode) byhigh voltage. They pass through a hole inthe anode to form a narrow beam, whichcan be focused by electron lenses.

electronic energy levels See energy lev-els.

electronics /i-lek-tron-iks/ The study anduse of circuitry involving such componentsas semiconductors, thermionic tubes andother vacuum devices, resistors, capacitors,and inductors.

electron lens A device for focusing abeam of electrons. Electron lenses use elec-tric fields, produced by a system of metalelectrodes, or magnetic fields produced bycoils.

electron microscope An apparatus forproducing a magnified image by using abeam of electrons focused by electronlenses.

In the transmission electron microscopethe electron beam passes through the sam-ple and is focused onto a fluorescent screento produce a visual image. Magnificationsabove 200 000 can be obtained.

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electron microscope

The scanning electron microscope canbe used with thicker samples. A beam ofprimary electrons is scanned across thespecimen and the secondary electrons emit-ted are focused onto a screen. The magnifi-cation and resolution are lower than in thetransmission microscope, but three-dimen-sional images can be obtained.

In optical microscopes the ultimate res-olution depends on the wavelength of thelight. Better resolution is obtained usinghigh-energy electrons because their wave-length can be shorter at sufficiently highenergies.

See de Broglie wave.

electron optics The use of electric andmagnetic fields to focus and direct beamsof electrons. Similar methods are used withbeams of positive or negative ions.

electron probe microanalysis (EPM) Amethod of quantitative analysis used forsmall samples in which a beam of electronsis focused onto the surface of the sample sothat x-rays of characteristic intensities areemitted.

electron radius Symbol re The radius ofan electron, a fundamental constant equalto 2.817 77 × 10–15 m. The concept of anelectron radius occurred in theories of theelectron put forward in the late nineteenthand early twentieth centuries. This conceptis now thought to be invalid since it is for-bidden both by special relativity theoryand by quantum mechanics. See alsoCompton wavelength.

electron rest mass Symbol me The massof an electron at rest, a fundamental con-stant equal to 9.109 558 × 10–31 kg.

electron shell A group of electrons,around an atomic nucleus, that have thesame principal quantum number. Startingwith the innermost shell, the quantumnumbers are 1, 2, 3, etc. and are sometimesdesignated K, L, M, etc. Each shell may besub-divided into sub-shells, designated s, p,d, f, corresponding to azimuthal (orbital)quantum numbers (l) of 0, 1, 2, 3.

electron spin resonance (ESR) A branchof microwave spectroscopy that uses mi-crowave radiation (of known wavelengthand frequency) to increase the energy ofunpaired electrons in a strong magneticfield. It is employed to investigate chemicalbonding, paramagnetism, and electronbands in conductors.

electron tube An electronic componentthat depends on flow of electrons in a gasor vacuum; for example, a thermionic tubeor discharge tube.

electronvolt /i-lek-tron-vohlt/ Symbol: eVA unit of energy equal to 1.602 191 7 ×10–19 joule. It is defined as the energy re-quired to move an electron charge across apotential difference of one volt. It is nor-mally used only to measure energies of ele-mentary particles, ions, or states.

electrophoresis /i-lek-troh-fŏ-ree-sis/ Themovement of charged colloid particlesunder the influence of an electric field. Itsprincipal application is in the separation ofproteins.

electrophorus /i-lek-trof-ŏ-rŭs/ A simpledevice for supplying electrical charge byelectrostatic induction. It consists of a flatinsulating plate and a separate metal platewith an insulating handle. The insulatingplate is charged by friction; the metal plateis placed on it and momentarily earthed,leaving it with an induced charge.

electroplating /i-lek-trŏ-play-ting/ Seeelectrodeposition.

electroscope /i-lek-trŏ-skohp/ An instru-ment for detecting electrical potential dif-ference; it can also detect the presence andsign of an electric charge. A common typeconsists of a pair of light conducting leaves(often of gold foil) suspended side by sidefrom an insulated rod. When a charge isapplied to the plate on the top of the rod,the leaves swing apart because they receiveelectric charges of the same sign and repeleach other.

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electrostatic field /i-lek-trŏ-stat-ik/ Anelectric field produced by stationary (sta-tic) electric charge.

electrostatic generator A machine de-signed to produce a continuous supply ofelectric charge by electrostatic means. Typ-ical examples are the Wimshurst machineand the Van de Graaff generator.

electrostatic induction The productionof electric charge at some point by separa-tion of positive and negative charges in anelectric field. If a body with a positivecharge (say) is brought close to a neutralconductor, the free electrons in the con-ductor flow such that they tend to accumu-late in the end near the body. This end thushas a negative charge, the other is positive.There is a resulting force of attraction be-tween the body and the conductor. Simi-larly, an insulator is charged by inductionby polarization.

electrostatic precipitation A method ofremoving unwanted solid or liquid parti-cles from gases (as in pollution control).The particles are given a charge by an elec-tric field, and then attracted to chargedplates.

electrostatics /i-lek-trŏ-stat-iks/ (staticelectricity) The study of the effects associ-ated with electric charge at rest. The fun-damental principle of electrostatics is thatsimilarly charged bodies repel each other,whereas oppositely charged bodies attracteach other. Electric charges at rest generateelectric fields. Electrostatics is governed byCOULOMB’S LAW.

electrostatic shield A hollow conductingcontainer surrounding an apparatus, usedfor protection against electric fields. Fara-day demonstrated that the electric fieldinside a closed conductor is zero. (Electro-static shields are often called Faradaycages.)

electrostatic units See c.g.s. system.

electrostriction /i-lek-troh-strik-shŏn/ Achange in the dimensions of a dielectric

when it is placed in an electric field. It canbe regarded as the converse of the piezo-electric effect.

electroweak theory /i-lek-trŏ-week/ Atheory unifying the electromagnetic andthe weak INTERACTIONS.

element /el-ĕ-mĕnt/ In optics, a single lensforming part of a doublet or other com-pound lens.

elementary particles (fundamental parti-cles; subatomic particles) Indivisible parti-cles from which all matter is formed. Atone time atoms were believed to be the ele-mentary particles. Later it was realized thatthey were divisible; that is, made of pro-tons, neutrons, and electrons. More re-cently many new particles have beenidentified and attempts made to groupthem into families and explain their rela-tionships with each other.

Elementary particles are characterizedby their mass, charge, spin, and certainother properties (‘strangeness’, ‘charm’,etc.). One form of classification is into lep-tons and hadrons, distinguished by the wayin which the particles interact. Hadrons arefurther divided into baryons and mesons.Finally, baryons are subdivided into nucle-ons and hyperons. Another classification isinto fermions (having half-integral spin)and bosons (having integral spin).

See table overleaf. See also antiparticle;quark; resonance.

elements, magnetic See magnetic ele-ments.

elevation of boiling point An increase inthe boiling point of a liquid that generallyoccurs when a solid is dissolved in it. Thisincrease is proportional to the concentra-tion of particles dissolved. The elevation ofthe boiling point of a liquid is an exampleof a COLLIGATIVE PROPERTY.

ellipse A conic with an eccentricity be-tween 0 and 1. An ellipse has two foci. Aline through the foci cuts the ellipse at twovertices. The line segment between the ver-tices is the major axis of the ellipse. The

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point on the major axis mid-way betweenthe vertices is the center of the ellipse. Aline segment through the center perpendic-ular to the major axis is the minor axis. Ei-ther of the chords of the ellipse through afocus parallel to the minor axis is a latusrectum. The area of an ellipse is πab, wherea is half the major axis and b is half theminor axis. (Note that for a circle, in whichthe eccentricity is zero, a = b = r and thearea is πr2.)

The sum property of an ellipse is thatfor any point on the ellipse the sum of thedistances from the point to each focus is aconstant. The ellipse also has a reflectionproperty; for a given point on the ellipsethe two lines from each focus to the pointmake equal angles with a tangent at thatpoint.

In Cartesian coordinates the equation:x2/a2 + y2/b2 = 1

represents an ellipse with its center at theorigin. The major axis is on the x-axis andthe minor axis on the y-axis. The majoraxis is 2a and the minor axis is 2b. The fociof the ellipse are at the points (+ea,0) and(–ea,0), where e is the eccentricity. The twodirectrices are the lines x = a/e and x = –a/e.The length of the latus rectum is 2b2/a. Seealso conic.

ellipsoid /i-lip-soid/ A three-dimensionalfigure that can be formed by rotating an el-lipse about one of its axes of symmetry. Inthe case of rotation about the major axisthe ellipsoid is called a prolate ellipsoid,with the ellipsoid formed by rotation aboutthe minor axis being called an oblate ellip-soid.

elliptical polarization A type of polar-ization of electromagnetic radiation in

ellipsoid

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ELEMENTARY PARTICLES

Note: it is common to measure the mass of particles in units of energy/c2, where c is thespeed of light. The values above are in units of MeV/c2 = 178 x 10–30 kg.

Particle Charge Symbol Mass Spinleptons

electron -1 e– 0.511 ½neutrino 0 ν 0 ½

0 νµ 0 ½muon -1 µ– 105.66 ½

baryonsproton +1 p 938.26 ½neuron 0 n 939.55 ½xi particle 0 ≡ο 1314.9 ½

-1 ≡– 1321.3 ½sigma particle +1 ∑+ 1189.5 ½

0 ∑o 1192.5 ½-1 ∑– 1197.4 ½

lambda particle 0 ∧ 1115.5 ½omega particle -1 Ω– 1672.5 ¾

mesonskaon -1 k– 493.8 0

+1 k+ 493.8 0pion +1 Π+ 139.6 0

0 Πo 135 0-1 Π– 139.6 0

phi particle 0 φ 1020 1psi particle 0 ψ 3095 1eta particle 0 ηo 548.8 0

ELEMENTARY PARTICLES

which the radiation can be considered toconsist of two plane-polarized radiationstraveling together, out of phase by 90° andof unequal amplitude.

emanation The name formerly given tocertain isotopes of radon, which diffusedout of the parent material containing ra-dium, from which they are formed byalpha decay. 220Radon is a member of the232thorium decay series and it was there-fore known as thoron or thorium emana-tion. The radon isotope that is a member ofthe actinium series was known as actiniumemanation or actinon. Summarizing:radium emanation is now known as 222Rn;thoron emanation is now known as 220Rn;actinium emanation is now known as219Rn.

e.m.f. See electromotive force.

emission spectrum See spectrum.

emissive power See emissivity.

emissivity /em-ă-siv-ă-tee/ (emissivepower) Symbol: ε The power radiated by asurface compared to that radiated by ablack body, all other things being equal.There is no unit. Strictly this should be de-fined for a given wavelength λ (and calledspectral emissivity). Kirchhoff’s radiationlaw equates the emissivity of a surface to itsabsorptance. Thus a perfect reflector haszero absorptance and zero emissivity; ablack body has an absorptance of 1 and anemissivity of 1.

emittance /i-mit-ăns/ See exitance.

emitter See transistor.

e.m.u. Electromagnetic unit. See c.g.s. sys-tem.

emulsion A dispersion of droplets of oneliquid in another.

endoergic /en-doh-er-jik/ Describing anuclear process that absorbs energy. Com-pare exoergic.

endothermic /en-doh-th’er-mik/ Describ-ing a process in which heat is absorbed (i.e.heat flows from outside the system, or thetemperature falls). The dissolving of a saltin water, for instance, is often an endother-mic process. Compare exothermic.

energy Symbol: W A property of a system– its capacity to do work. Energy and workhave the same unit: the joule (J). It is con-venient to divide energy into KINETIC EN-ERGY (energy of motion) and POTENTIAL

ENERGY (‘stored’ energy). Names are givento many different forms of energy (chemi-cal, electrical, nuclear, etc.); the only realdifference lies in the system under discus-sion. For example, chemical energy is thekinetic and potential energies of electronsin a chemical compound. See also internalenergy; mass-energy.

energy bands Ranges of energy that areeither allowed or forbidden for valenceelectrons in a solid. In a solid each quan-tum state that contains a valence electronin an atom, and each empty state, con-tributes to a state that extends over a vol-ume containing many atoms. The energiesfor these states are distributed continu-ously over bands, which are typically a fewelectronvolts wide.

In a metal there is one (valence-conduc-tion) band of energies within which thereare far more quantum states than there areelectrons. All the states of low energies arenormally filled, and the high ones areempty. Over a small range above andbelow the Fermi level there are comparablenumbers of occupied and empty states.When there is a potential gradient in themetal, electrons move freely from occupiedstates to adjacent empty states at the sameenergy (kinetic plus potential), so metalsare good conductors.

In a nonmetal there is a lower allowedband (the valence band) and an upper al-lowed band (the conduction band). Be-tween these is a range of energies (theforbidden band) in which there are few orno quantum states. In pure substances, thenumber of electrons is exactly equal to thenumber of states in the valence band. Atlow temperatures, the valence band is filled

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energy bands

and the conduction band is empty. If thereis a potential gradient, no conduction canresult as there are no empty quantum statesof the same energy adjacent to occupiedones, and the Pauli principle excludes morethan one electron in a state. Hence non-metals at low temperatures are usually verygood insulators. At higher temperatures acertain proportion of the electrons movefrom the valence band into the conductionband. Conduction is now possible in bothbands as there are adjacent occupied andempty states of the same energy. The mech-anism of conduction in the almost full va-lence band is complicated; the solidbehaves as if positive charges (holes) weremoving in the opposite direction to theelectrons.

If the energy gap between the top of thevalence band and the bottom of the con-duction band is more than about 2e V thesubstance is regarded as an insulator; if it isless it is regarded as a semiconductor. Im-purities can give rise to very narrow bandsof allowed energies within the forbiddenband. This can have very large effects uponthe properties, and doping with suitablesubstances can cause either n-type or p-type conductivity.

energy level The energy of a particle,such as an electron, in a system. See alsoquantum state.

engine A device that turns thermal energyinto work. Practical engines work by burn-ing fuel and are also known as HEAT EN-GINES.

enrich To increase the fraction of one iso-tope in a mixture of isotopes of the same el-ement. It usually refers to the enrichmentof uranium by the 235U isotope (naturalabundance about 0.7%) to obtain suitablefissile material for nuclear reactors or nu-clear weapons. It can also be used to de-scribe the process of obtaining heavy waterfrom natural water. See isotope separation.

enrichment See enrich.

entanglement See Bell’s paradox.

enthalpy /en-thal-pee, en-thal-/ Symbol: HThe sum of the internal energy (U) and theproduct of pressure (p) and volume (V) ofa system: H = U + pV. In a chemical reac-tion carried out at constant pressure, thechange in enthalpy measured is the internalenergy change plus the work done by thevolume change:

∆H = ∆U + p∆V

entropy /en-trŏ-pee/ Symbol: S In any sys-tem that undergoes a reversible change, thechange of entropy is defined as the heat ab-sorbed divided by the thermodynamic tem-perature: δS = δQ/T. A given system is saidto have a certain entropy, although ab-solute entropies are seldom used: it ischange in entropy that is important. Theentropy of a system measures the availabil-ity of energy to do work.

In any real (irreversible) change in aclosed system the entropy increases. Al-though the total energy of the system hasnot changed (first law of thermodynamics)the available energy is less – a consequenceof the second law of thermodynamics.

The concept of entropy has beenwidened to take in the general idea of dis-order – the higher the entropy, the moredisordered the system. For instance, achemical reaction involving polymeriza-tion may well have a decrease in entropybecause there is a change to a more orderedsystem. The ‘thermal’ definition of entropyis a special case of this idea of disorder –here the entropy measures how the energytransferred is distributed among the parti-cles of matter.

epidiascope /ep-ă-dÿ-ă-skohp/ A form ofprojector able to project images of bothtranslucent objects (e.g. slides) and flatopaque objects (e.g. diagrams and pic-tures). It is a combined episcope and dias-cope. Epidiascopes are now rarely used.

episcope /ep-ă-skohp/ See opaque projec-tor.

epitaxy /ep-ă-taks-ee/ (epitaxial growth)The growth of a crystal of one substanceon the surface of a crystal of a base sub-stance substance (called the substrate) in

energy level

86

87

equilibrium

neutral unstable (W maximum)

unstable (W pointof inflection)

stable (Wminimum)

Positions of equilibrium

which the crystal structure of the substancethat is being grown has the same crystalstructure as the substrate. Epitaxy is usedextensively in the semiconductor industryto produce thin layers of material with spe-cific properties.

EPR experiment See Bell’s paradox.

equation of state An equation that re-lates the pressure, volume, and tempera-ture of a substance. The simplest equationof state is the ideal gas equation (see gaslaws) in which it is assumed that the mole-cules of the gas do not occupy any volumeor interact with each other. There are sev-eral equations of state for gases that arebased on less idealized assumptions. An ex-ample is the VAN DER WAALS’ EQUATION.

equations of motion Equations that de-scribe the motion of an object with con-stant acceleration (a). They relate thevelocity v1 of the object at the start of tim-ing to its velocity v2 at some later time tand the object’s displacement s.

The five variables are given in the table.Each of the five equations relates four ofthe variables, as in the second table, inwhich the omitted variable is shown inbrackets.

Variable

accelerationfirst velocitysecond velocitytimedisplacement

Symbol

av1 (u)v2 (v)ts

Unit symbol

m /s2 (ms–2)m /s (ms–1)m /s (ms–1)sm

Equations of motion

Variables

a, v1, v2, t, (s)v1, v2, t, s, (a)a, v1, t, s, (v2)a, v2, t, s, (v1)a, v1, v2, s, (t)

Equation

v2 = v1 + at2

s = (v1 + v2 )t / 2s = v1t + at2/ 2s = v2t – at2/ 2v2

2 = v12 + 2 as

QUANTITIES USED IN THE EQUATIONSOF MOTION

QUANTITIES USED IN THE EQUATIONS OF MOTION

constant momentum. An object is in equi-librium if:1. its linear momentum does not change (itmoves in a straight line at constant speedand has constant mass, or is at rest);2. its angular momentum does not change(its rotation is zero or constant).For these conditions to be met:1. the resultant of all outside forces actingon the object must be zero (or there are nooutside forces);2. there is no resultant turning-effect (mo-ment).An object is not in equilibrium if any of thefollowing are true:

1. its mass is changing;2. its speed is changing;3. its direction is changing;4. its rotational speed is changing.

2. A state of a system in which the proper-ties do not change with time. For examplea saturated vapor in contact with its liquidis at equilibrium. The pressure, density,temperature, etc., are unchanging. In thiscase molecules are still leaving the liquid tothe gas phase, but are re-entering from thevapor at the same rate. This type of systemis said to be in dynamic equilibrium. If twobodies at different temperatures are placedtogether, heat transfer occurs until they

equator, magnetic See isoclinic line.

equilibrant /i-kwil-ă-brănt/ A single forcethat is able to balance a given set of forcesand thus cause equilibrium. It is equal andopposite to the resultant of the givenforces.

equilibrium /ee-kwă-lib-ree-ŭm, ek-wă-/(pl. equilibriums or equilibria) 1. A state of

have the same temperature. They are thenat thermal equilibrium.

A system in which the free energy is at aminimum value is said to be in thermody-namic equilibrium. Both the above casesare examples of thermodynamic equilib-rium.

equipartition of energy /ee-kwă-par-tish-ŏn, ek-wă-/ The principle that the total en-ergy of a molecule is, on average, equallydistributed among the available DEGREES OF

FREEDOM. It is only approximately true inmost cases.

equipotential /ee-kwă-pŏ-ten-shăl, ek-wă-/ A line or surface such that all pointson it are at the same potential. Equipoten-tials in a field cut the lines of force at rightangles.

equivalence principle A fundamentalprinciple of mechanics, which can be statedin several ways. One statement of the prin-ciple is that the inertial mass and the grav-itational mass of a body are equal.

erbium /er-bee-ŭm/ A soft malleable sil-very element of the lanthanoid series ofmetals. It occurs in association with otherlanthanoids. Erbium has uses in the metal-lurgical and nuclear industries and in mak-ing glass for absorbing infrared radiation.

Symbol: Er; m.p. 1529°C; b.p. 2863°C;r.d. 9.066 (25°C); p.n. 68; r.a.m. 167.26.

erect Describing an image that is the sameway up as the object.

erecting prism (inverting prism) A prismused to invert an image in an optical systemwithout change of size or shape. Erectingprisms operate by internal reflection.

erg A former unit of energy used in thec.g.s. system. It is equal to 10–7 joule.

error A difference between the true valueof a quantity and the value of that quantityfound in an experiment or observation.The effects of random errors can be over-come by taking several measurements andaveraging out the results. Systematic errors

occur if the scales or positions in the mea-suring apparatus are incorrect.

escape velocity The minimum velocitythat an object must have in order to escapefrom the surface of a planet (or moon)against the gravitational attraction. The es-cape velocity is equal to √(2GM/r), whereG is the gravitational constant, M is themass of the planet, and r is the radius of theplanet.

e.s.u. Electrostatic unit. See c.g.s. system.

ether /ee-th’er/ (aether) A hypotheticalfluid, formerly thought to permeate allspace and to be the medium through whichelectromagnetic waves were propagated.

europium /yû-roh-pee-ŭm/ A silvery ele-ment of the lanthanoid series of metals. Itoccurs in association with other lan-thanoids. Its main use is in a mixture of eu-ropium and yttrium oxides widelyemployed as the red phosphor in televisionscreens. The metal is used in some super-conductor alloys.

Symbol: Eu; m.p. 822°C; b.p. 1597°C;r.d. 5.23 (25°C); p.n. 63; r.a.m. 151.965.

eutectic /yoo-tek-tik/ Describing a mix-ture of substances with the lowest possiblefreezing temperature – i.e., no other mix-ture of the same substances freezes at a lowtemperature.

evaporation 1. A change of state fromsolid or liquid to gas (or vapor). Evapora-tion can take place at any temperature; therate increases with temperature. It occursbecause some molecules have enough en-ergy to escape into the gas phase (if theyare near the surface and moving in the rightdirection). Because these are the moleculeswith higher kinetic energies, evaporationresults in a cooling of the liquid. See alsovapor pressure.2. The process of vaporizing a metal at ahigh temperature in a vacuum. It is used tocoat objects with thin metal films.

exa- Symbol: E A prefix denoting 1018.

equipartition of energy

88

For example, 1 exaohm (EΩ) = 1018 ohms(Ω).

exchange force A type of force such asthat postulated between nucleons in a nu-cleus. This strong NUCLEAR FORCE operateswithin a range of up to about 2 × 10–13 cm.The theory holds that protons and neu-trons are constantly being transformedinto each other, the mediating particlebeing a meson.

excitation /eks-ÿ-tay-shŏn/ 1. The pro-duction of a magnetic field by an electriccurrent in the winding of an electromagnet.2. The process of producing an excitedstate of an atom, molecule, etc.

excitation energy The energy that is re-quired to change an atom, molecule, etc.,from one quantum state to a state with ahigher energy. The excitation energy(sometimes called excitation potential) isthe difference between two energy levels ofthe system.

excitation potential See excitation en-ergy.

excited state A state of an atom, mol-ecule, or other system, with an energygreater than that of the ground state. Com-pare ground state.

exclusion principle (Pauli principle) Therule that no two identical fermions canhave the same set of quantum numbers in asystem. For example: all the conductionelectrons in a piece of copper must havedifferent sets of quantum numbers; all theprotons in a nucleus must have differentsets, etc. The rule was proposed by theSwiss physicist Wolfgang Pauli (1900–58)in 1925 for electrons in atoms in order toexplain atomic structure. See Fermi–Diracstatistics.

exclusive OR gate See logic gate.

exitance /egz-ă-tăns, eks-ă-tăns/ Symbol:M The (radiant or luminous) flux emittedfrom a surface per unit area. Radiant exi-tance (Me) is measured in watts per square

meter (W m–2); luminous exitance (Mv) ismeasured in lumens per square meter(lm m–2). Exitance was formerly calledemittance.

exoergic /eks-oh-er-jik/ Denoting a nu-clear process that gives out energy. Com-pare endoergic.

exothermic /eks-oh-th’er-mik/ Denotinga chemical reaction in which heat isevolved (i.e. heat flows from the system orthe temperature rises). Combustion is anexample of an exothermic process. Com-pare endothermic.

exotic nuclei Types of nucleus that havethe highest and lowest possible neutronnumbers for a given atomic number. Suchnuclei are very unstable but considerationof them is very important in the theory ofpossible nuclei

expansion, thermal The change of sizeof a sample (solid, liquid, or gas) whensamples increase in size (expand) whenwarmed and decrease (contract) whencooled. The effect is due to increased mo-tion (energy) of the atoms or molecules athigher temperatures. (Gases also expandwhen the pressure is reduced.) See alsoBoyle’s law; Charles’ law; expansivity.

expansion cloud chamber See cloudchamber.

expansivity /eks-pan-siv-ă-tee/ A measureof the tendency of a substance to undergothermal expansion. A solid bar, for exam-ple, of length l1 and temperature θ1, in-creases to length l2 when its temperaturerises to θ2:

l2 = l1(1 + α(θ2 – θ1))Here, α is the linear expansivity of the ma-terial of the bar. In fact, the expansivity it-self varies with temperature, so the meanvalue of α is obtained between tempera-tures θ1 and θ2. A more accurate equationis:

l = l0(1 + aθ + bθ2 + cθ3 + …)l0 is the length at 0°C, a, b, c, etc., are con-stants.

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expansivity

Solids also have a superficial expansiv-ity (β) relating to the increase in area. It canbe shown that, to a good approximation, β= 2α, and

A2 = A1(1 + β(θ2 – θ1))Similarly, the cubic expansivity (γ) relatesto increase in volume; γ = 3α:

V2 = V1(1 + γ(θ2 – θ1))For liquids, only the cubic expansivity (γ) isuseful. There are two values defined. If theexpansivity is measured by observing thevolume change in a container, the apparentexpansion is found. This is because the sizeof the container also changes. The absoluteexpansion is the actual change of volume,allowing for the container. Expansivitieswere formerly called coefficients of expan-sion. See also comparator, Regnault’s ap-paratus.

extensive variable A quantity that is pro-portional to the size of the system. Mass,energy, and volume are examples of exten-sive variables. For example, if two systemswith the same mass are brought together toform a larger system, then the mass dou-bles. Compare intensive variable.

external combustion engine See inter-nal combustion engine.

extraordinary ray See birefringent crys-tal.

extremely high frequency (EHF) Aradio frequency in the range between 300GHz and 30 GHz (wavelength 1 mm–1cm).

extrinsic semiconductor /eks-trin-sik, -zik/ See semiconductor.

eye A sense organ able to produce opticalimages and to send corresponding nervesignals to the brain. Light enters throughthe transparent cornea and passes throughthe watery liquid (aqueous humor), lens,and gelatinous substance (vitreous humor)onto the retina at the back of the eye. Thecornea, aqueous humor, and lens form aconverging system, which allows an imageto be focused on the retina. The focal dis-tance of their system can be varied by the

ciliary muscles, which control the curva-ture of the lens. The quantity of light ad-mitted is varied by the circular iris; thiscontracts or relaxes, changing the apertureof the eye (the pupil). Light-sensitive cellsin the retina produce electrical signals,which are carried along the optic nerve tothe brain. The cells are most concentratedin the yellow spot (macula lutea), and es-pecially in its central part (fovea). Imagesproduced here are seen in greatest detail.Two types of cell are found in the retina:the cones, which are used for photopic(‘daylight’) vision and COLOR VISION; androds, which are used for peripheral andscotopic (‘night-time’) vision. The conesare particularly concentrated in the yellowspot whereas the rods cover a large areaaround this. See also accommodation; hy-peropia; myopia; presbyopia.

eye lens The lens nearest the eye in a com-pound EYEPIECE. Compare field lens.

eyepiece (ocular) The lens or combina-tion of lenses nearest the eye in an opticalinstrument. It is used to produce a final vir-tual magnified image of the previous imagein the system. Various compound lens sys-tems may be used to reduce aberrations.Often crosswires or a graticule is includedin the structure of the eyepiece to assistwith location or measurement.

extensive variable

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intermediateimage plane

field lens

eye lens(achromat)

Eyepiece (Kellner)

Fabry–Perot interferometer /fab-reepair-roh/ A type of interferometer firstconstructed by Charles Fabry and AlfredPerot in the early 19th century, in whichmonochromatic light passes through a pairof parallel half-silvered plates, with it beingpossible to change the distance between theplates by adjusting one of the plates. Thisproduces an interference pattern consistingof circular fringes. The device has beenused in spectroscopy.

Fahrenheit scale A TEMPERATURE SCALE

in which the ice temperature is taken as 32°and the steam temperature is taken as 212°(both at standard pressure). It is not usedfor scientific purposes. To convert betweendegrees Fahrenheit (F) and degrees Celsius(C) the formula C/5 = (F – 32)/9 is used.The scale was devised by the Germanphysicist Daniel Fahrenheit (1686–1736).

fallout Radioactivity precipitated fromthe atmosphere, usually originating fromnuclear explosions, occasionally from re-leases of radioactivity from nuclear estab-lishments. It consists of fission fragments,the most worrying of which are 131I (half-life 8 days), which becomes concentratedin the thyroid gland if ingested, and 90Sr(half-life 28 years), which accumulates inbone. Both may reach the human popula-tion in milk from cows grazing on landcontaminated by fallout and by other lesssignificant routes.

farad /fa-răd, -rad/ Symbol: F The SI unitof capacitance. When the plates of a capac-itor are charged by one coulomb and thereis a potential difference of one volt betweenthem, then the capacitor has a capacitanceof one farad. 1 farad = 1 coulomb volt–1

(C V–1). It is named for the English physi-

cist and chemist Michael Faraday(1791–1867).

faraday /fa-ră-day/ An old unit of electri-cal charge equal to the FARADAY CONSTANT.

Faraday cage See electrostatic shield.

Faraday constant Symbol: F The electriccharge of one mole of electrons, equal to9.648 670 × 104 coulombs per mole. It isthe Avogadro constant multiplied by theelectron charge. See Faraday’s laws (ofelectrolysis).

Faraday disk See homopolar generator.

Faraday effect The rotation of the planeof polarization of radiation in a dielectricmedium in a magnetic field. The angle ofrotation (θ) is proportional to the fieldstrength B, and to the length l of the pathin the medium in the field: θ is proportionalto Bl. See also Kerr effect.

Faraday’s laws (of induction) Three lawsdescribing the electromagnetic induction ofan e.m.f. in a conductor by a changingmagnetic flux:(1) If the number of lines of force linkedwith a conducting circuit is changing, acurrent is induced in the circuit.(2) The direction of the induced current issuch that the magnetic field it producestends to keep the flux linkage constant.(This is a statement of Lenz’s law).(3) The total quantity of electricity passinground the circuit is directly proportional tothe total change in lines of force (and in-versely proportional to the resistance of thecircuit).

Faraday’s laws (of electrolysis) Two laws

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F

Faraday's laws of electromagnetic induction

92

resulting from the work of Michael Fara-day on electrolysis:(1) The amount of chemical change pro-duced is proportional to the charge passed.(2) The amount of chemical change pro-duced by a given charge depends on the ionconcerned. More strictly it is proportionalto the relative ionic mass of the ion, and thecharge on it. Thus the charge Q needed todeposit m grams of an ion, relative ionicmass, M, carrying Z charges, is given by:

Q = FmZ/MF, the Faraday constant, has a value of onefaraday, i.e. 9.648 670 × 104 coulombs permole.

Faraday’s laws of electromagnetic in-duction See electromagnetic induction;Faraday’s laws (of induction).

far infrared The longer-wavelength partof the infrared region of the electromag-netic spectrum; i.e. the part farthest inwavelength from the visible region andnearest to the radio-wave region.

far point The farthest point from the eyeat which an image can be focused on theretina. The eye is completely relaxed (min-imum power) in focusing an object at itsfar point. In the normal eye the far point isat infinity. In the myopic (short-sighted)eye, light from distant objects is focused infront of the retina. The far point is thenonly a few meters from the eye. See alsomyopia.

far sight See presbyopia.

fast neutron A high-energy neutronwhich, when produced by NUCLEAR FISSION,is too energetic to produce further fissionand thereby sustain a nuclear chain reac-tion. See also moderator; slow neutron.

fast reactor See nuclear reactor.

fatigue Physical weakness in a materialresulting from many small repeatedstresses.

feedback The action of returning some ofthe output energy of a device (e.g. an am-

plifier) to the input. There are two types –positive feedback and negative feedback –according to the relative phases of the feed-back voltage and the input signal. Thefeedback is negative if these voltages areout of phase, and positive if the voltagesare in phase.

Although negative feedback reduces theinput voltage and input energy, and hencealso the gain of the amplifier, the advan-tage is that noise and distortion are also re-duced, while stability is improved. Positivefeedback increases the gain and energy out-put of the amplifier, with the result that theamplifier becomes an oscillator. Feedbackis made through a loop circuit using a pas-sive component.

Negative feedback is also used in othercontrol systems. For example, the stabilizerfitted to an ocean-going ship utilizes nega-tive feedback by generating a voltage pro-portional to the instability (e.g. the angle oftilt) and using this voltage to drive the con-trol system. Thus the effect of the voltage isto reduce the cause which generated it. An-other, non-electrical, example is the cen-trifugal governor.

femto- Symbol: f A prefix denoting 10–15.For example, 1 femtometer (fm) = 10–15

meter (m).

Fermat’s principle The basic law of geo-metrical optics. It states that a ray will takea path through a medium such that thetime required to cover a given distance isminimum. The law leads to the concept ofrectilinear propagation and the laws of re-flection and refraction. It is named for theFrench mathematician Pierre de Fermat(1601–65).

fermi /fer-mee/ A unit of length equal to10–15 meter. It was formerly used in atomicand nuclear physics.

Fermi–Dirac statistics /fair-mee dee-rak/The statistical rules for studying systems ofidentical fermions. It is assumed that (a) allidentical particles are to be regarded as ab-solutely indistinguishable; and (b) fermionsobey the Pauli exclusion principle, that isthat no two identical fermions can have the

same set of quantum numbers in a givensystem. The distribution of electron ener-gies in a solid is one extremely importantsubject to which these rules apply. The sta-tistics are named for the Italian physicistEnrico Fermi (1901–54) and the Britishmathematician and physicist Paul Dirac(1902–84). See also Bose–Einstein statis-tics; Maxwell–Boltzmann statistics; energybands.

Fermi level The energy level in a solid atwhich a quantum state would be equallylikely to be empty or to contain an elec-tron. In a metal the Fermi level is in theconduction band. At absolute zero all thequantum states up to this level would beoccupied and all states with higher energywould be empty. At non-zero temperaturessome states below this level are empty andsome above it are occupied. In insulatorsand semiconductors the Fermi level is inthe forbidden band between the valenceband and the conduction band.

When two different substances arebrought into contact (for example an n-type and a p-type semiconductor) electronsflow until the Fermi levels of the two sub-stances are at the same energy.

fermion /fer-mee-on/ A particle that obeysFermi–Dirac statistics and has half-integralspin.

Elementary fermions are conserved innumber in all interactions. The productionof a new fermion is always accompanied bythe production of an ANTIPARTICLE which iscounted as minus the particle. The lepton isone type of fermion which appears mostoften in the charged form, the electron.When an electron is created in beta decayan antineutrino is also produced. This canbe regarded as an uncharged antiparticle,and is counted as minus one lepton. Thepositron is regarded as a charged antiparti-cle to the electron. When electron–positronpairs are generated by radiation or annihi-late to radiation the total number of lep-tons is conserved.

Similarly baryons are conserved. In ahigh-energy reaction a proton–antiprotonpair may be generated. The proton countsas plus one baryon and the antibaryon as

minus one. Thus the number remains con-stant on production of the pair, and simi-larly when the antiproton subsequentlyannihilates with a proton, producingpions.

See boson; elementary particles;Fermi–Dirac statistics.

fermium /fer-mee-ŭm/ A radioactivetransuranic element of the actinoid series,not found naturally on Earth. It is pro-duced in very small quantities by bom-barding 239Pu with neutrons to give 253Fm(half-life 3 days). Several other short-livedisotopes have been synthesized.

Symbol: Fm; p.n. 100; most stable iso-tope 257Fm (half-life 100.5 days).

ferrimagnetism /fe-ri-mag-nĕ-tiz-ăm/ Atype of magnetic behavior shown by cer-tain solids (e.g. ferrites). Ferrimagnetic ma-terials are similar to ferromagneticmaterials in behavior, but have a weakermagnetization. They contain two types ofmagnetic particle with unequal magneticmoments aligned antiparallel, producing anet magnetization. See also antiferromag-netism.

ferrite /fe-rÿt/ One of a class of iron com-pounds with weak permanent magnetism.Ferrites are important as they are electricalinsulators so cannot suffer from eddy-cur-rent power loss, but they do have a perma-nent magnetization as a result of theirferrimagnetism. They are used as cores inhigh-frequency circuits.

The composition of the ferrites isFe2O3.MO, where M is a divalent metal.One common example is magnetite, inwhich M is Fe2+.

ferroelectric /fe-roh-i-lek-trik/ A type ofsolid material that has a spontaneous di-pole moment. The name comes from theanalogy with a spontaneous magnetic mo-ment in a ferromagnetic material. Like fer-romagnets, ferroelectric materials have adomain structure and undergo hysteresis.Barium titanate and Rochelle salt are ex-amples of ferroelectric materials.

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ferroelectric

ferromagnetism /fe-roh-mag-nĕ-tiz-ăm/The MAGNETISM of substances caused by adomain structure. Such substances have alarge susceptibility and relative permeabil-ity. Rough values of relative permeabilityare: iron 1000, cobalt 50, nickel 40. Seealso Curie’s law; hysteresis cycle.

fertile material Material that can be con-verted into fissile material by irradiationwith neutrons. 238U and 232Th are fertilematerials, being converted into 239Pu (via239U) and 233U (via 233Th) respectively.Conversion is commonly carried out inbreeder reactors. Present breeder reactorsuse 238U as the fertile material.

FET See field-effect transistor.

Feynman diagram /fÿn-măn/ A drawingconvention that represents interactions be-tween elementary particles, which are rep-resented as directional lines; photons aredrawn as wavy lines. The diagrams arenamed for the American physicist RichardFeynman (1918–88).

fiber optics The use of fine transparentfibers to transmit light. The light passesalong the fibers by a series of internal re-flections. Optical fibers of this type can beused to view inaccessible objects and tocarry laser signals in telecommunications.

field The concept of a field was intro-duced to explain the interaction of parti-cles or bodies through space. An electriccharge, for instance, modifies the spacearound it such that another charge in thisregion experiences a force. The region is anelectric field (a field of force). Magneticand gravitational fields can be similarly de-scribed.

field coil The winding in a generator orelectric motor that produces the magneticfield.

field-effect transistor (FET) A solid-state electronic device with three terminalsthat, like the junction TRANSISTOR, is usedin amplifiers. It controls the current be-tween two terminals, the source and the

drain, by the voltage at a third, the gate. Ann-type FET consists of a single piece of n-type semiconductor, which has the sourceat one end and the drain at the other. Aheavily-doped p-type region in the middleforms the gate. If the gate voltage is morenegative than the source, electrons movefrom the n-type region to the p-type regionleaving an area round the gate with fewerelectrons to carry current. This has the ef-fect of narrowing the conducting channelthrough which the source-drain currentflows by an amount that depends on thesource-gate voltage difference. In the FET,only one type of charge carrier – electronsin the n-type FET and holes in the p-typeFET – determines the current and it istherefore known as a unipolar transistor.In the bipolar junction transistor, bothpositive and negative charge carriers con-tribute to the other current.

field emission (cold emission) The releaseof electrons from a surface as a result of astrong external electric field. Very highelectric fields are necessary; these are ob-tained at sharp points.

field-emission microscope (FIM) A typeof electron microscope which uses fieldemission from a metal point at very highvoltage to investigate atoms in the surfaceof the material. Electrons emitted from thepoint are accelerated to a conducting fluo-rescent screen, on which they form a mag-nified image of the metal tip.

field ionization The ionization of atomsat a surface caused by a high electric field.It is used in the field-ion microscope, whichoperateson a similar principle to the field-emission microscope.

field lens The lens farthest from the eye ina compound eyepiece. Compare eye lens.

field magnet An electromagnet or perma-nent magnet that provides the magneticfield in an electric machine, such as amotor or generator.

field strength, electric See electric fieldstrength.

ferromagnetism

94

fifth force See interaction.

filament A fine thread of metal, glass, etc.

filter 1. A device that passes only certainfrequencies of radiation. A red filter, forexample, is a piece of translucent materialthat transmits red light, absorbing otherwavelengths.2. An electronic circuit that transmits cur-rents within a certain range of frequencies,while reducing (attenuating) other frequen-cies.

filter pump A simple type of laboratoryvacuum pump in which there is a narrownozzle in the middle of the pump throughwhich water is forced. There is a reductionin pressure near the nozzle (see Bernoullieffect), causing air to flow in from a sidetube that connects the pump to the vesselthat is being evacuated. The water and airare forced through the bottom of thepump.

fine structure Closely spaced lines seen athigh resolution in a spectral line or band.Fine structure may be caused by vibra-tional motion of the molecules or by elec-tron spin. Hyperfine structure, seen at veryhigh resolution, is caused by interactionsbetween the spin of the atomic nucleus andthe orbiting electrons affecting the possibleenergy levels of the atom.

fine structure constant Symbol α. Aconstant that characterizes the electromag-netic interaction at the quantum level. It isdefined by α = e2/h

_c, where e is the charge

of an electron, h_

is the Dirac constant, i.e.the Planck constant divided by 2π, and c isthe speed of light in a vacuum. It has beensuggested that the value of α has changedduring the evolution of the Universe but atpresent there is not conclusive evidence forthis.

fissile material /fiss-ăl/ Material that un-dergoes nuclear fission, sometimes sponta-neously but usually when irradiated byneutrons. Examples are 235U, 239Pu, and233U. Fissile material is the fuel of nuclear

reactors and the explosive material of nu-clear weapons.

fission /fish-ŏn/ See nuclear fission.

fission products Isotopes that resultfrom NUCLEAR FISSION, usually havingabout the same mass.

fission reactor See nuclear reactor.

fission-track dating A method of mea-suring the age of glasses and other mineralsthat depends on the tracks made in thesesolids by fragments from the spontaneousfission of contained uranium. The densityof tracks in the material depends on theuranium content, the age of the material,and any fading of the tracks. After count-ing the tracks, the uranium content is esti-mated by irradiating the materials withneutrons to induce fissions. The number ofextra tracks produced depends on the ura-nium content, which can then be esti-mated, giving the age since solidification.

fixed point See International PracticalTemperature Scale; temperature scale.

flash point The lowest temperature atwhich a volatile substance producesenough flammable vapor to produce aflash when a flame is applied.

flavor See quark.

F-layer See Appleton layer.

Fleming’s rules A method of remember-ing the relationship between the directionsof current, magnetic field, and motion inelectric motors and generators. Fleming’sleft-hand rule applies to motors. If the lefthand is held with the thumb and first twofingers all mutually at right angles, thethumb shows motion (force); the first fin-ger, field; and the second finger, current.Fleming’s right-hand rule is similar butwith the fingers of the right hand showingthe operation of an electrical generator.The rules were formulated by the Britishphysicist and electrical engineer Sir JohnAmbrose Fleming (1849–1945).

95

Fleming’s rules

flint glass See optical glass.

flip-flop See bistable circuit.

floating objects, law of See flotation;law of.

flotation, law of An object floating in afluid displaces its own weight of fluid. Thisfollows from Archimedes’ principle for thespecial case of floating objects. (A floatingobject is in equilibrium, its only supportcoming from the fluid. It may be totally orpartly submerged.)

fluctuations Random differences be-tween the average value of a quantity andthe actual values found. Fluctuations areimportant in statistical mechanics, espe-cially the theory of phase transitions andBrownian motion, and in quantum me-chanics.

fluid A substance that flows; i.e. a liquidor a gas.

fluidics /floo-id-iks/ The study and use offluid flow through pipes in an analogousway to the flow of electric current throughcircuits. Fluidic circuits may be useful incircumstances in which there are high mag-netic fields or radiation levels, whichwould affect electrical circuitry.

fluidity The property of a fluid that en-ables it to flow easily; it is the opposite ofVISCOSITY.

fluidization /floo-id-ă-zay-shŏn/ Amethod of passing a gas through a finelypowdered solid so that is acquires the char-acteristics of a fluid (so that it flows, can bepumped, etc.).

fluid mechanics The study of the me-chanics of fluids, i.e. liquids and gases. Thestudy of fluids that are at rest is called fluidstatics and the study of fluids in motion iscalled fluid dynamics. The specific study ofliquids at rest is called hydrostatics. Fluiddynamics is divided into hydrodynamics,which is the study of motion in liquids, and

aerodynamics, which is the study of mo-tion in gases.

fluorescence /floo-ŏ-ress-ĕns/ The ab-sorption of energy by atoms, molecules,etc., followed by immediate emission ofelectromagnetic radiation as the particlesmake transitions to lower energy states.Fluorescence is a type of LUMINESCENCE inwhich the emission of radiation does notpersist after the exciting source has been re-moved. The excited states have very shortlifetimes.

Fluorescence, like luminescence, can beproduced in a number of ways. Examplesare by bombardment with electrons and byabsorption of other electromagnetic radia-tion. In the case of electromagnetic radia-tion the emitted radiation often has lowerfrequency than the absorbed radiation. Aparticular example is the absorption of ul-traviolet radiation followed by emission ofvisible radiation. This effect is used in fluo-rescent paints and in ‘fabric brighteners’added to detergents. The inside coating offluorescent tubes is another example of amaterial that converts ultraviolet radiation(from the discharge) into visible radiation.

fluorescent lamp /floo-ŏ-ress-ĕnt/ Alamp consisting of an electric glow dis-charge tube, the inner surface of which iscoated with phosphor. The gas in the tube(often mercury vapor) gives visible lightand ultraviolet. The ultraviolet radiationgenerates further visible light in the phos-phor by fluorescence. The fluorescence in-creases the visible output and also, by asuitable choice of phosphor, it is possibleto obtain a combination of wavelengths vi-sually equivalent to white light.

fluorine /floo-ŏ-reen, -rin/ A slightlygreenish-yellow highly reactive gaseous el-ement belonging to the halogens. It isslightly more abundant than chlorine, ac-counting for about 0.065% of the Earth’scrust. Fluorine is the most reactive andmost electronegative element known; infact it reacts directly with almost all the el-ements, including the rare gas xenon.

flint glass

96

Symbol: F; b.p. –188.14°C; m.p.–219.62°C; d. 1.696 kg m–3 (0°C); p.n. 9;r.a.m. 18.99840.32.

fluoroscope /floo-ŏ-rŏ-skohp/ An instru-ment that makes x-rays, or other non-vis-ible radition, visible by means of afluorescent screen.

flux In general, a flow or apparent flow.1. A flow of particles per unit area.2. The density of lines of force in a field.See magnetic flux.3. See luminous flux.

flux density See magnetic flux density.

fluxmeter /fluks-mee-ter/ An instrumentfor measuring magnetic flux. The mostcommon type uses a small movable explor-ing coil (a search coil), which is placed inthe field and then removed quickly. The in-duced current can be measured by a ballis-tic galvanometer. See also Earth inductor.

flywheel A large heavy wheel (with alarge moment of inertia) used in mechani-cal devices. Energy is used to make thewheel rotate at high speed; the inertia ofthe wheel keeps the device moving at con-stant speed, even though there may be fluc-tuations in the torque. A flywheel acts asan ‘energy-storage’ device.

FM See frequency modulation.

f-number For an optical instrument, es-pecially a camera, the ratio of the focal dis-tance (f) to the aperture diameter (d):

f-number = f/dIf the ratio is 16 the f-number is writtenf16, f:16, or f/16.

focal distance (focal length) A measureof the power of a lens or mirror to con-verge a parallel beam. The focal distance ofa lens or mirror is the distance between thepole and the focal point. Normally, posi-tive values relate to converging lenses andmirrors, and negative values relate to di-verging ones, (real is positive, virtual isnegative convention). The New Cartesianconvention is less common. It gives posi-tive focal distances to diverging mirrorsand converging lenses, and negative valuesfor converging mirrors and diverginglenses.

For a refracting surface:f = n1r/(n2 – n1)

where n is refractive constant and r is ra-dius of curvature.

For a reflecting surface:f = r/2

For a thin lens in air:1/f = (n – 1)(1/r1 – 1/r2)

For two thin lenses in contact:1/f = 1/f1 + 1/f2

focal length See focal distance.

97

focal length

F focalpoint

focal planecaustic surface

Focal point

FOCAL POINTS FOR LENSES AND MIRRORSFocal point Position Focal distance

converging lens real far side of lens positivediverging lens virtual near side of lens negativeconverging mirror real in front of mirror positivediverging mirror virtual behind mirror negative

focal plane The plane perpendicular tothe axis centered on the focal point of alens or mirror.

focal point (focus; principal focus) Apoint through which rays close and paral-lel to the axis pass or appear to pass afterreflection or refraction. A reflector has onefocal point. As radiation can enter a lensfrom either side, a symmetrical lens has afocal point on each side, at the same dis-tance from the lens. Only rays close andparallel to the axis pass through the focalpoint. These are called paraxial rays. Raysparallel to the axis but not close to it focussomewhere on the caustic surface. Raysclose to the axis but not parallel to it focussomewhere on the focal plane. See illustra-tion on page 97.

focal power See diopter; power.

focus (pl. focuses or foci) 1. See focalpoint.2. An image is in focus if it is sharp ratherthan blurred (out of focus). Only then dothe set of rays from a point on the object allpass through a single point.3. A point through which each member ofa set of rays passes or appears to pass afterreflection or refraction. Paraxial rays focusat the focal point; other sets may focus onthe focal plane or on the caustic surface.Others again, from the surface of an object,focus on the image plane to form theimage.

foot Symbol: ft The base unit of length inthe f.p.s. system (one third of a yard). It isequal to 0.304 8 meter.

foot lambert An obsolete unit of lumi-nance equal to the luminance of a surfacethat reflects or emits one lumen per squarefoot. It is equal to 3.426 259 candelas persquare meter.

foot pound A f.p.s. unit of energy orwork equal to the work required to move aone-pound mass one foot in the directionof the applied force. It is equal to1.355 818 joules.

forbidden band See energy bands.

force Symbol: F That which tends tochange an object’s momentum. Force is avector; the unit is the newton (N). In SI,this unit is so defined that:

F = d(mv)/dt(from Newton’s second law). See Newton’slaws of motion.

forced convection See convection.

forced oscillation The oscillation of asystem or object subjected to an externalperiodic force. The oscillations have thesame frequency as the applied force. Theamplitude depends greatly upon the differ-ence between the driving frequency and thefrequency of free oscillation of the system.Compare free oscillation. See also reso-nance.

force meter An instrument for directlymeasuring force (in newtons). It resemblesa spring balance.

force ratio (mechanical advantage) For asimple machine, the ratio of the outputforce (load) to the input force (effort).There is no unit; the ratio is, however,often given as a percentage. It is quite pos-sible for force ratios far greater than one tobe obtained. Indeed the design of manymachines is to make this so, to make asmall effort overcome a large load.

However efficiency cannot be greaterthan one; a large force ratio implies a largedistance ratio. See also efficiency; machine.

forces, parallelogram (law) of See par-allelogram of vectors.

forces, triangle (law) of See triangle ofvectors.

formula (pl. formulas or formulae) 1. Ageneral rule, often represented by symbols.For example, A = πr2 is a formula givingthe area of a circle in terms of the radius.2. A representation of a compound (ormolecule) using the chemical symbols forthe elements.

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98

Foucault pendulum /foo-koh/ A simplependulum consisting of a heavy bob on along string. The plane of vibration rotatesslowly over a period of time as a result ofthe rotation of the Earth below it. The ap-parent force causing this movement is theso-called Coriolis force. The pendulum isnamed for the French physicist JeanBernard Léon Foucault (1819–68).

Fourier methods /foo-ree-ay/ Methodsfor analyzing periodic functions in whichthe periodic function is represented as asum of sine waves in which the frequenciesof all the waves are simple multiples of afundamental frequency. There are manyimportant applications of Fourier methodsin physics, such as the theory of sound andthe analysis of patterns in x-ray crystallog-raphy. This analytical approach is namedfor the French mathematician and physicistJean Baptiste Joseph Fourier (1768–1830).

fovea /foh-vee-ă/ (pl. foveae) An areaabout half a millimeter across in the centerof the yellow spot of the human retina.Here the cones are most dense and thereare no rods. It is the part with the greatestvisual acuity but has low sensitivity to dimlight. See eye; yellow spot.

fps units A system of units based on thefoot, pound, and second. It has been re-placed in scientific use by SI units.

frame of reference A set of coordinateaxes by which the position of any objectmay be specified as it changes with time.The origin of the axes and their spatial di-rection must be specified at every instant oftime for the frame to be fully determined.

francium /fran-see-ŭm/ A radioactive ele-ment of the alkali-metal group. It is foundon Earth only as a short-lived product ofradioactive decay, occurring in uraniumores in minute quantities. A large numberradioisotopes of francium are known.

Symbol: Fr; m.p. 27°C; b.p. 677°C; p.n.87; most stable isotope 223Fr (half-life 21.8minutes).

Fraunhofer diffraction /frown-hoh-fer/Diffraction observed with incident parallellight. In Fraunhofer diffraction the wave-fronts are parallel. Although a special caseof FRESNEL DIFFRACTION, it is far more im-portant in most practical cases. Thus it isused to explain single – and multiple – slitpatterns, as well as those produced by cir-cular holes. The Fraunhofer diffraction isnamed for the German optician and physi-cist Josef von Fraunhofer (1787– 1826).

Fraunhofer lines The dark lines in thespectrum of light from the Sun, caused bythe absorption of particular wavelengthsby certain elements in its cooler outer re-gions. The wavelengths of these lines areused as reference points in specifying quan-tities that vary with wavelength, e.g. re-fractive constants.

free electron An electron that can movefreely from one atom or molecule to an-other under the influence of an externalelectric field. The moving free electronsconstitute an electric current, as in con-ducting metals or electrons moving in athermionic tube.

free energy A measure of the ability of asystem to do useful work. See Gibbs func-tion; Helmholtz function.

free fall Movement of a body in a gravi-tational field with no other forces acting onit. See acceleration of free fall; weightless-ness.

free oscillation (free vibration) An oscil-lation at the natural frequency of the sys-tem or object. Thus a pendulum can beforced to swing at any frequency; it willswing freely at only one, which depends onits length. Compare forced oscillation. Seealso resonance.

free surface energy See surface tension.

free vibration See free oscillation.

freezing The change from the liquid to thesolid state that occurs when energy is trans-ferred from a substance. For pure sub-

99

freezing

stances this happens at a characteristictemperature known as the freezing point(or melting point). This depends on pres-sure, so is usually measured at standard at-mospheric pressure. Impurities generallylower the freezing point.

freezing mixtures Two or more sub-stances mixed together to produce a lowtemperature. A mixture of salt and ice inwater is a common example.

freezing point See freezing.

Frenkel defect /frenk-ĕl/ See defect.

frequency Symbol: f, v The number of cy-cles per unit time of an oscillation (e.g. apendulum, vibrating system, wave, alter-nating current, etc.). The unit is the hertz(Hz).

Angular frequency (pulsatance) are re-lated to frequency by ω = 2πf. The unit isthe radian per second (rad s–1).

frequency modulation (FM) A type ofmodulation in which a carrier wave ismade to carry the information in a signal(audio or visual) by fluctuations in the fre-quency of the carrier. The variation of thecarrier frequency is proportional to the fre-quency of the signal, while the amplitudeof the carrier remains constant. Frequencymodulation is superior to amplitude MOD-ULATION because a wider band of frequen-cies may be transmitted with lessinterference and noise, although it is lim-ited to line-of-sight distances. See also car-rier wave.

Fresnel biprism /fray-nel/ See biprism,Fresnel’s.

Fresnel diffraction Diffraction observedwhen either source or screen (or both) areclose to the diffractor. In Fresnel diffrac-tion, the wavefronts are not plane (as inFraunhofer diffraction) and analysis is dif-ficult. The approach is useful in explaining(for instance) diffraction around a circularobstacle. Fresnel diffraction is named forthe French physicist Augustin Jean Fresnel(1788–1827).

Fresnel lens A type of lens with one sur-face cut in steps so that transmitted light isrefracted just as if by a much thicker (andheavier and more expensive) conventionallens. Lighthouse lamp lenses have longbeen of this type. Very cheap plastic Fres-nel lenses now have many uses, for exam-ple in overhead projectors, flashlamps, etc.The angle of each step is made to producethe desired effect.

Fresnel zones See half-period zones.

friction Friction is the name given to var-ious forces that oppose the relative mo-tions of bodies.

Fluid friction is usually caused by tur-bulent flow for large systems and highspeeds, and by viscosity for low speeds andsmall systems, for example thin films of lu-bricant.

When two solid surfaces are in contacteach exerts a force of friction on the other,preventing sliding, up to a limiting value,the force of static or limiting friction. Ifsliding occurs there are dissipative forces ofkinetic friction. When a body rolls on a flatsurface its motion is opposed by rollingfriction.The laws of friction are:1. The frictional forces are independent of

the apparent area of contact for thesame normal force.

2. The forces of limiting, kinetic, androlling friction are proportional to thenormal forces.

These laws are fairly accurate for limitingand kinetic friction but less so for rollingfriction.

freezing mixtures

100

to poleof lens

Fresnel lens

The coefficient of limiting friction is de-fined by

µL = F/Swhere F is the limiting value of the force offriction and S is the normal (support) force.µL is very nearly constant for given surfacesand typically has values from 0.5 to 2.

The coefficient of kinetic friction is de-fined by

µK = F1/Swhere F1 is the force of friction when thebodies are sliding at constant speed. µK isgenerally less than µL for the same surfacesand is independent of speed, except at highspeeds.

The coefficient of rolling friction is de-fined by

µR = FR/Swhere FR is the force opposing the motionof the rolling body. Generally µR is muchless than µL and µK for the same materials.It increases slightly with increase of S anddepends in a complicated way upon speed.It is smaller for rollers or wheels of largeradius.

Friction generally is caused by imper-fect elasticity in the substances interacting.In the case of hard materials such as metals

the real area of contact is much less thanthe apparent area. The bodies interact bymicroscopic irregularities (asperities),which occur even on those surfaces whichappear smooth on optical examination ortouch. The asperities are subject to largestresses and therefore undergo plastic flowor even weld together. Lubricants keep thesurfaces apart and so prevent the asperitiesfrom touching. For softer substances thereal areas of contact are larger and frictioninvolves elastic hysteresis in the surfacelayers.

Rolling friction is caused mainly byelastic hysteresis, for example in the case ofa car tire on hard ground it is caused byhysteresis in the rubber. Lubrication hasvery little effect on rolling friction sincethere is generally no slip between the sur-faces.

fringes The light and dark bands obtainedby interference or diffraction of light.

frost 1. Hoarfrost or white frost: a depositof needle-like ice crystals on the ground orother exposed surfaces. It is formed by di-rect condensation of water vapor on sur-

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frost

relative motion(a = O)

W

R PF

W

RF 1 P 1

W

R

F

Slip about to occur:µs = F /R = P /Wµs is coefficient of sliding friction

Slip at steady speed:µk = F 1 /R = P 1 /Wµk is coefficient of sliding (kinetic) frictionP 1 < P µk < µs

Slip on a slope:µ = F /R = tan (This can be applied either to static or tosliding friction)

Friction

faces below the freezing point. See alsodew.2. Glazed frost: a thin clear layer of iceformed on a cold surface by impact ofwater droplets, or by the freezing of a layerof water.

fuel cell A type of cell in which fuel is con-verted directly into electricity. In one form,hydrogen gas and oxygen gas are fed to thesurfaces of two porous nickel electrodesimmersed in potassium hydroxide solu-tion. The oxygen reacts to form hydroxyl(OH–) ions, which it releases into the solu-tion, leaving a positive charge on the elec-trode. The hydrogen reacts with the OH–

ions in the solution to form water, givingup electrons to leave a negative charge onthe other electrode. Large fuel cells cangenerate tens of amperes. Usually the e.m.f.is about 0.9 volt and the efficiency around60%.

full-wave rectifier An electrical devicethat ensures that current flows almost en-tirely in one direction by using two pairs ofdiodes. In this way, every half-cycle con-tributes to the current. The signal pro-duced in this way can be smoothed byusing a capacitor.

fundamental The simplest way (mode) inwhich an object can vibrate. The funda-mental frequency is the frequency of thisvibration. The less simple modes of vibra-tion are the higher harmonics; their fre-quencies are higher than that of thefundamental. See also quality of sound.

fundamental constants (universal con-stants) Quantities that do not changeunder any known circumstances. Examplesare the speed of light in a vacuum and thecharge on an electron. It has been specu-lated that the values of the fundamentalconstants could change over the history ofthe universe. There is some tentative evi-dence that this is the case in the FINE STRUC-TURE CONSTANT. At the time of writing, thisevidence cannot be regarded as firmly es-tablished.

fundamental interval See temperaturescale.

fundamental particles See elementaryparticles.

fundamental units The base units of ameasurement system, especially those thatdeal with force and motion. Usually these

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102

SOME FUNDAMENTAL CONSTANTS

Quantity Magnitude Unitspeed of light 2.997 925 × 108 m s–1

Planck constant 6.626 069 × 10–34 J sBoltzmann constant 1.380 625 5 × 10–23 J K–1

Avogadro constant 6.022 142 × 1023 mol–1

mass of proton 1.672 622 × 10–27 kgmass of neutron 1.674 927 × 10–27 kgmass of electron 9.109 383 × 10–31 kgcharge of proton or electron ±1.602 176 5 × 10–19 Cspecific charge of electron –1.758 820 × 1011 C kg–1

molar volume at s.t.p. 2.241 40 × 10–2 m3mol–1

Faraday constant 9.648 534 × 104 C mol–1

triple point of water 273.16 Kabsolute zero –273.15 °Cpermittivity of vacuum 8.854 187 8 × 10–12 F m–1

permeability of vacuum 4π × 10–7 H m–1

Stefan constant 5.670 400 × 10–8 W m–2K–4

molar gas constant 8.314 472 J mol–1K–1

gravitational constant 6.674 2 × 10–11 N m2kg–2

are the units of length, mass, and time, plusat least one electrical unit. In SI, the funda-mental units are the meter, the kilogram,the second, and the ampere. See also baseunit.

fuse A protective device in an electric cir-cuit consisting of a low-melting wire thatmelts and breaks the circuit if too muchcurrent flows through it. See also circuitbreaker.

fusion 1. The interaction of light nucleisuch that heavier nuclei are produced.There are two distinct classes of fusion re-actions.

In the Sun and other stars fusion of pro-tons to form helium nuclei takes placeslowly by processes involving weak inter-actions (see carbon cycle; proton-protonchain reaction). On Earth nuclei of heavyisotopes of hydrogen can be made to reactby strong interactions, as follows:

21H + 21H → 3

2He + 10n21H + 21H → 3

1H + 11H31H + 21H → 4

2He + 10nIn each case two particles are produced,one heavier and the other lighter than theoriginal ones. The large energy release ap-pears as kinetic energy of the products.More energy is released by the subsequentreactions of the neutrons with nearby ma-terials.

In both classes of reaction the nucleihave to approach so closely that the short-range nuclear field of force can act. This isopposed by the long-range electric repul-sion of the positive charges. This is over-come by the substance being at a very hightemperature (107–108 K) so that the nucleihave sufficient kinetic energies to makeenough close collisions for the interactionsto occur. Hence such fusion processes arecalled thermonuclear reactions. At suchhigh temperatures matter is in the form ofa plasma of free nuclei and free electrons;there are no atoms.

Fusion can be initiated by the explosionof an atomic bomb using nuclear fission. Ahydrogen bomb contains a quantity ofheavy isotopes of hydrogen which arecaused to fuze by the detonation of a fis-sion bomb. Controlled fusion reactions foroperating electrical generating stations arethe subject of much research. The gas isheated to form a plasma at high tempera-tures by electric discharges, or possibly bylaser radiation. The plasma is contained byintense magnetic fields. Such plasmas arefound to be subject to many kinds of insta-bility and there are large problems to beovercome before fusion power becomes acommercial proposition.2. See melting.

fusion reactor See nuclear reactor.

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fusion reactor

104

gadolinium /gad-ŏ-lin-ee-ŭm/ A ductilemalleable silvery element of the lanthanoidseries of metals. It occurs in associationwith other lanthanoids. Gadolinium isused in alloys, magnets, and in the elec-tronics industry.

Symbol: Gd; m.p. 1313°C; b.p.3266°C; r.d. 7.9 (25°C); p.n. 64; r.a.m.157.25.

gain A ratio measuring the efficacy of anelectronic system, usually an amplifier oran antenna. The voltage gain of an ampli-fier is the ratio of the output voltage devel-oped across a load to the input voltage.The gain of a power amplifier is the ratio ofthe output power to the input power.

galactic dynamics The mathematicalstudy of the dynamics of galaxies. Galacticdynamics is based on the Newtoniantheory of gravity. An example of galacticdynamics is the orbit of a galaxy about thecenter of gravity of the galaxy cluster towhich the galaxy belongs.

galaxy A collection of a large number of

stars (up to 100 billion) and their satellitesexisting as a discernable unit held togetherby gravity. The galaxy to which our Sun(and the Earth) belong is called the MilkyWay Galaxy, or, often, just the Galaxy(capital letter ‘G’).

Galilean telescope /gal-ă-lee-ăn/ A typeof refracting telescope having a convergingobjective and a diverging eyepiece. TheGalilean arrangement produces an uprightfinal image. However the field of view issmaller than that of the Keplerian telescope(which gives an inverted image). Thearrangement is used in cheap binoculars(opera glasses). The normal adjustment ofthis telescope has the intermediate image inthe focal planes of both lenses. These aretherefore separated by a distance fO – fE(New Cartesian sign convention). This wasthe first kind of telescope to be used in as-tronomy. With its aid, the Italian as-tronomer and physicist Galileo(1564–1642) discovered the four largestmoons of Jupiter in 1610. See also refrac-tor.

gallium /gal-ee-ŭm/ A soft silvery low-melting metallic element. Gallium is usedin low-melting alloys, high-temperaturethermometers, and as a doping impurity insemiconductors. Gallium arsenide is asemiconductor used in light-emittingdiodes and in microwave apparatus.

Symbol: Ga; m.p. 29.78°C; b.p.2403°C; r.d. 5.907 (solid at 20°C), 6.114(liquid); p.n. 31; r.a.m. 69.723.

galvanic cell /gal-van-ik/ See cell.

galvanometer /gal-vă-nom-ĕ-ter/ An in-strument for measuring small direct cur-rents. See moving-coil instrument; tangent

G

observer

divergingeye lensconverging

object lens

first image(virtual)

final virtualimage

Galilean telescope

galvanometer. See also ballistic gal-vanometer.

gamma /gam-ă/ (γ) The ratio of the prin-cipal specific thermal capacity of a gas atconstant pressure to that at constant vol-ume (cp/cv). See adiabatic change; sound;specific thermal capacity.

gamma decay A type of radioactivedecay in which gamma rays are emitted bythe specimen. Gamma decay occurs when anuclide is produced in an excited state,gamma emission occurring by transition toa lower energy state. It can occur in associ-ation with alpha decay and beta decay.

gamma radiation Properly, gamma radi-ation is a form of electromagnetic radia-tion emitted by atomic nuclei, but often theterm is used loosely for radiations withsimilar (or higher) quantum energies de-rived from other sources.

Gamma rays from nuclei have wave-lengths typically in the range 10–10 m to10–13 m, with quantum energies in therange 10 keV to 10 MeV (10–15 J to10–12 J). Homogeneous gamma radiation isabsorbed exponentially in matter, causingionization by secondary electrons. Thisionization is the basis of methods of de-tecting the radiation. In living cells it cancause chemical changes that can be harm-ful.

Penetration of matter by gamma radia-tion depends very much upon the wave-length, and the atomic numbers of theatoms. For radiations of the shorter wave-lengths shields of lead several centimetersthick are needed, whereas some long wave-length rays may be absorbed almost totallyin thin foils.

Nuclei emit gamma radiation whenthey return to the ground state after excita-tion. The excited states have lifetimes thatare usually of the order of a picosecond(10–12 s) or less, but some states are knownwith much longer lifetimes. The emissionof alpha or beta rays, or the capture of elec-trons by the nucleus, often leaves the nu-cleus in excited states, as doesbombardment with nuclear particles – par-ticularly neutrons. Gamma emission does

not change the proton or neutron numbersof the nucleus.

gamma-ray burst A dramatic cosmicevent in which a powerful source ofgamma rays briefly appears in the sky (fortimes ranging from less than a second to afew minutes). It is thought that gamma-raybursts occur because of the formation of aBLACK HOLE, either by the merging of twoneutron stars or the gravitational collapseof a single large star.

gamma rays Streams of gamma radiation

gas See states of matter.

gas constant (universal molar gas con-stant) Symbol: R The universal constant8.314 472 J mol–1K–1 appearing in theequation of state for an ideal gas.

gas-cooled reactor A nuclear reactor inwhich cooling of the core is achieved bycirculation of a gas. Early reactors werecooled by air. Magnox reactors are cooledby high-pressure carbon dioxide. Ad-vanced gas-cooled reactors (AGR) are alsocooled by carbon dioxide. The high-tem-perature gas-cooled reactor (HTGR) iscooled by helium.

gas equation The equation of state for anideal gas. See gas laws.

gas laws Laws relating the temperature,pressure, and volume of a fixed mass ofgas. The main gas laws are Boyle’s law andCharles’ law. The laws are not obeyed ex-actly by any real gas, but many commongases obey them under certain conditions,particularly at high temperatures and lowpressures. A gas that would obey the lawsover all pressures and temperatures is aperfect or ideal gas. Boyle’s and Charles’laws can be combined into an equation ofstate for ideal gases:

pVm = RTwhere Vm is the molar volume and R themolar gas constant. For n moles of gas

pVm = nRTAn ideal gas is defined as one that obeys

Boyle’s law at all temperatures and pres-

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sures. It is realized by extrapolating resultsobtained for real gases to zero pressure. IfpVm is plotted against p at a given temper-ature, where Vm is the molar volume, thevalue (pVm)p=0 is used to define the idealgas temperature T

(pVm)p=0 = RTwhere the molar gas constant R is the samefor all gases. Real gases often conformclosely to Boyle’s law over a considerablerange of p and T, and the equation of statefor this range can be written

pVm = RTMore exact equations are needed whenthere are significant departures fromBoyle’s law. See van der Waals’ equation.

gas thermometer A thermometer thatuses a fixed mass of gas as its working sub-stance. It can take two forms. A constantvolume gas thermometer depends on thedirect proportion relationship between thepressure of a fixed mass of gas and its ab-solute temperature at constant volume. Aconstant pressure gas thermometer is de-pendent on the similar relationship be-tween the volume and temperature of thegas.

Constant volume gas thermometersmay use helium, hydrogen, or nitrogen.The typical arrangement is a bulb con-nected to a U-tube containing mercury. Asthe temperature changes the heights ofmercury are adjusted such that the volumeof gas in the bulb is constant. The pressureis measured by differences in the heights ofthe mercury. Corrections can be made forexpansion of the bulb, temperature of themercury, and nonideal behavior of the gas.

gate 1. A signal that enables a circuit tofunction.2. An electrode in a semiconductor deviceto which a biasing voltage is applied tomodify the conductivity. See field-effecttransistor.3. A circuit that has one or more inputs butonly one output. This is a digital gate asused in logic circuits.4. A circuit that admits an input for only aspecified time, producing an output pro-portional to the input, or to some other

function of the input. See also semiconduc-tor.

gauss /gows/ Symbol: G The unit of mag-netic flux density in the c.g.s. system. It isequal to 10–4 tesla.

Gauss’s law A result in electrostatics stat-ing that the total electric flux at right an-gles to a closed surface with electriccharges inside is proportional to the alge-braic sum of these charges. It is named forthe German mathematician Carl FriedrichGauss (1777–1855), who discovered thelaw in the 1830s.

Gay-Lussac’s law See Charles’ law.

gear In a machine, a toothed wheel thatmeshes with another toothed wheel totransfer rotation from one shaft to an-other. Generally the shafts are parallel, butbevel gears meshing at right angles changethe direction of rotation through 90°. Theratio of the numbers of teeth on two mesh-ing gear wheels is the gear ratio. If they aredifferent, the second (driven) shaft rotatesat a different speed from the drive shaft.

Geiger counter /gÿ-ger/ (Geiger-Müllercounter) A device for detecting ionizing ra-diation to provide a count of individualparticles and photons. The construction isa gas-filled tube with a cylindrical metalcathode and a thin axial wire anode. Thepotential difference applied between thetwo depends on the design, but is usuallybetween about 400 and 2000 volts. Thegas may be low-pressure air or argon withethanol vapor. Low-energy particles canenter through a thin ‘window’, often ofmica. Passage of an alpha or beta particleor a photon of gamma radiation throughthe gas produces ions, which move to-wards the electrodes. The electrons acceler-ating towards the central anode acquiresufficient kinetic energy to ionize other gasmolecules, initiating an ‘avalanche’ of elec-trons, which produces a measurable pulseat the anode. The pulse of current can beused to operate counting equipment. SomeGeiger tubes contain a small amount ofhalogen vapor to quench the avalanche

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rapidly so that the tube returns quickly toa state in which it is ready to detect anotherpulse. Several thousand particles per sec-ond can be counted in this way. The deviceis named for the German physicist HansWilhelm Geiger (1882–1945), who in-vented it in 1912. The design was im-proved by the German physicist WaltherMüller (1905–79) in 1928.

Geiger–Nuttall law /nut-awl/ A relation-ship between the decay constant γ of analpha emitter and the kinetic energy E ofthe alpha particle emitted. The rule is thatE is directly proportional to log γ.

Geissler tube /gÿs-ler/ An electric dis-charge tube consisting of a glass tube withsealed-in electrodes and containing tracesof gas at very low pressure. When a highvoltage is applied to the electrodes, the gasionizes and light is emitted from excitedatoms and ions (fluorescence). The tube isnamed for the German physicist JohannHeinrich Wilhelm Geissler (1815–79).

gel /jel/ A semi-rigid COLLOID.

general theory See relativity.

generator A large machine for convertingmechanical energy into electrical energy. Ithas two sets of coil windings. One (the sta-tor) is fixed and the other (the rotor) ro-tates. The relative motion of the two sets ofcoils induces an electric current in them.This is the reverse of a motor. In an electri-cal power station, generators are usuallyturned by steam turbines or water turbines.The turbine turns the generator, oftencalled an alternator, which produces alter-nating current of a fixed frequency. Dieselmotors are used to turn smaller generatorsof the type kept for emergency use in hos-pitals, etc. See also dynamo; electric motor.

geomagnestism /jee-ŏ-mag-nĕ-tiz-ăm/See Earth’s magnetism.

geometrical optics See optics.

geophysics The branch of physics con-cerned with the Earth and its interior. It is

often taken to include also meteorologyand oceanography.

geothermal energy Energy that comesfrom within the Earth. Examples ofsources of geothermal energy include vol-canoes, hot springs, and geysers. In someparts of the World, it is possible to utilizesources of geothermal energy.

germanium /jer-may-nee-ŭm/ A hardbrittle gray metalloid element. Most ger-manium is recovered during zinc or copperrefining as a by-product. Germanium wasextensively used in early semiconductor de-vices but has now been largely supersededby silicon. It is used as an alloying agent,catalyst, phosphor, and in infrared equip-ment.

Symbol: Ge; m.p. 937.45°C; b.p.2830°C; r.d. 5.323 (20°C); p.n. 32; r.a.m.72.61.

getter /get-er/ A chemical substance usedfor removing residual gases after a vacuumhas been produced by pumping. Gettersare usually metals that combine with oxy-gen or nitrogen to produce a very high vac-uum.

GeV Gigaelectronvolts; 109 electronvolts.Often BeV is used in the USA.

ghost A faint image near the image re-quired, caused by radiation that has takena different path. In the case of traditional‘silvered’ glass mirrors, the main imagesare caused by light from the backing of theglass. Ghost images, formed by reflectionfrom the front surface of the glass, may bea tenth as bright as the main images. Other‘ghost’ images may arise following reflec-tions inside the glass.

Ghost effects can also arise with non-visible electromagnetic radiations. Thus,ghost television images can appear on thescreen if some radio waves reach the an-tenna after reflection by large nearby ob-jects. This effect can be used to obtain avalue for the speed of radio waves.

Gibbs function (Gibbs free energy) Sym-bol: G A thermodynamic function defined

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by G = H – TS, where H is the enthalpy, Tthe thermodynamic temperature, and S theentropy. The function is useful for specify-ing the conditions of chemical equilibriumfor reactions for constant temperature and pressure (for which G is a minimum).The Gibbs function is named for the Amer-ican scientist and mathematician JosiahWillard Gibbs (1839–1903). See also freeenergy.

giga- Symbol: G A prefix denoting 109.For example, 1 gigahertz (GHz) = 109 hertz(Hz).

gilbert The e.g.s. unit of magnetomotiveforce, equal to 0.795 775 ampere.

glass A solid substance in which there is anon-regular arrangement of atoms. Glassesare thus not crystalline – their atoms havea fairly random arrangement and theysoften over a range of temperature, show-ing no definite melting point. They can beregarded as supercooled liquids. See alsooptical glass.

glass electrode An half-cell electrodeconsisting of a platinum wire in a bulbousthin glass membrane containing diluteacid, used to measure hydrogen-ion con-centration (as in pH measurements).

global warming See greenhouse effect.

glow discharge A silent discharge of elec-tricity through a gas at low pressure. Usu-ally luminous, it consists of dark and lightbands between the electrodes.

gluon /gloo-on/ A massless spin-1 particlethat is responsible for transferring thestrong interactions between QUARKS inquantum chromodynamics, just as photonstransfer the electromagnetic interactions inquantum electrodynamics. Isolated gluonshave never been observed.

gold A transition metal that occurs native.It is unreactive and is very ductile and mal-leable. Gold is used in jewelry, often al-loyed with copper, and in electronics and

colored glass. Pure gold is 24 carat; 9 caratindicates that 9 parts in 24 consist of gold.

Symbol: Au; m.p. 1064.43°C; b.p.2807°C; r.d. 19.320 (20°C); p.n. 79; r.a.m.196.96654.

gold-leaf electroscope See electroscope.

governor A mechanical device to controlthe speed of rotation of a machine. A sim-ple governor consists of two masses at-tached to a shaft so that as the speed ofrotation of the shaft increases, the massesmove farther outward from the center ofrotation, while still remaining attached tothe shaft. As the weights move outwardthey operate a control that reduces the fuelor energy input to the machine. As they re-duce speed and move inward they increasethe fuel or energy input. Thus, on the prin-ciple of negative feedback, the speed of themachine is kept constant under varyingconditions of load.

grad See vector calculus.

grade A unit of angle equal to 1/100 of aright angle. 1g = 0.9°.

Graham’s law (of diffusion) Gases dif-fuse at a rate that is inversely proportionalto the square root of their density. Lightmolecules diffuse faster than heavy mol-ecules. The principle is used in the separa-tion of isotopes. The law is named for theScottish chemist Thomas Graham(1805–69).

gram Symbol: g A unit of mass defined as10–3 kilogram.

gram-atom See mole.

gram-molecule See mole.

grand unified theory (GUT) A theorythat attempts to unify the strong, weak,and electromagnetic INTERACTIONS into asingle theory. Several different GUTs havebeen proposed. These all postulate that athigh energies the interactions merge into asingle interaction, with the STANDARD

MODEL emerging from the GUT as a result

giga-

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of spontaneous symmetry breaking associ-ated with the HIGGS MECHANISM. The ener-gies at which the interactions cometogether in GUTs has been calculated to beabout 1015 GeV. This is much higher thanany conceivable accelerator of the futurebut was attained in the very EARLY UNI-VERSE. For that reason GUTs are of rele-vance to the early Universe; for example,they provide a solution to the problem ofmatter–antimatter asymmetry in the Uni-verse.

GUTs suggest that very massive bosonscalled x-bosons mediate interactions be-tween quarks and leptons. This leads to themain prediction of GUTs, which is thatprotons decay to positrons and pions, withbaryon number ceasing to be a conservedquantity. The lifetime of the proton is pre-dicted to be much larger than the age of theUniverse. Nevertheless, the probabilisticnature of quantum mechanics means that ifsufficiently many protons are present in anobserved sample then some should decayeach year. Extensive experiments havebeen performed in attempts to detect pro-ton decay. These have indicated that if pro-ton decay does occur then the lifetime ofthe proton must be longer than the predic-tions of GUTs. This finding rules out manyGUTs. However, if GUTs are combinedwith SUPERSYMMETRY to give supersymmet-ric grand unified theories (SUSY GUTs),then such theories predict a lifetime abouta thousand times longer than the predic-tions of nonsupersymmetric GUTs. It ishoped that experiments in the next fewyears will be able to test this prediction ofSUSY GUTs.

Most GUTs correctly predict that neu-trinos have nonzero masses. Many alsopredict the existence of MAGNETIC

MONOPOLES and/or COSMIC STRINGS fortopological reasons but there is no experi-mental evidence for such entities.

GUTs were first proposed in the mid-1970s by Howard Georgi, SheldonGLASHOW, and others and combined withsupersymmetry in the early 1980s.

graticule /grat-ă-kyool/ A grid of squaresused with the eyepieces of many optical in-

struments to provide easier measurementand/or reference.

grating See diffraction grating.

gravimeter /gră-vim-ĕ-ter/ An instrumentfor measuring the Earth’s gravitationalfield (the force of gravity), usually by de-tecting the effect of a changing field on asuspended or vibrating weight.

gravitation The concept originated byIsaac Newton around 1666 to account forthe apparent motion of the Moon aboutthe Earth, the essence being a force of at-traction, called gravity, between the Moonand the Earth. Newton used this theory ofgravitation to give the first satisfactory ex-planations of many diverse physical facts,such as Kepler’s laws of planetary motion,the ocean tides, and the precession of theequinoxes. See also Newton’s law of uni-versal gravitation.

gravitational acceleration See accelera-tion of free fall.

gravitational collapse The collapse of abody that occurs because of the gravita-tional attraction between all the particlesof the body. Gravitational collapse hap-pens when there is insufficient opposingforce to counteract the gravitational force.For example, the gravitational collapse of astar occurs when the nuclear fuel of the staris exhausted. The end point of this type ofgravitational collapse is a WHITE DWARF, aNEUTRON STAR, or a BLACK HOLE, dependingon the original mass.

gravitational constant Symbol: G Theconstant of proportionality in the equationthat expresses NEWTON’S LAW OF UNIVERSAL

GRAVITATION: F = Gm1m2/r2, where F is thegravitational attraction between two pointmasses, m1 and m2, separated by a distancer. The value of G is 6.674 2 × 10–11

N m2 kg–2. It is regarded as a fundamentalconstant, although it has been suggestedthat the value of G may be changing slowlywith time owing to the expansion of theUniverse.

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gravitational field The region of space inwhich one body attracts other bodies as aresult of their mass. Bodies on or near thesurface of the Earth are influenced by theEarth’s gravitational field. To escape fromthis field a body has to be projected out-ward with a certain velocity (the escape ve-locity). The strength of the gravitationalfield at a point on the Earth’s surface isgiven by the ratio force/mass, which isequivalent to the acceleration of free fall.At a point, it is defined as GM/r2, where Gis the gravitational constant, M the mass ofthe Earth, and r the distance between thecenter of the Earth and the point in ques-tion. The standard value of the accelera-tion of free fall is 9.806 65 m s–2, but itvaries with altitude (i.e. with r2).

gravitational interaction See interac-tion.

gravitational lens A massive heavenlybody that has a high enough gravitationalfield to bend the direction of light rayspassing close to its surface. This type oflight bending is predicted to occur in gen-eral relativity theory and has been ob-served in certain circumstances.

gravitational mass The mass of a bodyas measured by the force of attraction be-tween masses, the value being given byNewton’s law of universal gravitation. In-ertial and gravitational masses are equal ina uniform gravitational field. See also iner-tial mass.

gravitational red shift See red shift.

graviton /grav-ă-ton/ A fundamental par-ticle postulated in order to explain the veryweak gravitational interaction in a waythat fits in with quantum mechanics.Gravitons have zero rest mass, spin twoand travel at the speed of light between thetwo interacting masses. None has yet beenobserved.

gravity The gravitational pull of the Earth(or other celestial body) on an object. Theforce of gravity acting on a mass is identi-cal to weight.

gravity, center of See center of mass.

gravity waves Waves that are the analogin general relativity theory of electromag-netic waves in classical electrodynamics.Like electromagnetic waves, gravity wavespropagate at the speed of light. Gravitywaves are far more difficult to detect thanelectromagnetic waves and, despite a num-ber of experiments, have never been de-tected directly. However, their existencecan be inferred from the analysis of the pe-riod of a binary pulsar system (see binarystar).

gray Symbol: Gy. The derived SI unit ofabsorbed IONIZING RADIATION dose; equiv-alent to an absorption per unit mass of onejoule per kilogram of irradiated material. Itis named for the British physician L.Harold Gray (1905–65). See rad; sievert.

greenhouse effect A heating effect thatoccurs in the atmosphere of planets such asthe Earth as a result of the presence of cer-tain gases in the atmosphere that absorb in-frared radiation. Radiation from the Sun,mainly ultraviolet and visible radiation,passes through the atmosphere and is ab-sorbed at the Earth’s surface. Most of thisenergy is re-radiated by the surface of theEarth in the form of infrared radiation andradiation at these wavelengths is absorbedin the atmosphere by certain compounds(greenhouse gases). This raises the temper-ature of the atmosphere and consequentlythe Earth itself. It is generally believed thatthis effect may be the cause of globalwarming, a measurable increase in averageglobal temperatures with time that has oc-curred over a period of years. The maingreenhouse gas is carbon dioxide, which isproduced by burning fossil fuels (petro-leum, natural gas, and coal). There is con-siderable international concern about theeffects of global warming on the environ-ment and international action is beingtaken to reduce so-called carbon emissionsfrom the burning of coal, gas, gasoline, etc.The term takes its name from the effect ina greenhouse, where the glass allows ince-dent light and some ultraviolet radiationthrough, but absorbs the infrared radiation

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re-emitted from surfaces within the green-house.

Gregorian telescope /grĕ-gor-ee-an, -goh-ree-/ An early type of reflecting telescopesimilar to the Cassegrainian arrangement,except that both mirrors were converging.The telescope is named for the Scottish as-tronomer and mathematician James Gre-gory (1638–75). See also reflector.

grid 1. An open wire mesh interposed be-tween the anode and cathode of athermionic tube. See also thermionic tube;triode.2. The system of distributing electrical en-ergy nationally at high voltage.

grounding (earthing) The connection ofan electrical conductor to a large conduct-ing body, such as the Earth, which is usedas the zero in the scale of electrical poten-tial. In electrical appliances, any metal cas-ings are usually grounded for safety

ground state The lowest energy state ofan atom, molecule, or other system. Com-pare excited state.

ground wave A radio wave that travelsclose to the surface of the Earth betweenthe transmitter and the receiver. Comparesky wave.

group A mathematical structure that isused to study symmetry. Formally, a groupG is a collection of elements a, b, c, etc.,with the elements being related to eachother by certain rules.(1) For any two members a and b of G theproduct ab must also be a member of G.(2) For any three elements a, b, c, there isan associative relation a (bc) = (ab)c.(3) There is an element called the identityelement (sometimes called the unit el-ement), usually denoted e, such that ae = ea= a for all elements a.(4) Each element a has an inverse, denoteda–1, which is also a member of G.

Two elements a, b of a group G are saidto commute if ab = ba. If ab = ba for allpairs a, b of elements of G then G is said tobe an Abelian group. If this is not the case

then G is said to be a non-Abelian group. Ifa group has a finite number of elementsthen the group is said to be a discretegroup. For example, the set of reflectionand rotation symmetries of shapes thatmolecules can have, such as triangles andtetrahedra, gives discrete point groups. Ifthe group has an infinite number of contin-uous elements then the group is said to bea continuous group. For example, the set ofrotations about a fixed axis forms a con-tinuous group called the rotation group.

Because of the connection betweensymmetries and conservation laws there isa close relation between group theory andconserved quantities. For example, the ro-tation group is closely associated with an-gular momentum. Group theory is ofparticular importance in quantum mechan-ics.

group velocity If a wave motion has aphase velocity that depends on wavelength,the disturbance of a progressive wave trav-els with a different velocity from the phasevelocity. This is called the group velocity.The group velocity is the velocity withwhich the group of waves travels. It isgiven by U = c – λdc/dλ, where c is thephase velocity. The group velocity is theone that is usually obtained by measure-ment. If there is no dispersion, as for elec-tromagnetic radiation in free space, thegroup and phase velocities are equal.

GUT See grand unified theory.

gyromagnetic ratio /jÿ-roh-mag-net-ik/Symbol g For an atom or nucleus, the ratioof the magnetic moment to its angular mo-mentum.

gyroscope /jÿ-rŏ-skohp/ A rotating objectthat tends to maintain a fixed orientationin space. For example, the axis of the ro-tating Earth always points in the same di-rection toward the Pole Star (except for asmall PRECESSION). A spinning top or a cy-clist are stable when moving at speed be-cause of the gyroscopic effect. Practicalapplications are the navigational gyrocom-pass and automatic stabilizers in ships andaircraft.

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hadron /had-ron/ A type of ELEMENTARY

PARTICLE. The hadrons are subdivided intobaryons and the mesons. The hadrons aredistinguished from the leptons by theirtype of interaction.

hafnium /haf-nee-ŭm/ A transition metalfound in zirconium ores. Hafnium is diffi-cult to work and can burn in air. It is usedin control rods for nuclear reactors and incertain specialized alloys and ceramics.

Symbol: Hf; m.p. 2230°C; b.p. 5197°C;r.d. 13.31 (20°C); p.n. 72; r.a.m. 178.49.

Hagen’s formula /hah-gĕnz/ SeePoiseuille’s formula.

half-adder An electronic logic circuit thatis used to perform addition of binary arith-metic, i.e. the four possibilities: 0 + 0, 0 +1, 1 + 0, 1 + 1. There are several ways ofcombining logic gates to get a half-adder.

half cell A metal electrode in contact witha solution of the metal ions. In generalthere will be an e.m.f. set up between metaland solution, depending on the tendency ofthe element to form ions in solution. Thee.m.f. cannot be measured directly sincesetting up a circuit results in the formationof another half cell. See electrode potential.

half-life (half-life period) Symbol: T½ Thetime taken for half the nuclei of a sample ofa radioactive nuclide to DECAY. The half-life of a nuclide is a measure of its stability.(Stable nuclei can be thought of as havinginfinitely long half-lives). Half-lives ofknown nuclear species range from less thana picosecond to thousands of millions ofyears. If N0 is the original number of nu-clei, the number remaining at the end of

one half-life is N0/2, at the end of two half-lives is N0/4, etc.

half-period zones (Fresnel zones) Thecircular bands on a spherical wavefront re-quired in the analysis of Fresnel diffrac-tion. Each band is half a wavelength closeto, or further from, the point of observa-tion than its neighbor. Their radii are√(ndλ), where n (the order of the zone) isan integer, and d is the distance from theobservation point to the center of thewavefront.

half-wave antenna (dipole antenna) Anantenna that is used to transmit and receiveradio signals, consisting of two metal rodsconnected to a circuit, with the length ofeach rod being λ/4, where λ is the wave-length of the radio wave being transmittedor received.

half-wave plate See retardation plate.

half-width See monochromatic radiation.

Hall effect When an electric current ispassed through a conductor and a mag-netic field is applied at right angles, a po-tential difference is produced between twoopposite surfaces of the conductor. The di-rection of the potential gradient is perpen-dicular to both the current direction andthe field direction. It is caused by deflectionof the moving charge carriers in the mag-netic field. The size and direction of the po-tential difference gives information on thenumber and type of charge carriers. The ef-fect is named for the American physicistEdwin Herbert Hall (1855–1938). Com-pare Nernst effect.

halo A rainbow-colored ring, sometimes

H

white, seen around the Moon or Sun. It iscaused by the refraction of light by tiny icecrystals in the Earth’s atmosphere.

hard (high) vacuum See vacuum.

hardness The resistance of a solid sub-stance to scratching or local deformationby indentation.

harmonic One of the possible simple (si-nusoidal) components of a complex wave-form or vibration. The first harmonic is thefundamental (frequency f); the second har-monic has twice the fundamental fre-quency (2f), and so on. A waveform maycontain frequencies other than these har-monics. See also partials; quality of sound.

harmonic motion A regularly repeatedsequence that can be expressed as the sumof a set of sine waves. Each component sinewave represents a possible simple har-monic motion. The complex vibration ofsound sources (with fundamental andovertones), for instance, is a harmonic mo-tion, as is the sound wave produced. Seealso simple harmonic motion.

harmonic series In sound, a sequence inwhich each sound is a harmonic of a fun-damental note. Mathematically, it is the se-quence 1 + 1/2 + 1/3 + 1/4 + ...

hassium /hass-ee-ŭm/ A transactinide ele-ment formed artificially.

Symbol: Hs; p.n. 108; most stable iso-tope 265Hs (half-life 2 × 10–3s).

heat Symbol: Q The name often given toenergy that is transferred from regions ofhigh temperature to those of lower temper-ature. The energy transferred when a sys-tem changes temperature is equal to theproduct of the temperature change, themass of the object, and its specific thermalcapacity. The energy transferred when asample changes state is the product of massand specific latent thermal capacity. Seealso internal energy; kinetic theory.

heat capacity See thermal capacity.

heat engine A device that does work onbeing supplied by heat from a high temper-ature source. Ideally, a working substanceis taken through a cycle of operations inwhich heat is taken from a furnace andwaste heat is discharged into the surround-ings. By the first law of thermodynamics,the work done by the engine is equal to thedifference between the heat supplied andthe heat discharged. In real heat engines theworking substance may be expelled at theend of a cycle and then replaced. The the-ory of ideal heat engines has played a largepart in the development of thermodynam-ics. See also Carnot cycle; efficiency; heatpump; Otto cycle; refrigerator.

heat exchanger A device for transferringheat from one fluid to another. Typically, aheat exchanger consists of a series of tubesthrough which one fluid flows. These aresurrounded by the other hotter or coolerfluid. A car radiator is an example of a heatexchanger for transferring energy from thecoolant to the surroundings.

heat pump A device, similar to a refriger-ator, that continually extracts heat from abody and discharges heat at a higher tem-perature. By the second law of thermody-namics, this is possible only because workis done upon the system, usually by an elec-tric motor. The heat discharged is equal tothe heat taken from the cooler body plusthe work done.

Heat pumps are used for space heating.The hotter body is then the building beingheated, while the colder body is the atmos-phere, the soil, or water such as a river. Un-like an ordinary electric heater the heatpump provides heat at a much higher ratethan the electric supply does work. How-ever, it involves much higher capital costs,which may only be justified in a severe cli-mate. See also heat engine; refrigerator.

Heaviside layer /hev-ee-sÿd/ (E-layer;Kennelly–Heaviside layer) A region of theIONOSPHERE at an altitude of 90–150 kmthat reflects medium-frequency radiowaves. The existence of the Heaviside layerwas predicted by and named for the Eng-lish physicist and electrical engineer Oliver

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Heaviside (1850–1925) and independentlyby the British–American electrical engineerArthur Edwin Kennelly (1861–1939). Seealso Appleton layer.

heavy hydrogen See deuterium.

heavy water See deuterium.

hectare Symbol: ha A metric unit of areaequal to 10 000 square meters.

hecto- Symbol: h A prefix denoting 102.For example, 1 hectometer (hm) = 102 me-ters (m).

Heisenberg’s uncertainty principle /hÿ-zĕn-bergz/ (principle of indeterminacy) Ac-cording to quantum mechanics the laws ofphysics can control only the probability ofcertain events or values, and are not deter-ministic. Heisenberg’s principle expressesapproximately this inherent uncertainty inphysical laws. It can be expressed by the re-lations:

∆x∆px ≥ h/4π ∼ h/2π∆t∆E ≥ h/4π ∼ h/2π

Here h is the Planck constant, ∆x is the in-herent uncertainty in the x-coordinate ofthe position of a particle, ∆px is the uncer-tainty in the x-coordinate of the momen-tum (similar rules apply to the y and zcomponents), ∆E is the uncertainty in theenergy, and ∆t the uncertainty in the time.The uncertainties refer to the inherent na-ture of the laws and not to limitations ofexperimental method. They are expressedas root-mean-square deviations.

For example, consider the second rela-tion. An excited state of an atom may typ-ically last 10–9 s. Any measurement of theexcitation energy must in principle bemade within this time, so the uncertainty∆t cannot be greater than about 10–9 s.Hence the uncertainty ∆E cannot be lessthan about (h/2π) ÷ 10–9 ∼ 10–25 joule.Since the excitation energy will be about10–18 joule its value can only be determi-nate to within about one in 107, howeverrefined the measurements are. The Germanphysicist Werner Heisenberg (1901–76)formulated his uncertainty principle in1927.

helium /hee-lee-ŭm/ A colorless mon-atomic gas; the first member of the raregases (group 18 of the periodic table). He-lium has the electronic configuration 1s2

and consists of a nucleus of two protonsand two neutrons (equivalent to an α-par-ticle) with two extra-nuclear electrons. Ithas an extremely high ionization potentialand is completely resistant to chemical at-tack of any sort. The gas accounts for only5.2 × 10–4% of the atmosphere; up to 7%occurs in some natural gas deposits. He-lium is the second most abundant elementin the universe, the primary process on theSun being nuclear fusion of hydrogen togive helium. Helium is recovered commer-cially from natural gas in both the USA andcountries of the former USSR and it alsoforms part of ammonia plant tail gas if nat-ural gas is used as a feedstock. Its applica-tions are in fields in which inertness isrequired and where the cheaper alterna-tives, such as nitrogen, are too reactive; forexample, high-temperature metallurgy,powder technology, and as a coolant in nu-clear reactors. Helium is also used for bal-loons (it is less dense than air) and forlow-temperature physics research.

Helium is unusual in that it is the onlyknown substance for which there is notriple point (i.e., no combination of pres-sure and temperature at which all threephases can co-exist). This is because the in-teratomic forces, which normally partici-pate in the formation of solids, are so weakthat they are of the same order as the zero-point energy. At 2.2 K helium undergoes atransition from liquid helium I to liquid he-lium II, the latter being a true liquid but ex-hibiting superconductivity and animmeasurably low viscosity (superfluidity).The low viscosity allows the liquid tospread in layers a few atoms thick, de-scribed by some as ‘flowing uphill’.

Helium also has an isotope. 3He isformed in nuclear reactions and by decayof tritium. This also undergoes a phasechange at temperatures close to absolutezero.

Symbol: He; m.p. 0.95 K (pressure);b.p. 4.216 K; d. 0.1785 kg m–3 (0°C); p.n.2; r.a.m. 4.002602.

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Helmholtz coils /helm-holts/ A pair ofidentical coils designed so that when a cur-rent is carried the magnetic field betweenthem is fairly uniform. The two coils are setparallel at a distance equal to the radius ofeach. They are connected in series so thateach carries the current in the same direc-tion. Helmholtz coils are named for theGerman scientist Hermann Ludwig Ferdi-nand von Helmholtz (1821–94).

Helmholtz function (Helmholtz free en-ergy) Symbol: F A thermodynamic func-tion defined by F = U – TS, where U is theinternal energy, T the thermodynamic tem-perature, and S the entropy. It is a measureof the ability of a system to do useful workin an isothermal process. See also free en-ergy.

henry /hen-ree/ Symbol: H The SI unit ofinductance, equal to the inductance of aclosed circuit that has a magnetic flux ofone weber per ampere of current in the cir-cuit. 1 H = 1 Wb A–1.

The unit is named for the Americanphysicist Joseph Henry (1797–1878).

Henry’s law The mass of gas dissolved bya liquid is proportional to the pressure ofthe gas, at constant temperature and aslong as the gas does not react with the liq-uid. The law is named for the Britishchemist William Henry (1774–1836).

hertz /herts/ Symbol: Hz The SI unit of fre-quency, defined as one cycle per second(s–1). Note that the hertz is used for regu-larly repeated processes, such as vibrationor wave motion. An irregular process, suchas radioactive decay, for which the SI unitis the becquerel, would have units thatcould also be expressed as s–1 (per second).The unit is named for the German physicistHeinrich Rudolf Hertz (1857–94).

Hertzian waves /hert-see-ăn/ An obsoletename for radio waves.

heterodyne /het-ĕ-rŏ-dÿn/ A technique inradio reception that makes use of the phe-nomenon of beats (see beats). A locallygenerated radio wave is superimposed on

the incoming wave to bring it within audiorange. In a superheterodyne receiver, theintermediate frequency is supersonic and isamplified before being demodulated.

HF See high frequency.

hidden variables See Bell’s paradox.

Higgs boson A hypothetical particle withzero spin postulated in explaining the uni-fication of the electromagnetic interactionand the weak interaction. So far it has notbeen detected but it is expected to be dis-covered as higher-energy accelerators areconstructed. The Higgs field is a field asso-ciated with this particle. The particle isnamed for the British theoretical physicistPeter Ware Higgs (1929– ) and others inthe mid-1960s.

Higgs mechanism The mechanism bywhich the W BOSON and the Z BOSON and,more generally, all massive particles, ac-quire their mass. In the mid 1960s PeterHIGGS, and independently Robert Broutand François Englert, predicted the exis-tence of a massive spin-zero particle is nowknown as the Higgs boson. The Higgsboson is associated with a scalar field, nowknown as the Higgs field.

In the WEINBERG–SALAM MODEL the Wboson and the Z boson which mediate theweak interaction acquire their masses bythe Higgs mechanism. Higgs bosons havenot been found experimentally, althoughthorough searches up to 130 GeV havebeen conducted. It is thought that fermionsin the STANDARD MODEL acquire theirmasses by the Higgs mechanism but it hasnot been possible to implement this sugges-tion.

high frequency (HF) A radio frequencyin the range between 30 MHz and 3 MHz(wavelength 10 m=100 m).

high-temperature gas-cooled reactorSee gas-cooled reactor.

high-temperature superconductivitySuperconductivity occurring at higher tem-peratures (above 100K), found in certain

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high-temperature superconductivity

mixed yttrium-barium-copper oxides. Ithas a different mechanism from normal su-perconductivity but so far no full theoryhas been developed.

high tension (H.T.) High voltage.

hole See semiconductor.

holmium /hohl-mee-ŭm/ A soft malleablesilvery element of the lanthanoid series ofmetals. It occurs in association with otherlanthanoids. It has few applications.

Symbol: Ho; m.p. 1474°C; b.p.2695°C; r.d. 8.795 (25°C); p.n. 67; r.a.m.164.93032.

holography /hŏ-lôg-ră-fee/ A method ofrecording (usually photographically) athree-dimensional image of an object. Nor-mally laser light is used, but other radia-tions (including sound) can giveholograms. The object is illuminated withlaser light and the reflected light from theobject is combined with direct light fromthe source, to give an interference patternon a photographic plate. A three-dimen-sional image of the object is reconstructedby illuminating the interference patternwith the original light. The pattern in-cludes information about phase and direc-tion as well as intensity and color.

homopolar generator /hoh-mŏ-poh-ler,hom-ŏ-/ (Faraday disk) A direct-currentgenerator. It consists of a metal disk rotat-ing in a magnetic field at right angles to theplane of the disk. The e.m.f. is induced be-tween the center of the disk and the edge.

Hooke’s law The principle that if a bodyis deformed the strain produced is directlyproportional to the applied stress. A graphof stress against strain for a material obey-ing Hooke’s law is a straight line. When thestress is removed, the material returns to itsoriginal dimensions. Above a certain stressthe material ceases to obey Hooke’s lawand the graph becomes non-linear. Thepoint at which this occurs is the propor-tional limit of the material. The law isnamed for the English scientist RobertHooke (1635–1703). See also elasticity.

horizontal intensity Symbol: BH Thestrength of the Earth’s magnetic field in ahorizontal direction at a given point on ornear the surface. The value is changingwith time. See also Earth’s magnetism;magnetic variation.

horsepower Symbol: hp 1. Any of vari-ous f.p.s. units of power either equal to ornearly equal to 746 watts (W) in SI derivedunits. Horsepower units typically wereused to measure mechanical power, themost important such unit being equal to550 foot-pounds of force per second, or745.7 W.2. An m.k.s. unit of power known as themetric horsepower, equal to 75 kilogrammeters of force per second. It is equal to735.5 W.

hot-wire instrument An electrical mea-suring instrument in which the current ispassed through a fine resistance wire, caus-ing a rise in temperature. This may be mea-sured by a thermocouple, or by the ‘sag’ inthe wire caused by expansion. Hot-wire in-struments can be used for alternating ofcurrents without a rectifier. The deflectionis roughly proportional to the square of thecurrent.

hour Symbol: h A unit duration of timeequal to 60 minutes or 3600 seconds, or1/24 of a mean solar day.

H.T. High tension (voltage).

HTGR High-temperature gas-cooled re-actor. See gas-cooled reactor.

Hubble constant Symbol H. The quan-tity which appears as a constant in HUB-BLE’S LAW.

Hubble’s law A law stating that the ve-locity v with which a distant galaxy is re-ceding from the Earth is proportional tothe distance d from us. This law can bestated in the form v = Hd, where H is theHubble constant. Hubble’s law can be ex-plained in terms of the description of an ex-panding Universe by general relativitytheory. The Hubble constant has an in-

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verse called the Hubble time which is ameasure of the age of the Universe. The lawis named for the American astronomerEdwin Hubble (1889–1953), who found itempirically in 1929.

hue A pure color in the visible spectrum,relating to one visible wavelength. Any huecan be mixed with a certain other hue toproduce the sensation of white. If a hue ismixed with white, the result is a tint. Seealso complementary colors.

humidity The amount of water vapor inthe air. ABSOLUTE HUMIDITY, that is, themass of water vapor per unit volume of air,is one way of expressing humidity. How-ever, condensation and evaporation alsodepend on the air temperature, and so theRELATIVE HUMIDITY at a given temperatureis more often used. Another measure is spe-cific humidity, the mass of water vapor perunit mass of air.

hundredweight A unit of mass equal to100 lbs (45.359 kg). The long hundred-weight of 112 lbs (50.802 kg) was used inthe UK (and in the Canadian province ofNewfoundland).

Huygens’ construction /hÿ-gĕnz/ Amethod of constructing a subsequentwavefront from an existing one. Each

point on the original wavefront is thoughtof as a secondary point source, emitting ra-diation of the same frequency as thesource, with a speed depending on themedium. The new wavefront is the surfacetangential to all the secondary waveletsproduced by those point surfaces in the for-ward direction. The construction can easilybe used to show the effects of rectilinearpropagation, reflection, and refraction.Huygens’ principle also gives good expla-nations for interference and diffraction.The construction is named for the Dutchscientist Christiaan Huygens (1629–95).

hybrid IC See integrated circuit.

hydraulic press A machine in whichforces are transferred by way of pressure ina fluid. In this case (and in the related hy-draulic braking system and hydraulic jack)the force the user exerts (effort) is less thanthe force the machine exerts (load): theforce ratio is greater than one. The forceratio F2/F1 is equal to A2/A1. This machineis not very efficient; frictional effects arelarge.

hydraulics The branch of physics (andengineering) concerned with the propertiesof fluids at rest and in motion.

hydrodynamics /hÿ-droh-dÿ-nam-iks/See fluid mechanics.

hydrogen /hÿ-drŏ-jĕn/ A colorless gaseouselement; the least dense and most abun-dant element in the Universe and the ninthmost abundant element in the Earth’s crustand atmosphere (by mass). It occurs princi-pally in the form of water and petroleumproducts; traces of molecular hydrogen arefound in some natural gases and in the

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hydrogen

first wavefront

part of newwavefront

•Psecondary waveletsecondary waveletsecondary waveletfrom Pfrom Pfrom P

Huygens' construction of wavefronts

F2

output piston,area A2

F2 (load)

liquid under pressure

master piston,area A1

F1 (effort)

F1

Hydraulic press principle

upper atmosphere. Hydrogen occupies aunique position among the elements as hy-drogen atoms are the simplest of all atoms.The hydrogen atom consists of a proton(positive charge) with one extranuclearelectron (1s1).

Atomic nuclei possess the property of‘spin’ and for diatomic molecules there ex-ists the possibility of having the spins of ad-jacent nuclei aligned (ortho) or opposed(para). Because of the small mass of hydro-gen, these forms are more important in hy-drogen molecules than in other diatomicmolecules. The two forms are in equilib-rium with parahydrogen dominant at lowtemperatures, rising to 75% orthohydro-gen at room temperatures. Although chem-ically identical the melting point andboiling point of the para form are bothabout 0.1° lower than the 3:1 equilibriummixture.

Natural hydrogen in molecular or com-bined forms contains about one part in2000 of deuterium, D, an isotope of hy-drogen that contains one proton and oneneutron in its nucleus.

Symbol: H; m.p. 14.01 K; b.p. 20.28 K;d. 0.089 88 kg m–3 (0°C); p.n. 1; r.a.m.1.0079.

hydrogen electrode An electrode basedon hydrogen, and assigned zero electrodepotential, so that other elements may becompared with it. The hydrogen is bubbledover a platinum electrode, coated in ‘plat-inum black’, in 1M acid solution. Hydro-gen is adsorbed on the platinum black,enabling the equilibrium, H(g) = H+(aq) +e–, to be set up. See also electromotive se-ries.

hydrometer /hÿ-drom-ĕ-ter/ An instru-ment for measuring the relative density of afluid, usually a liquid. The most commontype is a weighted glass bulb that, whenfloated in a liquid, shows the liquid’s rela-tive density by the depth of immersion.There is usually a calibrated scale markedon the glass.

hydrophone /hÿ-drŏ-fohn/ A type oftransmitter or microphone (transducer) de-

signed for use underwater with sound orultrasound. See echolocation; sonar.

hydrosol /hÿ-drŏ-sol, -sohl/ A solution ofa COLLOID in water.

hydrostatics /hÿ-drŏ-stat-iks/ The studyof fluids (liquids and gases) in equilibrium.

hygrometer /hÿ-grom-ĕ-ter/ An instru-ment for measuring humidity. In a chemi-cal hygrometer, air is drawn through adrying agent. Saturated air at the sametemperature is then drawn through anidentical sample of drying agent. The ratioof the different amounts of water absorbedindicates relative humidity. A wet and drybulb hygrometer consists of two ordinarythermometers, one used normally and theother with a bulb kept moist by a dampwick. The cooling of the wet bulb by evap-oration depends on the humidity of the airsurrounding it.

hygroscope /hÿ-grŏ-skohp/ A device thatindicates the humidity of the air, often inthe form of a substance that changes colorin the presence of moisture. See also hy-grometer.

hyperbola /hÿ-per-bŏ-lă/ A conic with aneccentricity greater than 1. The hyperbolahas two branches and two axes of symme-try. An axis through the foci cuts the hy-perbola at two vertices. The line segmentjoining these vertices is the transverse axisof the hyperbola. The conjugate axis is aline at right angles to the transverse axisthrough the center of the hyperbola. Achord through a focus perpendicular to thetransverse axis is a latus rectum.

In Cartesian coordinates the equation:x2/a2 – y2/b2 = 1

represents a hyperbola with its center at theorigin and the transverse axis along the x-axis. 2a is the length of the transverse axis.2b is the length of the conjugate axis. Thisis the distance between the vertices of a dif-ferent hyperbola (the conjugate hyperbola)with the same asymptotes as the given one.The foci of the hyperbola are at the points(ae,0) and (–ae,0), where e is the eccentric-ity. The asymptotes have the equations:

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x/a – y/b = 0x/a + y/b = 0

The equation of the conjugate hyper-bola is

x2/a2 – y2/b2 = –1The length of the latus rectum is 2b2/ae.

A hyperbola for which a and b are equal isa rectangular hyperbola:

x2 – y2 = a2

If a rectangular hyperbola is rotated sothat the x- and y-axes are asymptotes, thenits equation is

xy = kwhere k is a constant.

See also conic.

hyperfine structure /hÿ-per-fÿn/ See finestructure.

hypermetropia /hÿ-per-mĕ-troh-pee-ă/See hyperopia.

hyperons /hÿ-pĕ-ronz/ A group of ele-mentary particles classified as baryons.They are heavier than the nucleons (protonand neutron) and have very short lifetimes.See also elementary particles.

hyperopia /hÿ-pĕ-roh-pee-ă/ (hyperme-tropia) Long sight caused if the distancebetween the eye lens and the back of theeyeball is too short. Rays from a distantobject would focus behind the retina if theeye were fully relaxed. The eye must ac-commodate to allow clear vision of distantobjects. This means that light from closeobjects cannot be focused onto the retina.Longsighted people have a distant nearpoint. The defect is corrected with con-verging spectacle or contact lenses.

hypsometer /hip-som-ĕ-ter/ An instru-ment used for calibrating thermometers atthe steam temperature. The thermometerbulb is placed above pure water boiling ata known pressure, and therefore a knowntemperature. See temperature scale.

hysteresis /his-tĕ-ree-sis/ In general, anapparent lag of an effect behind whateveris causing it. Magnetic hysteresis is the be-

havior of ferromagnetic materials as theyare magnetized and demagnetized. Theflux density, B, lags behind the externalfield strength H. See hysteresis cycle.

hysteresis cycle A closed loop obtainedby plotting the flux density, B, of a ferro-magnetic substance against the magnetiz-ing field strength, H. The substance is firstbrought to magnetic saturation from anunmagnetized state – this produces curveOA (see illustration). As the field strengthis taken through one cycle of reductions,reversals, and increases, the curve followsthe path ACDEFGA. This is known as ahysteresis loop.

The area of the loop equals the energyloss in taking the sample once through thecycle. This is known as hysteresis loss anddepends on the substance.

OC (or OF) represents the remanence,the magnetic flux density remaining in thespecimen when the saturating field is re-moved. OD (or OG) represents the coer-civity, the value of the magnetizing fieldstrength needed to reduce this remainingflux density to zero. All these details arereadily explained by the domain behaviorof ferromagnetics.

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hysteresis cycle

B

A

H

G

F

O

E

D

C

initi

al

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IC See integrated circuit.

Iceland spar See calcite.

ice point The freezing point of water sat-urated with dissolved air, at standard at-mospheric pressure. It was used as astandard fixed point in thermometry forover 200 years but has now been replacedby the triple point of pure water. The icepoint (273.15 K) is 0.01 K lower than thetriple point because of the pressure differ-ence and the dissolved air.

See also International Practical Temper-ature Scale.

ideal gas See gas laws; kinetic theory.

ideal solution A (hypothetical) solutionthat exactly obeys RAOULT’S LAW.

illumination /i-loo-mă-nay-shŏn/ Symbol:E A measure of the visible-radiation en-ergy reaching a surface in unit time. Oncecalled ‘intensity of illumination’, it is mea-sured in lux (lx). One lux is an illuminationof one lumen per square meter. See alsophotometry.

image The point or region from whichrays from an object appear to have comeafter reflection or refraction. Rays actuallypass through a real image (like that pro-duced on a screen by the LENS of a reflexcamera or slide projector). Rays do not ac-tually pass through a virtual image (likethat produced behind a make-up MIRROR

or by a magnifying lens).Image position is measured in terms of

image distance (v) – the distance betweenthe image and the lens or mirror. It relatesto object distance (u) and focal distance (f)by the equation:

l/f = 1/v + 1/u (in the real is positive, virtual is negativeconvention).

Truly sharp images are formed onlywith rays of a single wavelength passingfairly close and parallel to the principalaxis of the lens or mirror.

To describe an image, three other fac-tors are used in addition to its distancefrom the lens or mirror.(1) Is it real or virtual?(2) Is it upright or inverted – the same wayup as the object or the other way up?(3) How large is it compared to the object– magnified, same size, or diminished?See also magnification.

image converter An electron tube thatconverts invisible images (those formed by‘illumination’ with radiation outside thevisible spectrum, such as infrared) into vis-ible images.

image intensifier A type of image con-verter that produces a brighter image thanthat of the original visible image.

image plane The plane perpendicular tothe axis centered on the image.

immersion objective A type of high-power microscope objective whose effec-tiveness is obtained by filling the spacebetween lens and microscope slide with asuitable liquid. Traditionally oil is used,hence the common name oil-immersionobjective. However, sugar solution ispreferable. The liquid increases the effec-tive aperture of the objective because of itshigh refractive constant. In turn this maxi-mizes the resolution obtainable.

impedance /im-pee-dăns/ Symbol: Z A

I

measure of the opposition of a circuit to analternating current. Impedance is the resul-tant of total REACTANCE X and resistanceR:

Z2 = R2 + X2

See also alternating current circuit;phasor.

imperfections Entities that violate thestructure of a perfect crystal. Defects andimpurities are examples of imperfections.

Imperial units The f.p.s. system of ratio-nalized weights and measures establishedby the British Weights and Measures Act of1824, during the reign of George IV, andsubsequently adopted throughout Britain’scolonies and possessions. Although Imper-ial units for quantities of length and weight(or mass) remained essentially the same astheir predecessors, those for volume andcapacity differed significantly. In particularthe Imperial gallon was made equal to thevolume of 10 pounds of water at 62 de-grees Fahrenheit, or 4.546 09 cubicdecimeters (dm3) in SI units. This value was20% larger than the old English wine gal-lon, equal to 3.785 412 dm3, that had longago been adopted in the former colonieswhich had become the United States. Fur-ther, the Imperial quart was divided into40 fluid ounces (equal to 1.136 522 dm3)whereas the U.S. quart was divided into 32fluid ounces (equal to 0.946 353 dm3),making the U.S. fluid ounce larger. In theImperial system the bushel is equal to 8 Im-perial quarts, and dry and liquid measuresare the same, unlike the situation in theUnited States.

impulse (impulsive force) A force actingfor a very short time, as in a collision. If theforce is constant the impulse is Fδt; if it is avariable force the impulse is the integral ofthis over the short time period. An impulseis equal to the change of momentum that itproduces.

impulse noise See noise.

impulsive force See impulse.

incandescence /in-can-dess-ĕns/ The radi-

ation of visible light by a surface at a hightemperature. Radiant electric heaters andthe filament lamp are domestic examples ofincandescent sources. See also black body.

inch A unit of length in f.p.s. systems. It isequal in SI units to 25.4 millimeters.

incidence, angle of See angle of inci-dence.

inclination (angle of dip) Symbol: δ Theangle between the Earth’s magnetic fieldand the horizontal at a given point on theEarth’s surface. It is measured with an in-clinometer and changes to some extentwith time. See also Earth’s magnetism;magnetic variation.

inclined plane A type of simple machine.Effectively a plane at an angle, it can beused to raise a weight by movement up anincline.

Both distance ratio and force ratio de-pend on the angle of inclination. Efficiencycan be fairly high if friction is kept low.The screw and the wedge are both exam-ples of inclined planes.

inclinometer /in-klă-nom-ĕ-ter/ (dipcircle) An instrument used to measure in-clination (the angle of dip). A magneticneedle is pivoted so that it is free to movein a vertical plane in front of a circularscale. The instrument is leveled and thenrotated through a horizontal axis until theneedle is vertical. The needle is now underthe influence only of the vertical compo-nent of the Earth’s field. When the dip cir-cle is turned through 90° (into themeridian) the needle lines up along theEarth’s magnetic field. Then the angle be-tween the needle and the horizontal is theinclination at that point.

indium /in-dee-ŭm/ A soft silvery metallicelement. It is found in minute quantities,primarily in zinc ores, and is used in alloys,in several electronic devices, and in electro-plating.

Symbol: In; m.p. 155.17°C; b.p.2080°C; r.d. 7.31 (25°C); p.n. 49; r.a.m.114.818.

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indium

induced current Electric current in a con-ductor caused by e.m.f. set up by a chang-ing magnetic field surrounding it. Seeelectromagnetic induction.

induced magnetism The creation ofMAGNETISM in a ferromagnetic material byplacing it in a magnetic field. This causesthe material’s magnetic domains to becomealigned. The inducing field may come fromanother permanent magnet or from anelectromagnet. See domain.

inductance /in-duk-tăns/ A measure of thee.m.f. produced in a circuit as a result ofthe magnetic effect of a changing electriccurrent, either in that circuit or in another.See mutual induction; self-induction.

induction /in-duk-shŏn/ In general, theproduction of an effect by interaction witha field. 1. The production of magneticorder in a material by an external field. Seemagnetic induction.2. The separation of electric charge in amaterial by an external electric field. Seeelectrostatic induction.3. The production of an e.m.f. (or resultingcurrent) in a conductor in a changing mag-netic field. See electromagnetic induction.See also mutual induction; self-induction.4. See magnetic flux density.

induction coil A device that produces aseries of high-voltage pulses by means ofelectromagnetic induction. It consists of acoil of insulated wire with only a few turns,wound on an iron core and surrounded byanother with many more turns. When thecurrent in the first coil is interrupted sud-denly, a large e.m.f. is induced in the sec-ond. A pulsed current in the first coilinduces a large pulsed e.m.f in the second.

induction heating (eddy-current heating)The temperature rise that occurs in con-ductors in a varying magnetic field. It iscaused by the induced eddy currents insidethe block of material. Induction heatingcan be used for heating metals in a furnace.Some stoves work by heating the metalpots in this way. However, induction heat-ing also results in power losses from elec-

trical machines, although usually this canbe minimized with careful design.

induction motor An alternating-currentELECTRIC MOTOR in which the changingmagnetic field of one coil, connected to thepower supply, induces a current in anotherwinding not connected to the supply. Themagnetic force between the two coils turnsthe motor. Unlike most other electric mo-tors, no brushes are needed to connectmoving and stationary electrical parts.This eliminates sparking and thereforelarge motors are often of this type. See alsosynchronous motor.

inductor /in-duk-ter/ (choke) A circuitcomponent that has a significant induc-tance. See inductance.

inelastic collison /in-i-las-tik/ A collisionfor which the restitution coefficient is lessthan one. In effect, the relative velocityafter the collision is less than that before;kinetic energy is not conserved in the colli-sion, even though the system may beclosed. Some of the kinetic energy is con-verted into internal energy. See also restitu-tion; coefficient of.

inertia /i-ner-shă/ An inherent property ofmatter implied by Newton’s first law ofmotion: ‘a body continues in a state of restor constant velocity unless acted on by anexternal force’. An object automaticallyopposes a change of motion by reason ofits inertia. See also inertial mass; Newton’slaws of motion.

inertial mass /i-ner-shăl/ The mass of anobject as measured by the property of iner-tia. It is equal to the ratio force/accelera-tion when the object is accelerated by aconstant force. In a uniform gravitationalfield, it is equal to GRAVITATIONAL MASS,since all objects have the same gravita-tional acceleration at the same place.

inertial system A FRAME OF REFERENCE inwhich an observer sees an object that is freeof all external forces to be moving at con-stant velocity. The observer is called an in-ertial observer. Any frame that moves with

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constant velocity and without rotation rel-ative to an inertial frame is also an inertialframe. NEWTON’S LAWS OF MOTION are validin any inertial frame (but not in an acceler-ated frame), and the laws are therefore in-dependent of the velocity of an inertialobserver.

inflation See early Universe.

information theory The branch of math-ematics that analyzes the concept of infor-mation mathematically. Informationtheory has been used extensively in severalbranches of physics, particularly in connec-tion with the concept of entropy. It hasbeen suggested that the fundamental prin-ciples of physics can be expressed in termsof information theory.

infrared /in-fră-red/ (IR) Electromagneticradiation past the red end of the visiblespectrum. The range of wavelengths is ap-proximately 0.7 micrometer to 1 millime-ter. Infrared is sometimes called thermalradiation; most of the energy radiated bysurfaces below about 6000 K is infrared.Many materials transparent to visible lightare opaque to infrared, including glass.Rock salt, quartz, germanium, or polyeth-ylene prisms and lenses are suitable for usewith infrared. Infrared radiation close tovisible light in wavelength can be detectedby thermometers with blackened bulbs andwith photographic film. Otherwise a ther-mocouple or a bolometer can be used.

Infrared radiation is produced by move-ment of charges on the molecular scale; i.e.by vibrational or rotational motion of mol-ecules. See also electromagnetic spectrum.

infrasound /in-fră-sownd/ Vibrations in amedium with frequencies below about 16hertz. The ear distinguishes such vibrationsas a series of pulses, rather than a continu-ous sound.

instantaneous value /in-stăn-tay-nee-ŭs/The value of a varying quantity (e.g. accel-eration, current, power, etc.) at a particu-lar instant in time.

insulation, electrical The use of noncon-ductors to coat or separate electrical con-ductors (for safety or prevention of shortcircuits). Rubber, PVC, and ceramics arecommon insulators.

insulation, thermal Any means of pre-venting or reducing the transfer of thermalenergy. Lagging of hot-water tanks andfoam-filled cavity walls are examples. Seealso insulator; thermal.

insulator, electrical A material with avery high electrical resistivity. Most non-metallic materials are good electrical insu-lators. Compare conductor (electrical),semiconductor.

insulator, thermal A material that doesnot readily transmit heat. Many insulators,such as asbestos, are porous or fibroussolids that trap small pockets of air withinthem. Gases do not conduct heat well, andconvection is prevented because the aircannot flow. See also conductor (thermal).

integral /in-tĕ-grăl, in-teg-răl/ The resultof integrating a function. See integration.

integrated circuit (IC) A circuit that in-corporates numerous components into oneunit. In a monolithic IC a single chip of sil-icon is the base or substrate onto which allthe individual components are integratedduring manufacture. Hybrid ICs consist ofone or more monolithic ICs mounted on asubstrate, or several components similarlymounted and interconnected. After manu-facture neither type can be dismantled.

integration The continuous summing ofchange in a function, f(x), over an intervalof the variable x. It is the inverse process ofdifferentiation in calculus, and its result isknown as the integral of f(x) with respectto x. An integral:

∫f(x)dxcan be regarded as the area between thecurve and the x-axis, between the values x1and x2. It can be considered as the sum ofa number of column areas of width ∆x andheights given by f(x). As ∆x approacheszero, the number of columns increases infi-

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integration

nitely and the sum of the column areas ap-proaches the area under the curve. The in-tegral of velocity is distance. Integralsbetween definite limits are known as defi-nite integrals. An indefinite integral is onewithout limits. The result of an indefiniteintegral contains a constant – the constantof integration. For example,

∫xdx = x2/2 + Cwhere C is the constant of integration. Atable of integrals is given in the Appendix.See also differentiation.

intensity A measure of the rate of energytransfer by radiation. The unit of radiantintensity is the watt per square steradian(W sr–1). 1. The intensity of visible radia-tion is related to brightness. In photometryspecial units are used because it is neces-sary to consider the sensitivity of the eye todifferent visible radiations. Thus the inten-sity of a light source – sometimes called lu-minous intensity – is measured with thecandela. The intensity of illumination of asurface is measured in lux. The intensity ofvisible radiation itself is measured in lu-mens.2. The intensity of sound relates to the sen-sation of loudness, which also depends onfrequency. It is inversely proportional tothe square of the distance from the sourceand is measured in watts per square meter.The intensity level of a sound is the inten-sity relative to an agreed standard. Seedecibel.

intensity, electric See electric fieldstrength.

intensity, magnetic See magnetic fieldstrength.

intensive variable A quantity in a systemfor which the value of that quantity doesnot depend on the size of that system. Ex-amples of intensive variables include pres-sure, temperature, and density. Forexample, if two systems with the same tem-perature are brought together to form alarger system, the temperature does notchange. Compare extensive variable.

interaction A mutual effect between twoor more systems or bodies, so that the over-all result is not simply the sum of the sepa-rate effects. There are four separateinteractions distinguished in physics:1. Gravitational interaction The weakestof the four, about 1040 times weaker thanthe electromagnetic interaction. It is an in-teraction between bodies or particles onaccount of their mass, and operates overlong distances. See Newton’s law of uni-versal gravitation.2. Electromagnetic interaction The interac-tion between charged bodies or particles(stationary or moving). It falls off with thesquare of distance and operates over alldistances. See also Coulomb’s law.3. Strong interaction An interaction be-tween hadrons, about 100 times greaterthan the electromagnetic interaction. It op-erates at very short range (up to around10–15 m) and is the force responsible forholding nucleons together in the atomicnucleus.4. Weak interaction An interaction about1010 times weaker than the electromag-netic interaction. It can occur for both lep-tons and hadrons and is the interaction inbeta decay.

So far it has not proved possible to for-mulate a unified field theory for all fourtypes of interaction, although there hasbeen some success in unifying the electro-magnetic and weak interactions.

interface The common surface (boundaryof contact) between two adjacent PHASES ina system. Either or both of the surfacesmay be a gas, liquid, or solid.

interference When similar waves with aregular phase relationship pass through thesame region they are said to interfere. Theresultant displacement at any point is thesum of the individual displacements, tak-ing into account their directions andphases. The waves emerge from the over-lapping region unaffected. The combina-tion of such coherent waves is to becontrasted with the combination of inco-herent waves, for example light from twolamps falling on a surface, where the resul-

intensity

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tant intensity is just the sum of the separateintensities.

There are two simple cases. If the WAVES

travel in the same or very nearly the samedirection, interference fringes are pro-duced. If waves of comparable intensitytravel in opposite directions stationarywaves are produced. In all other cases, acomplex system of interference fringes andstationary waves is caused, which does notadmit simple analysis or description.

Interference fringes can be observedwith all types of waves. They can be un-derstood most easily by considering wavesfrom just two sources but the ideas canthen be generalized to more complicatedsystems. The two sources must give wavesof the same frequency and with a regularphase relationship. This is easily achievedusing sources of sound, ripples or ra-diowaves but in optics it is normally neces-sary to derive the two sources from oneoriginal source by division of wavefront ordivision of amplitude. The first method isused in Young’s double slit, Fresnel’sbiprism, and Lloyd’s mirror. The second isused in Newton’s rings, the air wedge, andthin films.

Interference fringes are normally ob-served at a distance from the sources that isvery large compared with their separation.Thus the waves travel in almost exactly thesame direction and, if the sources areequal, they have equal intensity. There arethen maxima of intensity (light fringes)where the path difference is zero or an in-tegral number of wavelengths, and minima(dark fringes) where the path difference isan odd number of half wavelengths.

See also wave.

interferometry /in-ter-fĕ-rom-ĕ-tree/ Thetechnique of producing interference pat-terns and using these for accurate wave-length measurement, measuring smalldistance changes, testing flat surfaces, etc.Devices, such as etalons, used for produc-ing and using interference patterns are in-terferometers.

intermolecular forces /in-ter-mŏ-lek-yŭ-ler/ Forces of attraction between molecules

or neutral atoms. See van der Waals’forces.

internal combustion engine A type ofHEAT ENGINE in which fuel is burned withinthe engine. For example, in a normal auto-mobile engine, combustion of gasoline,diesel, or some other fuel within the cylin-der causes expansion of gas, which movesthe piston in the engine and performswork. In contrast, a STEAM ENGINE is an ex-ternal combustion engine. In this case thecombustion takes place outside the body ofthe engine and steam at high pressure ispassed to the cylinder.

internal conversion A process in whichthe nucleus of an atom decays from an ex-cited state into the ground state but, in-stead of releasing the available energy aselectromagnetic radiation (a photon),transfers it by electromagnetic coupling toa bound electron in the atom (creating anion, which may then itself emit an electronor a gamma-ray photon). See also Auger ef-fect.

internal energy Symbol: U The energy ofa system that is the total of the kinetic andpotential energies of its constituent parti-cles (e.g. atoms and molecules). If the tem-perature of a substance is raised, bytransferring energy to it, the internal en-ergy increases (the particles move faster).Similarly, work done on or by a system re-sults in an increase or decrease in the inter-nal energy. The relationship between heat,work, and internal energy is given by thefirst law of thermodynamics. Sometimesthe internal energy of a system is looselyspoken of as ‘heat’ or ‘heat energy’.Strictly, this is incorrect; heat is the trans-fer of energy as a result of a temperaturedifference.

internal friction Another term for viscos-ity. See viscosity.

internal resistance Resistance of a sourceof electricity. In the case of a cell, when acurrent is supplied, the potential differencebetween the terminals is lower than thee.m.f. The difference (i.e. e.m.f. – p.d.) is

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proportional to the current supplied. Theinternal resistance (r) is given by:

r = (E – V)/Iwhere E is the e.m.f., V the potential dif-ference between the terminals, and I thecurrent.

international candle A former unit of lu-minous intensity, approximately equal to1.018 3 CANDELA. It was originally definedin terms of the light emitted per second bya specified electric lamp, but was super-seded by the candela in 1948.

International Practical TemperatureScale (IPTS) A scale of temperatures(1968) based on a number of fixed points,with agreed methods of measuring temper-atures over particular ranges. It is used forpractical measurements of thermodynamictemperature.

interstitial /in-ter-stish-ăl/ See defect

intrinsic semiconductor See semicon-ductor.

inverse Compton effect An increase inenergy of a photon when it is scattered by

an electrically charged particle such as anelectron. In this process the electricallycharged particle loses energy. It is thoughtthat this effect may be important in someprocesses in astronomy.

inverse square law A relationship inwhich the effect of a source is inverselyproportional to the square of the distancefrom the source. It applies to energy radi-ated from a point source and also to fieldsfrom point sources.

inversion temperature See Joule–Kelvineffect.

inverter gate (NOT gate) See logic gate.

international candle

126

sourcearea A

area 4Aarea 9A

ddistance 2d

distance 3d

Inverse square law

INTERNATIONAL PRACTICAL TEMPERATURE SCALE

Fixed point TK °Ctriple point of hydrogen 13.81 –259.34hydrogen with vapor pressure 25/76 atmosphere 17.042 –256.108boiling temperature of hydrogen 20.28 –252.87boiling temperature of neon 27.102 –246.048triple point of oxygen 54.361 –218.789boiling temperature of oxygen 90.188 –182.962triple point of water 273.16 0.01boiling temperature of water 373.15 100melting temperature of zinc 692.73 419.58melting temperature of silver 1235.08 961.93melting temperature of gold 1337.58 1064.43

Note: the scale given above is based on standard interpolation procedures to be usedexperimentally for measurements between the fixed points. The methods employed are:

–259.35° to 630.74°C resistance measurement with a platinum resistance thermometer

630.74°C to 1064.43°C e.m.f. measurement with a thermocouple made of platinum and platinum/10% rhodium alloy

above 1064.43°C radiation measurement and use of Planck radiation law

inverting prism See erecting prism.

iodine /ÿ-ŏ-dÿn, -deen/ A dark-violetvolatile solid element belonging to thehalogens.

Symbol: I; m.p. 113.5°C; b.p. 184°C;r.d. 4.93 (20°C); p.n. 53; r.a.m.126.90447.

ion /ÿ-on, -ŏn/ A charged particle consist-ing of an atom, or group of atoms, that haseither lost or gained electrons. Sodiumchloride (salt), for example, is made up ofpositive sodium ions – atoms that haveeach lost an electron – and negative chlo-rine ions – atoms that have each gained anelectron. See ionization.

ion engine A device consisting of a sourcefor producing ions and an electromagneticfield for accelerating the ions in a particu-lar direction. In practice, an ion engine canbe used in a low-pressure environment toproduce propulsion by reaction forces as-sociated with the rapidly moving ions. It isalso necessary to expel oppositely chargedparticles to the ions from the engine to en-sure charge neutrality. Ion engines havebeen investigated as possible powersources for spacecraft.

ionic radius The effective radius of an ionin a compound, most usually determinedby comparing the interionic distances be-tween the ion concerned and various other(oppositely charged) ions in crystals.

ionization /ÿ-ŏ-ni-zay-shŏn/ The processof producing ions. There are several waysin which ions may be formed from atomsor molecules. In certain chemical reactionsionization occurs by transfer of electrons;for example, sodium atoms and chlorineatoms react to form sodium chloride,which consists of sodium ions (Na+) andchloride ions (Cl–). Certain molecules canionize in solution; acids, for example, formhydrogen ions as in the reaction

H2SO4 → 2H+ + SO42–

Ions can also be produced by ionizing radi-ation; i.e. by the impact of particles or pho-tons with sufficient energy to break upmolecules or detach electrons from atoms:

A → A+ + e–. Negative ions can be formedby capture of electrons by atoms or mol-ecules: A + e– → A–.

ionization chamber A chamber in whichionizing radiation can be detected and/ormeasured. It contains a pair of electrodesbetween which is maintained a potentialdifference. Passage of ionizing radiationthrough the chamber produces electronsand positive ions, which separate andmove to the electrode of opposite sign.There is thus a small electric current be-tween the electrodes, which relates to theintensity of the radiation.

ionization potential Symbol: I The en-ergy required to remove an electron froman atom or molecule to form a positive ion.

ionizing radiation Radiation such thatthe individual particle or quantum has suf-ficient energy to ionize substances. Elec-trons with kinetic energy just greater thanthe ionization potential will cause ioniza-tion, but other particles (e.g. molecularpositive ions) require higher energies.Gamma-rays and x-rays ionize indirectlyby means of the electrons they eject fromsubstances by the photoelectric effect orCompton scattering. Short-wavelength ul-traviolet quanta may ionize individualmolecules by the photoelectric effect, butthe ejected electrons have insufficient ki-netic energy to cause further ionization un-less an electric field is applied.

At ordinary intensities electromagneticradiation with quantum energy below theionization potential cannot cause ioniza-tion. But by focusing laser beams it is pos-sible to ionize matter – even when theindividual photons have energy less than ahundredth of the ionization potential. Suchradiations are not ordinarily classified asionizing radiations.

Ionizing radiations can be dangerous tohealth and precautions should be takenwith their use.

ionosphere /ÿ-on-ŏ-sfeer/ A region in theEarth’s upper atmosphere containing ionsand free electrons. It is formed by ioniza-tion by ultraviolet radiation from the Sun.

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ionosphere

ion pair

128

It is divided into three layers: D-layer(50–90 km), E-layer (90–150 km), and F-layer (150–1000 km). Radio transmissioncan occur by reflection from the ionos-phere.

ion pair A pair of ions of opposite chargeproduced, for example, by an ionizing ra-diation: AB → A+ + B–.

IPTS See International Practical Temper-ature Scale.

IR See infrared.

iridium /i-rid-ee-ŭm/ A white transitionmetal that is highly resistant to corrosion.It is used in electrical contacts, in sparkplugs, and in jewelry.

Symbol: Ir; m.p. 2410°C; b.p. 4130°C;r.d. 22.56 (17°C); p.n. 77; r.a.m. 192.217.

iris /ÿ-ris/ An arrangement able to vary theamount of light that enters an optical in-strument. In the mammalian eye, this is acircular muscle that changes the size of thepupil. In many optical instruments, a simi-lar effect is obtained with a diaphragm. Ineither case the aperture is varied.

iris diaphragm See diaphragm.

iron /ÿ-ern/ A transition element occur-ring in many ores. It is used in the manu-facture of steel and various other alloys.

Symbol: Fe; m.p. 1535°C; b.p. 2750°C;r.d. 7.874 (20°C); p.n. 26; r.a.m. 55.845.

irradiance /i-ray-dee-ăns/ Symbol: E Therate of energy reaching unit area of a sur-face; i.e. the radiant flux per unit area. Un-like illumination, irradiance is notrestricted in use to visible radiation. Theunit is the watt per square meter (W m–2).

The solar constant is the irradiance ofthe Earth by the Sun. The value is 1.353kW m–2. When applying this figure to aconsideration of solar power, allowancemust be made for atmospheric absorptionand reflection, and for the angle of the Sunfrom the zenith.

irreversible change /i-ri-ver-să-băl/ Seereversible change.

isobars /ÿ-sŏ-barz/ 1. Two or more nu-clides that have the same nucleon numbersbut different proton numbers.2. Lines joining points of equal pressure.

isoclinic line /ÿ-sŏ-klin-ik/ An imaginaryline on the Earth’s surface joining pointswith the same inclination (angle of dip).The magnetic equator (or aclinic line) is theline that joins points of zero inclination.See also Earth’s magnetism.

isodynamic line /ÿ-sŏ-dÿ-nam-ik/ Animaginary line on the Earth’s surface join-ing points at which the Earth’s total mag-netic field strength is the same. See alsoEarth’s magnetism.

isoentropic process /ÿ-sŏ-trop-ik/ A ther-modynamic process in which the entropyof the system stays constant throughoutthe change.

isogonal /ÿ-sog-ŏ-năl/ See isogonic line.

isogonic line /ÿ-sŏ-gon-ik/ (isogonal) Animaginary line on the Earth’s surface join-ing points of equal declination. Isogoniclines run roughly East to West. Agoniclines are isogonic lines that join points hav-ing zero declination. See also Earth’s mag-netism.

isolated system See closed system.

isomers, nuclear See nuclear isomers.

isotherm /ÿ-sŏ-therm/ A line on a chart orgraph joining points of equal temperature.See also isothermal change.

isothermal change /ÿ-sŏ-therm-ăl/ Aprocess that takes place at constant tem-perature. If work is done on a body in sucha way as would otherwise increase its tem-perature (for example by compressing it) itis possible to keep the temperature con-stant by heat transfer from the body. Con-versely a body may expand doing externalwork, while heat is transferred to it to pre-

vent the temperature from falling. In thecase of an ideal gas, for which the internalenergy depends only on the temperature,the heat transferred from the substancemust be exactly equal to the work done onit. For real substances the work and heatmay not balance in an isothermal processsince the internal energy may depend alsoon the volume.

Although no real process can be per-fectly isothermal there are many phenom-ena that approximate very closely to it.Perfectly reversible isothermal volumechanges of an ideal gas are assumed in ther-modynamic analyses; for example, Kelvinbased his thermodynamic temperaturescale upon the behavior of an ideal gas in aCarnot cycle.

Isothermal changes are distinct from ad-iabatic changes, in which no heat enters orleaves the system so any work done on orby it changes the internal energy and hencethe temperature. See adiabatic change.

isotones /ÿ-sŏ-tohnz/ Two or more nu-clides that have the same neutron numbersbut different proton numbers.

isotopes /ÿ-sŏ-tohps/ Two or more speciesof the same element differing in their massnumbers because of differing numbers ofneutrons in their nuclei. The nuclei musthave the same number of protons (an ele-ment is characterized by its proton num-ber). Isotopes of the same element havevery similar chemical properties (the sameelectron configuration), but differ slightlyin their physical properties. An unstableisotope is termed a radioactive isotope orradioisotope. For example, potassium has3 naturally occurring isotopes of massnumbers 39, 40, and 41 respectively.13

99K has 19 protons and 20 neutrons

14

90K has 19 protons and 21 neutrons

14

91K has 19 protons and 22 neutrons

14

90K is radioactive with a half-life of 1.3 ×

109 years.

At least eight other isotopes of potas-sium can be produced by nuclear reactionsbut all are highly unstable (radioactive).

isotope separation The process of sepa-rating the different isotopes of an elementaccording to their atomic masses. Mostmethods depend on small differences inphysical properties between isotopes.

On the laboratory scale isotopes of ele-ments can be separated in the mass spec-trometer in which the paths of nucleidepend on the ratio of charge to mass. Sim-ilar methods have been used on a largerscale. The difference in rates of diffusion ofthe volatile compounds 238uranium hexa-fluoride and 235uranium hexafluoride hasbeen used on a large scale to separate theisotopes of uranium. The ultracentrifugeprocess is also used. 235UF6 tends to staynear the axis of the centrifuge and the238UF6 tends to drift to the perimeter.Slight separation occurs at each stage.

Early methods of isolating deuteriumused electrolysis of water. Deuterium ionsare discharged at a slightly slower rate;thus the residue becomes progressivelyricher in deuterium during electrolysis. Theprocess that is currently used is a chemicalexchange between water and hydrogensulfide.

isotopic mass /ÿ-sŏ-top-ik/ (isotopicweight) The mass number of given isotopeof an element.

isotopic number The difference betweenthe number of neutrons in an atom and thenumber of protons.

isotopic weight See isotopic mass.

isotropy /ÿ-sot-rŏ-pee/ A medium isisotropic if the value of a measured physi-cal quantity does not depend on the direc-tion. Compare anisotropy.

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isotropy

130

jansky Symbol: Jy /jan-ski/ A m.k.s.a. unitused to indicate the strength of radio sig-nals detected during astronomical observa-tions. One jansky is equal to a power of0.01 yoctowatt (yW) per square meter (m)per hertz (Hz) (1 Jy = 0.01 yW m–2 Hz–1).

Joly steam calorimeter /joh-lee/ An ap-paratus for measuring the specific thermalcapacity of a gas at constant volume. Twoidentical copper globes are suspended fromthe arms of a balance – one is evacuatedand the other filled with the sample. Thetwo globes are surrounded by a containerinto which steam is passed. More conden-sation occurs on the filled globe because ofthe higher thermal capacity. The specificheat capacity (Cv) of the gas can be calcu-lated from

mCv(θ2 – θ1) = msLwhere m is the mass of gas, θ2 the temper-ature of the steam, θ1 the initial tempera-ture of the globes, ms the mass of steamcondensed, and L the specific latent ther-mal capacity of evaporation of water. Thecalorimeter is named for the Irish physicistJohn Joly (1857–1933).

Josephson effect /joh-zĕf-sŏn/ Any ofvarious electrical effects observed withpairs of superconductors. Josephson junc-tions (between semiconductors) are findingvarious applications in investigating funda-mental constants, the phenomenon of elec-tron tunneling, and in very high-speedcomputers. The effect is named for its dis-coverer, the British physicist Brian Joseph-son (1940– ).

joule /jool/ Symbol: J The SI unit of energyand work, equal to the energy required orwork done when the point of applicationof a force of one newton moves an object

one meter in the direction of action of theforce. 1 J = 1 N m. The joule is the unit ofall forms of energy. The unit is named forthe British physicist James Prescott Joule(1818–89).

Joule–Kelvin effect /jool kel-vin/(Joule–Thomson effect) A temperaturechange that occurs when a thermally insu-lated gas expands through a small hole ora porous barrier into a region of lowerpressure. If the gas is initially above a cer-tain temperature, the inversion tempera-ture of the gas, the temperature rises. If it isinitially below the inversion temperature itcools. It can be shown that an ideal gaswould not show this effect.

The Joule–Kelvin effect is used in themethod of liquefying gases invented byLinde (1895). The gas, which has beencooled slightly by passing through the hole,flows back over the surface of the inputpipe, thereby cooling the gas approachingthe hole. Thus the temperature dropssteadily until liquefaction takes place. Themethod can be used for liquefying any gas,but in the important cases of hydrogen andhelium the gases must first be cooled tobelow their inversion temperatures, whichare far below room temperature. Heliummust be cooled by liquid hydrogen, whichis itself initially cooled by liquid nitrogen.

The Joule–Kelvin effect is essentiallythermodynamically irreversible and shouldnot be confused with adiabatic expansionof a gas in a cylinder or turbine, which canapproximate to an ideal reversible process.The Joule–Kelvin effect was discovered byJoule and William Thomson (subsequentlyLord Kelvin) in the 1850s (see kelvin).

Joule’s equivalent Symbol: J A constant,4.1855 × 107 ergs per calorie (15°), relating

J

former units of ‘heat’ energy to units of me-chanical energy. It arose from early exper-iments by Joule showing that mechanicalwork always relates to an equivalent quan-tity of ‘heat’. The constant is also called themechanical equivalent of heat.

In SI units, work, heat, and all forms ofenergy are measured in joules. The value ofJ (4.1855 joules per calorie) is the factordefining the calorie.

Joule’s laws 1. The electrical work doneper unit time (the power) when a current Iflows through a resistor of resistance Rwith a potential difference V is given by

power = VI = RI2 = V2/RIn the steady state this gives the rate ofemission of heat by the resistor. These rela-tionships follow from the modern defini-tions of potential difference and resistance,but Joule discovered them experimentallyin terms of arbitrarily defined quantities.

2. The internal energy of an ideal gas de-pends only on the temperature, i.e. it is in-dependent of pressure and volume if thetemperature is held constant. Joule origi-nally expressed the law for real gases onthe basis of insensitive methods. Later heshowed that the temperature of a real gasfalls slightly on expanding into a vacuumwith perfect insulation. Since in such a caseno work is done and no heat flows the in-ternal energy is constant, and for an idealgas the temperature would be constant.

Joule–Thomson effect See Joule–Kelvineffect.

J-particle Another name for a psi particle.See fundamental particles.

junction rectifier See rectifier.

junction transistor See transistor.

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132

kaon /kay-on/ (K-meson) A type ofmeson. There are four types of meson: pos-itively charged, negatively charged, andtwo types of neutral particle. They arestrongly interacting bosons of zero spinwith several alternative modes of decay.See also elementary particles.

keepers Pieces of ‘soft’ iron placed be-tween the poles of permanent magnetswhen stored to help retain the magnetism.Bar magnets are placed in pairs with oppo-site poles next to each other and keepersare placed across each end. The magnet’sinternal field opposes its external field; thiscauses a demagnetizing effect. When keep-ers are used, they become magnetized withan internal field in the same direction asthat of the magnet. Thus the demagnetiz-ing effect is reduced. See also magnetic in-duction.

kelvin Symbol: K The SI base unit of ther-modynamic temperature. It is defined asthe fraction 1/273.16 of the thermody-namic temperature of the triple point ofwater. Zero kelvin (0 K) is absolute zero.One kelvin is the same as one degree on theCelsius scale of temperature. The unit isnamed for British physicist William Thom-son, later made Lord Kelvin (1824–1907).

Kelvin temperature scale The TEMPERA-TURE SCALE that has its origin at absolutezero, with 273.16 K as the triple point ofwater. See absolute temperature; kelvin.

Kennelly–Heaviside layer /ken-ĕ-lee hev-ee-sÿd/ See Heaviside layer.

Keplerian telescope /kep-leer-ee-ăn/ (as-tronomical telescope) The most commontype of refracting telescope arrangement,

consisting of converging objective and eye-piece. Unlike the Galilean telescope, it pro-vides an inverted image and has a greaterlength. However the field of view is largerand image quality is higher.

The angular magnification is given by(fO + fE); the lens separation is (fO + fE). Forterrestrial use an inverting lens can be in-cluded between the objective and the eye-piece. This is placed so that it is a distance2fI (fI is its focal distance) from the firstimage formed by the objective. An erectimage is formed a distance 2f behind the in-verting lens, arranged to be at the principalfocus of the eyepiece. The magnification isnot affected but the distance from objectiveto eyepiece is now fO + fE + 4f. The tele-scope is named for the German astronomerJohannes Kepler (1571–1630). See also re-fractor.

Kepler’s laws /kep-lerz/ The laws of plan-etary motion deduced in about 1610 byJohannes Kepler using astronomical obser-vations made by Tycho Brahe:(1) the planets describe elliptical orbitswith the Sun at one focus of the ellipse.

K

observer

convergingeye lens

convergingobjective

first image(real)

final image(virtual)

Keplerian telescope

(2) the line between a planet and the Sunsweeps out equal areas in equal times.(3) the square of the period of a planet’sorbit is proportional to the cube of thesemi-major axis of the ellipse.

Kerr effect /ker/ The appearance of bire-fringence in certain isotropic substanceswhen placed in a strong electric field. Theeffect is proportional to the square of thefield strength. It is used in Kerr cells, whichcan switch light radiation extremelyrapidly (often within a few picoseconds).Benzene is an example of a substanceshowing the Kerr effect. It is named for theBritish physicist John Kerr (1824–1907).

keV kiloelectronvolts; 103 electronvolts.

kilo- Symbol: k A prefix denoting 103. Forexample, 1 kilometer (km) = 103 meters(m).

kilocalorie /kil-ŏ-kal-ŏ-ree/ An energyunit equal to 1000 calories, sometimescalled the Calorie (with a capital C), asused by dietitians.

kilogram /kil-ŏ-gram/ Symbol: kg The SIbase unit of mass, equal to the mass of theinternational prototype of the kilogram,which is a cylinder of platinum–iridiumkept at Sèvres in France. It is the only SIbase unit not defined in terms of funda-mental constants.

kilogram-force Symbol: kgf A m.k.s.unit of gravitational force equal to that act-ing on a mass of one kilogram at sea level.In SI derived units it is equal to 9.806 65newtons. The alternate term kilopond hasbeen used to avoid potential confusion ofthe kilogram-force with the kilogram.

kilopond Symbol: kp See kilogram-force.

kilowatt-hour /kil-ŏ-wot/ Symbol: kWhA unit of energy, usually electrical, equal tothe energy transferred by one kilowatt ofpower in one hour. It is the same as theBoard of Trade unit (BTU) and has a valueof 3.6 × 106 joules.

kinematics /kin-ĕ-mat-iks/ The study ofthe motion of objects. See also dynamics.

kinematic viscosity Symbol: v The ratioof a fluid’s VISCOSITY to its density.

kinetic energy /ki-net-ik/ Symbol: T Thework that an object can do because of itsmotion. For an object of mass m movingwith velocity v, the kinetic energy is givenby mv2/2. This gives the work the objectwould do in coming to rest. The rotationalkinetic energy of an object of moment ofinertia I and angular velocity ω is given byIω2/2.

See also energy.

kinetic equation A type of equation usedto describe the way in which a systemchanges with time in statistical mechanics.The first example, known as the Boltz-mann equation, was put forward by theAustrian physicist Ludwig Boltzmann(1844–1906) in 1872. Kinetic equationsare often used to calculate transport quan-tities, such as thermal or electrical conduc-tivity.

kinetic friction See friction.

kinetic theory (of gases) The moleculesor atoms of a gas are in continuous randommotion and the pressure (p) exerted on thewalls of a containing vessel arises from thebombardment by these fast moving parti-cles. These have average speeds, at normalpressures and temperatures, of around onekilometer per second. When the tempera-ture is raised these speeds increase; so con-sequently does the pressure. If moreparticles are introduced or the volume is re-duced there are more particles to bombardunit area of the walls and the pressure alsoincreases. When a particle collides with thewall it experiences a rate of change of mo-mentum, which is equal to the force ex-erted. For a large number of particles thisprovides a steady force per unit area (orpressure) on the wall.

Following certain additional assump-tions, the kinetic theory leads to an expres-sion for the pressure exerted by an idealgas. The assumptions are:

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kinetic theory

1. The particles behave as if they are hardsmooth perfectly elastic points.2. They do not exert any appreciable forceon each other except during collisions.3. The volume occupied by the particlesthemselves is a negligible fraction of thevolume of the gas.4. The duration of each collision is negligi-ble compared with the time between colli-sions.

By considering the change in momen-tum on impact with the walls it can beshown that p = ρc2/3 where ρ is the densityof the gas and c is the root-mean-squarespeed of the molecules. The mean squarespeed of the molecules is proportional tothe absolute temperature:

Nmc2 = RTSee also degrees of freedom; equiparti-

tion of energy.

Kirchhoff’s law (of radiation) /kersh-hofs/ For a given wavelength the emissiv-ity of a surface in a particular direction isequal to the absorptance for radiation inci-dent from that direction. The law is namedfor the German physicist Gustav RobertKirchoff (1824–87).

Kirchhoff’s laws A set of rules for calcu-lating unknown currents, resistances, andvoltages in an electric circuit. They are:1. The algebraic sum of the currents at anypoint in any circuit is zero. For example, if6 amperes enter a three-way junctionthrough one wire, then 6 amperes mustleave through the other two. A currentflowing away from a junction has an op-posite sign to one flowing toward the junc-tion.2. The algebraic sum of the e.m.f.s roundany closed loop in any circuit is equal tothe sum of the products of current and re-sistance around the loop. For example, in acircuit with e.m.f. E, current I, and resis-tances R and r, E = Ir + IR.

klystron /klis-tron, klÿs-tron/ A cavityresonator used for generating microwaveradiation. It is a velocity-modulated elec-

tron beam tube, originally used in radarequipment. See also magnetron.

K-meson See kaon.

knife edge A sharp wedge used as a ful-crum or support, as in a balance. The sharpedge minimizes the area of contact betweenmoving parts, thereby reducing the frictionbetween them. Knife edges are made ofhard material such as agate.

krypton /krip-ton/ A colorless odorlessmonatomic element of the rare-gas group,known to form unstable compounds withfluorine. It occurs in minute quantities(0.001% by volume) in air. Krypton is usedin fluorescent lights.

Symbol: Kr; m.p. –156.55°C; b.p.–152.3°C; d. 3.749 (0°C) kg m–3; p.n. 36;r.a.m. 83.80.

Kundt’s tube /kûnt/ A device for showingstationary waves in a gas (or liquid). A hor-izontal rod, clamped at its midpoint, has aflat disk (E) on one end. The disk just fitsinto the bore of a glass tube, which isclosed at the other end with a flat surface(R). Fine powder is sprinkled along the in-side of the tube. The rod is stroked to pro-duce longitudinal vibrations; sound wavesare generated by the disk, travel down thetube, and are reflected at the closed end.The position of the disk is changed (chang-ing the length of the column of gas) untilstanding waves are produced. The dustthen vibrates strongly and settles in regu-larly-spaced heaps along the tube. Theseare pressure antinodes (i.e. particle-veloc-ity nodes).

Kirchhoff’s law

134

A

node in rodnode in air

powderE

λ /2λ /2

R

Kundt’s tube

label A stable or radioactive nuclide usedto investigate some process, such as achemical reaction. It is also sometimescalled a tracer. See radioisotope.

lag The time or angle by which one peri-odic quantity is delayed with respect to an-other.

Lagrangian point /lă-gran-jee-ăn, -grahn-/ A point in the plane of a two-body sys-tem, such as the Earth and the Moon, inwhich small bodies, such as artificial satel-lites, can be trapped because the gravita-tional fields of the two bodies are equal atthat point. The idea was first put forwardby the French astronomer Joseph Louis La-grange in 1772.

lambda particle /lam-dă/ See elementaryparticles.

lambda point The temperature at whichliquid helium I becomes the superfluid he-lium II. See helium.

lambert /lam-bert/ The c.g.s. unit of lumi-nance defined as that of a perfectly diffus-ing surface which reflects one lumen persquare centimeter. In SI units it is equal to3183.099 candelas per square meter. It isapproximately 3.18 × 103 Cd m–2. The unitis named for the German mathematician,physicist, astronomer, and philosopher Jo-hann Heinrich Lambert (1728–77).

Lambert’s law 1. First proposed in 1760;then restricted to visible light, it is nowused with all radiations. The law concernsthe rate of absorption of radiation as ittravels deeper into a medium. It states thatequal thicknesses of the medium absorbequal proportions of the incident radia-

tion. In other words, the intensity I of thetransmitted radiation falls off exponen-tially with distance d in the medium:

I = I0exp–αdHere I0 is the intensity of the initially in-

cident radiation, and α is the linear ab-sorption coefficient of the medium. As wellas depending on the medium, α varies withwavelength.2. In photometry, the fact that the lumi-nous intensity of a diffuse surface varieswith angle of view:

I0 = I0cosθHere, I0 is the intensity along the normal,while I is that along a line at angle θ to thenormal. The principle is often called Lam-bert’s cosine law.

laminar flow /lam-ă-ner/ Steady flow inwhich the fluid moves past a surface in par-allel layers of different velocities. Compareturbulent flow. See also Poiseuille’s for-mula.

laminated iron /lam-ă-nay-tid/ A piece ofiron constructed in thin layers that are sep-arated by electrical insulator. Laminatediron cores are used in many electric ma-chines. The laminations are used to reduceeddy currents caused by a changing mag-netic field.

lanthanum /lan-thă-nŭm/ A soft ductilemalleable silvery metallic element that isthe first member of the lanthanoid series. Itis found associated with other lanthanoidsin many minerals, including monazite andbastnaesite. Lanthanum is used in severalalloys (especially for lighter flints), as a cat-alyst, and in making optical glass.

Symbol: La; m.p. 921°C; b.p. 3457°C;r.d. 6.145 (25°C); p.n. 57; r.a.m.138.9055.

135

L

Laplace equation

136

Laplace equation /lă-plass, -plahss lah-/An important equation of mathematicalphysics, which can be written as ∇2φ = 0,where φ is a scalar function such as thegravitational or electric potential of a sys-tem and ∇2 is the LAPLACIAN. The Laplaceequation is a special case of the POISSON

EQUATION. The equation was first put for-ward by the French mathematician PierreSimon Laplace (1749–1827). It is used inmany branches of physics, including fluidmechanics, electromagnetic theory, andgravity.

Laplacian /lă-plass-ee-ăn/ Symbol∇2. Amathematical operator defined by ∂2/∂x2 +∂2/∂y2 + ∂2/∂z2. The Laplacian occurs inmany equations of mathematical physicsincluding the LAPLACE EQUATION and thePOISSON EQUATION.

large-scale structure Structure in theUniverse that involves large numbers ofobjects, as in galaxies and clusters of galax-ies. It is thought that the inhomogeneousdistribution of matter into such structure isa consequence of quantum fluctuations inthe early Universe.

Larmor precession /lar-mor/ The preces-sion in the orbital motion of an electronabout the nucleus of an atom resultingfrom the application of a small externalmagnetic field. The precession is named forthe Irish physicist Sir Joseph Larmor(1857–1942).

laser /lay-zer/ (light amplification by stim-ulated emission of radiation) A device ableto produce a beam of radiation with un-usual properties. Generally the beam is: co-herent (the waves are in phase);monochromatic (the waves are of effec-tively the same wavelength); parallel; andintense (carrying a great deal of energy).

There are innumerable applications ofsuch beams in communications, engineer-ing, science, and medicine. Laser action isobtained in a volume of suitable material(solid, liquid, or gas) into which energy ispassed at a high rate.

The input energy excites the active par-ticles to a higher energy state W2 fromwhich they return to a comparatively sta-ble state W1 above the ground state, W0.They accumulate there, forming a popula-tion inversion. Passing photons of energy(W1–W0) stimulate decay to the groundstate. The photons emitted travel in phasewith, and in the same direction as, thosethat stimulated their production.

In practice, reflecting surfaces are usedat each end of the device – one totally re-flecting and the other partially reflecting.The radiation is reflected backward andforward, building up an intense beam,which is emitted through the partially re-flecting surface.

In solid lasers, such as the ruby laser,the population inversion is produced by anintense external light source. Generally it ispulsed. The wavelength is 694.3 nm. In gaslasers, a discharge is used. The carbondioxide laser gives a wavelength of 10.5µm. Helium-neon lasers produce a numberof separate wavelengths, including 1.153µm. Gas lasers can produce continuous(rather than pulsed) beams.

See also holography.

latent heat /lay-tĕnt/ The energy trans-ferred when a substance changes its statefrom solid to liquid, liquid to gas, solid togas, etc. For example, when a liquid boilsthe latent heat taken in is partly used toovercome attractive forces between themolecules, and partly to do work in ex-panding against atmospheric pressure. Thespecific latent heat (specific latent thermalcapacity) is the energy transferred in con-verting unit mass from one state to anotherat the same temperature. For instance, thespecific latent thermal capacity of fusion(solid-liquid) or the specific latent thermalcapacity of evaporation (liquid-gas). Theunits are joules per kilogram (J kg–1). La-tent heats are standard enthalpies for theseprocesses.

lateral inversion See perversion.

lattice See crystal.

lattice energy The energy required to sep-

arate an ion from a crystal to an infinitedistance. It is measure of the strength of anionic bond.

law of flotation See flotation; law of.

law of magnetic poles (law of magnet-ism) The rule describing the forces be-tween nearby poles – like poles repel eachother; unlike poles attract each other.

law of moments See moment.

lawrencium /lor-en-see-ŭm/ A radioactivetransuranic element of the actinoid series,not found naturally on Earth. Several veryshort-lived isotopes have been synthesizedby bombarding 252Cf with boron nuclei or249Bk with 18O nuclei.

Symbol: Lr; p.n. 103; most stable iso-tope 262Lr (half-life 261 minutes).

laws of conservation See conservationof mass and energy; constant energy (lawof), constant (linear) momentum (law of),constant mass (law of), constant angularmomentum (law of).

laws of electromagnetic induction Seeelectromagnetic induction.

laws of friction See friction.

laws of reflection See reflection; laws of.

laws of refraction See refraction; lawsof.

laws of thermodynamics See thermody-namics.

LCR circuit See alternating-current cir-cuit.

LDR See light-dependent resistor.

lead /led/ A dense, dull, gray, soft metallicelement; the end product of radioactivedecay series. It occurs in small quantities ina wide variety of minerals but only a feware economically important. Lead is usedin (lead–acid) accumulators, alloys, radia-tion shielding, and water and sound proof-

ing. It is also used in the petrochemical,paint, and glass industries.

Symbol: Pb; m.p. 327.5°C; b.p.1830°C; r.d. 11.35 (20°C); p.n. 82; r.a.m.207.2.

lead-acid accumulator A type of electri-cal accumulator used in vehicle batteries. Ithas two sets of plates: spongy lead platesconnected in series to the negative terminaland lead oxide plates connected to the pos-itive terminal. The material of the elec-trodes is held in a hard lead-alloy grid. Theplates are interleafed. The electrolyte is di-lute sulfuric acid.

The e.m.f. when fully charged is about2.2 V. This falls to a steady 2 V when cur-rent is drawn. As the accumulator begins torun down, the e.m.f. falls further. Duringdischarge the electrolyte becomes more di-lute and its relative density falls. Torecharge the accumulator, charge is passedthrough it in the opposite direction to thedirection of current supply. This reversesthe cell reactions, and increases the relativedensity of the electrolyte (c. 1.25 for a fullycharged accumulator).

The electrolyte contains hydrogen ions(H+) and sulfate ions (SO4

2–). During dis-charge, H+ ions react with the lead (IV)oxide to give lead (II) oxide and water

PbO2 + 2H+ + 2e– → PbO + H2OThis reaction takes electrons from theplate, causing the positive charge. There isa further reaction to yield soft lead sulfate:

PbO + SO42– + 2H+ → PbSO4 + H2O +

2e–Electrons are released to the electrode, pro-ducing the negative charge.

During charging the reactions are re-versed:

PbSO4 + 2e– → Pb + SO42–

PbSO4 + 2H2O → PbO2 + 4H+ + SO42–

+ 2e–

Le Chatelier principle /lă-sha-tel-yay/ Ifa constraint is applied to any system inEQUILIBRIUM, the system will tend to adjustitself to minimize the effect of the con-straint. The principle is usually applied tocases of chemical equilibrium. The princi-ple is named for the French chemist HenriLouis Le Chatelier (1850–1936).

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Le Chatelier principle

Leclanché cell /lă-klahn-shay/ A primaryvoltaic cell consisting, in its ‘wet’ form, ofa carbon-rod anode and a zinc cathode,with a 10–20% solution of ammoniumchloride as electrolyte. Manganese(IV)oxide mixed with crushed carbon in aporous bag or pot surrounding the anodeacts as a depolarizing agent. The dry form(dry cell) is widely used for flashlight bat-teries, transistor radios, etc. It has a mix-ture of ammonium chloride, zinc chloride,flour, and gum forming an electrolytepaste. Sometimes the dry cell is arranged inlayers to form a rectangular battery, whichhas a longer life than the cylinder type. Thecell is named for the French engineerGeorges Leclanché (1839–82).

LED /el-ee-dee/ See light-emitting diode.

LEED Low-energy electron diffraction.See electron diffraction.

Lees’ disk An apparatus for measuringthe thermal conductivity of a poor conduc-tor. The sample is a thin flat disk of known

area (A) and thickness (l) placed betweentwo disks of brass (or other good conduc-tor), each having a thermometer in a holein its side. The apparatus is suspended bystrings and the top disk is raised in temper-ature. Under steady conditions energypasses at a steady rate and the tempera-tures of the top and bottom metal disks areθ2 and θ1. The bottom conductor loses en-ergy by radiation: to measure the rate ofloss of energy, the bottom slab is warmedto the temperature θ2, the insulator placedon top, and a cooling curve plotted so thatthat rate of temperature fall can be ob-tained at the lower temperature θ1. Then kis found from the equation

kA(θ2 – θ1)/l = mcdθ/dtwhere m is the mass of the bottom slab, cits specific thermal capacity, and dθ/dt itsrate of temperature fall obtained from thecooling curve.

The apparatus can be modified for usewith liquids, these being contained in a in-sulating ring between the two metal disks.It is named for the English physicistCharles Herbert Lees (1864–1952).

Leclanché cell

138

converginglens

P = pole (optical center)F = focal point

axis P F

The paths of light rays through converging and diverging lenses

diverginglens

axis F P

left-hand rule See Fleming’s rules.

lens An optical component that refractsrays passing through, and either convergesor diverges them. With visible radiation,glass lenses in air are normally used; how-ever lenses of any transparent substancewould work. A lens is best described by itseffect on a parallel beam. Converginglenses make it convergent; diverging lensesmake it divergent. Focal distance is theusual measure of the power of a lens toconverge a parallel beam. Parallel rays arerefracted by converging and diverginglenses as shown in the diagram. Strictly,such focusing occurs only with rays paral-lel to and close to the principal axis. Raysfrom an object will be refracted so thatthey appear to come from somewhere else– the image. Two examples are given over-leaf to show how ray diagrams are drawn.

The object distance (u) and the imagedistance (v) relate to the focal distance (f)thus:1/f = 1/v + 1/u (in the real is positive, virtualis negative sign convention).

The formula applies to real or virtualfocal points, objects, and images. All theabove can be adapted to lenses for use withnonvisible radiations, including pressurewaves and electron beams.

Lenz’s law /lents-iz/ The direction of aninduced e.m.f. is such that it opposes thechange that produces it. For example, if apermanent bar magnet is moved toward acoil that forms part of a complete circuit,then current flows so that the magneticfield around the coil repels the magnet. Ifthis were not the case, no work would needto be done to cause charge to flow. The lawis named for the Estonian-born Germanphysicist Heinrich Friedrich Emil Lenz(1805–65).

lepton /lep-ton/ A type of elementary par-ticle including the electron, the muon, andthe neutrino. Leptons are distinguishedfrom hadrons by their type of interaction.See also elementary particles.

Leslie’s cube /lez-leez/ A cube-shaped canwith the four sides painted different colorsor given different finishes (polished, rough,etc.). It is filled with hot water and used inexperiments on the effect of surface onemissivity. The cube is named for the Scot-tish scientist Sir John Leslie (1766–1832).

lever A class of machine. Levers are rigidobjects able to turn around some point(pivot or fulcrum). The force ratio and thedistance ratio depend on the relative posi-

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lever

load F2

Teffort F1

First orderTurning-point between load and effort

l2l2l2 l1l1l1

lll111lll222

Tload F2 effort F1

Second orderLoad between turning point and effort

effort F1 load F2

T

lll111lll222

Third orderEffort between turning point and load

force ratio = F2 /F1 = l1 /l2distance ratio = l1 /l2

Lever

levorotatory

140

OBJECT AND IMAGE POSITIONS FOR CONVERGING LENS

Object position Image nature Image positioninfinity real F or F′ beyond 2F or 2F′ real between F′ (F) and 2F′ (2F)2F or 2F′ real 2F′ or 2Fbetween 2F (2F′) and F (F′) real beyond 2F′ or 2FF or F′ virtual infinitybetween F (F′) and P virtual between infinity and P

OBJECT AND IMAGE POSITIONS FOR DIVERGING LENS

Object position Image nature Image positioninfinity virtual F or F′ beyond 2F or 2F′ virtual between F or F′ and P2F or 2F′ virtual between F or F′ and Pbetween 2F (2F′) and F (F′) virtual between F or F′ and PF or F′ virtual between F or F′ and Pbetween F (F′) and P virtual between F or F′ and P

| | | |

observerI

2FFPF’O2F’

Object O is between 2F’ and F’Image I is real, inverted, magnified, andbeyond 2F

converging lens

Ray diagram showing a real (inverted) imageformed from a real object

| | | |

diverginglens

axis

2F O F I P F’ 2F’

observer

image I is betweenF and P, virtual,upright, anddiminished

Ray diagram showing a virtual (erect) imageformed from a real object

biconvex plano-convex

concavo-convex

(a)

Types of lens

biconcave plano-concave

concavo-concave

(b)

tions of the pivot, the point where the userexerts the effort, and the point where thelever applies force to the load. There arethree types (orders) of lever.

Levers can have high efficiency; themain energy losses are by friction at thepivot, and by moving the lever itself.

levorotatory /lee-voh-roh-tă-tor-ee. -toh-ree/ See optical activity.

Leyden jar /lÿ-d’n/ An early type of ca-pacitor made from a glass jar with metalfoil on its inner and outer surfaces. TheLeyden jar (sometimes spelt Leiden jar) isnamed for the Dutch town of Leyden,where it was invented.

LF See low frequency.

lift A force exerted by a fluid (gas or liq-uid) on an object in its flow. It acts upwardat right angles to the direction of the flow,and is therefore the force that enables birdsand winged aircraft to fly. See also airfoil;drag.

light (visible radiation) A form of electro-magnetic radiation able to be detected bythe human eye. Its wavelength range is be-tween about 400 nm (far ‘red’) and about700 nm (far ‘violet’). The boundaries arenot precise as individuals vary in their abil-ity to detect extreme wavelengths; this abil-ity also declines with age.

Light is produced by surfaces at tem-peratures above about 900 K. Below about6000 K, however, the majority of the radi-ation emitted is infrared. The standardhousehold filament lamp works at about2800 K; at this temperature only a few per-cent of the emitted radiation is visible.‘Cold’ sources, such as certain chemical re-actions, glowworms, lasers, and dischargetubes, are more efficient in this sense.

These produce light by specific transi-tions between electronic energy levels inatoms and molecules. Their spectra aretherefore not continuous, but sets of lines.

light-dependent resistor (LDR) A resis-tor whose resistance decreases when it is il-luminated. LDRs are made from

semiconductors such as cadmium sulfideand selenium.

light-emitting diode (LED) A semicon-ductor DIODE, made from certain materials(e.g. gallium arsenide), in which light isemitted in response to the forward-biascurrent. The light results from the recom-bination of electrons and positive holes,with a transition to a lower energy state.See also transistor.

lightning An electrical discharge in the at-mosphere between charged clouds and theEarth, or between the clouds.

lightning conductor A thick metal con-ductor (usually copper) that runs from thetop of a high building to the ground (wherethe end is buried). Its function is to conductany lightning strikes safely to earth.

light-year Symbol: ly A unit of distanceused in astronomy, defined as the distancethat light travels through space in one year.It is approximately equal to 9.460 528 ×1015 meters.

limit cycle A closed curve in phase spaceto which a system evolves. A limit cycle isa type of ATTRACTOR characteristic of oscil-lating systems.

limiting friction See friction.

linac /lin-ak/ See linear accelerator.

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linac

THE RANGE OF COLORS IN THE VISIBLE SPECTRUM

Wavelength range (nm) Color400–420 violet420–450 indigo450–500 blue500–550 green550–600 yellow600–650 orange650–700 red

Note that perception of different colorsvaries between individuals.

Linde process /lin-dĕ/ A method of lique-fying gases by compression followed by ex-pansion through a nozzle. The temperaturefalls by the Joule–Kelvin effect. The cooledgas is used to reduce the temperature of thecompressed gas. Eventually the tempera-ture falls below the boiling point and thegas liquefies. The gas must start thisprocess below its inversion temperature.Hydrogen can be liquefied by this methodif it is first cooled below its inversion tem-perature using liquid air. Helium is cooledbelow its inversion temperature by usingliquid hydrogen boiling under reducedpressure. The process is named for the Ger-man engineer Karl von Linde (1842–1934). See also cascade process.

linear accelerator (linac) A device for ac-celerating charged particles in a straightline. It consists of a series of cylindricalelectrodes of increasing length, alternateones of which are connected together andbetween which an alternating voltage is ap-plied. A charged particle is accelerated toenter the first cylinder. By the time itemerges the voltages of the cylinders havereversed, and it is now repelled from thefirst cylinder and attracted towards the sec-ond, so accelerating and gaining energyeach time it crosses a gap between cylin-ders. The cylinders have to be made pro-gressively longer as the particles speed upso that the particles arrive at the gaps at thecorrect point in the voltage cycle.

A more advanced type of linear acceler-ator used for electrons and protons has atraveling radio-frequency electromagneticwave in a waveguide. The particles are car-ried by the electric component of the wave.See also tandem generator.

linear charge density See charge density.

linear density See density.

linear expansivity See expansivity.

linear momentum See momentum.

linear momentum, conservation of Seeconstant (linear) momentum (law of).

linear motor An ELECTRIC MOTOR inwhich the ‘rotor’ is rectangular and travelsalong rails (which act as the ‘stator’). It is atype of INDUCTION MOTOR, used for suchapplications as opening automatic doors.

line defect See defect.

lines of force Imaginary lines drawn torepresent a force field. They show the di-rection of the field at each point; theircloseness represents the field strength (thecloser the lines, the greater the strength). Inthe case of magnetism, a line of forceshows the path a free N-pole would take inthe field.

Lines of force are a useful conventionfor showing fields; in magnetic fields theyare the original basis of magnetic flux.They have, however, no real existence.

line spectrum A SPECTRUM composed of anumber of discrete lines corresponding tosingle wavelengths of emitted or absorbedradiation. Line spectra are produced byatoms or simple (monatomic) ions in gases.Each line corresponds to a change in elec-tron orbit, with emission or absorption ofradiation.

line width The width of a spectral line inwavelength terms. The usual measure is thehalf-width of the line. See monochromaticradiation.

liquefaction /lik-wĕ-fak-shŏn/ A changeof state to a liquid. The term is often usedfor the conversion of gases to their liquidstate.

liquid See states of matter.

liquid barometer See barometer.

liquid crystal A compound that, al-though liquid at room temperature, showsbehavior normally expected only fromsolid crystalline substances. Some liquidcrystals change orientation in an electricfield and are used in liquid crystal displays(LCDs); others change color with tempera-ture, and are used for simple thermome-ters. See also Kerr effect.

Linde process

142

liquid crystal display (LCD) A type ofdigital display, used in calculators,watches, and other electronic equipment,based on the properties of LIQUID CRYSTALS.

liquid-drop model A model used in nu-clear physics in which the interaction be-tween nucleons is regarded as beinganalogous to the intermolecular forces be-tween water molecules in a drop of water.The liquid-drop model can be used to de-scribe certain nuclear phenomena and isparticularly successful in describing nu-clear fission. More complete quantitativeanalyses of nuclear physics require thecombination of the liquid-drop model withthe nuclear SHELL MODEL.

Lissajous’ figures /lee-sa-zhooz/ Patternsobtained by combining two simple har-monic motions in different directions.They can be demonstrated with an oscillo-scope, deflecting the spot with one oscillat-ing signal along one axis and with anothersignal along the other axis. A variety ofpatterns are produced depending on thefrequencies and phase differences. They arenamed for the French physicist Jules An-toine Lissajous (1822–80).

liter /lee-ter/ Symbol: L or l A unit of vol-ume defined as one cubic decimeter or 10–3

metre3. The name is not recommended forprecise measurements. Formerly, the literwas defined as the volume of one kilogramof pure water at 4°C and standard pres-sure. On this definition, 1l = 1000.028cm3.

lithium /lith-ee-ŭm/ A light silvery moder-ately reactive metal; it is a rare element ac-counting for 0.0065% of the Earth’s crust.

Symbol: Li; m.p. 180.54°C; b.p.1347°C; r.d. 0.534 (20°C); p.n. 3; r.a.m.6.941.

Lloyd’s mirror An arrangement in whichlight meets a mirror at grazing incidenceand is reflected to interfere with the directradiation. INTERFERENCE of the reflectedlight with the direct light produces fringes.The device is effectively a two-sourcearrangement. The apparatus is named forthe Irish physicist Humphrey Lloyd(1800–81).

logic gate An electronic circuit than canbe used to perform simple logical opera-tions. Examples of such operations are

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logic gate

(a) φ = 0, 2π (b) φ = π/4, 7π/4 (c) φ = π/2 (d) φ = 3π/4, 5π/4 (e) φ = π

Lissajous’ figures

screen

superposition region

virtual source

real source

Lloyd’s mirror

‘and’, ‘either–or’, ‘not’, ‘neither–nor’, etc.Logic gates operate on high or low inputand output voltages. Binary logic circuits,those that switch between two voltage lev-els (high and low), are widely used in digi-tal computers. The inverter gate or NOTgate simply changes a high input to a lowoutput and vice versa. In its simplest form,the AND gate has two inputs and one out-put. The output is high if and only if bothinputs are high. The NAND gate (not and)is similar, but with the output negated; thatis a low output if and only if both inputsare high. The OR gate has a high output ifone or more of the inputs are high. The ex-clusive OR gate has a high input only if oneof the inputs, but not more than one, ishigh. The NOR gate has a high output onlyif all the inputs are low. Logic gates areconstructed using transistors, but in a cir-cuit diagram they are often shown by sym-bols that denote only their logicalfunctions.

See also bistable circuit; multivibrator.

long hundredweight See hundred-weight.

longitudinal wave A wave motion inwhich the vibrations in the medium are inthe same direction as the direction of en-ergy transfer. Sound waves are an exampleof longitudinal waves. Compare transversewave.

long sight See hyperopia.

Lorentz–Fitzgerald contraction /lo-rents fits-je-răld/ According to classicaltheory, space contained an imponderablefluid ether providing an absolute referenceframe with respect to which bodies couldbe shown to be moving or at rest. The fail-ure of the Michelson–Morley experimentto show motion with respect to the etherwas explained by Lorentz and Fitzgeraldby the hypothesis that the length of any ob-ject contracts in the direction of its motionthrough the ether by the factor √(1 – v2/c2),where v is its speed in the ether and c thespeed of light. This was assumed to be areal physical change in the object and vari-

ous experiments were done to detect it,with negative results.

In the theory of relativity there is no ab-solute motion, the concept of an ether thatprovides a standard of rest is rejected.Hence the negative result of the Michel-son–Morley experiment is expected andthere is no justification for theLorentz–Fitzgerald hypothesis. In this the-ory the length of a body as measured byany observer with respect to whom thebody has a velocity v differs from thelength as measured by an observer at restwith respect to the body by the same factoras assumed by Lorentz and Fitzgerald. Thisis purely a mathematical result used by aparticular observer (observers with differ-ent uniform relative velocities would ob-tain different values) and does notrepresent any physical change in the body.The contraction is named for the Dutchphysicist Hendrik Antoon Lorentz(1853–1928) and the Irish physicistGeorge Francis Fitzgerald (1851–1901).

Lorentz force An aspect of the motor ef-fect; the force on a charge Q, moving at ve-locity v across a magnetic field B.

f = BQvsinθθ is the angle between v and B.

loudness The sensation that a sound pro-duces in a listener corresponding to its in-tensity (i.e. the energy flow per unit area).For a given frequency, the greater the in-tensity, the greater the loudness. Loudnessalso depends on the frequency of thesound. See phon.

loudspeaker A device for converting anelectrical signal into sound. Most loud-speakers consist of a small coil, throughwhich the signal flows, attached to the cen-ter of a diaphragm or cone. The coil is freeto move in an annular gap between thepoles of a magnet. The changing current inthe coil causes it to vibrate in the magneticfield and the cone sends out these vibra-tions as sound waves.

lowering of vapor pressure The lower-ing of the vapor pressure of a liquid thatoccurs when a solute is dissolved in the liq-

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uid. The reduction is proportional to thenumber of molecules of solute dissolvedper unit volume of liquid solvent, i.e. thelowering of vapor pressure is one of theCOLLIGATIVE PROPERTIES of matter.

low frequency (LF) A radio frequency inthe range between 300 kHz and 30 kHz(wavelength 1 km-10 km).

low tension (L.T.) Low voltage.

lumen (pl. lumens or lumina) /loo-mĕn/Symbol: lm The SI unit of luminous flux,equal to the luminous flux emitted by apoint source of one candela in a solid angleof one steradian. 1 lm = 1 cd sr.

luminance /loo-mă-năns/ Symbol: Lv Ameasure of the brightness of an extendedsource (one that cannot be considered apoint). In a given direction, it is the lumi-nous intensity per unit area projected atright angles to the direction. The unit is thecandela per square meter (cd m–2).

luminescence /loo-mă-ness-ĕns/ Theemission of radiation from a substance inwhich the particles have absorbed energyand gone into excited states. They then re-turn to lower energy states with the emis-sion of electromagnetic radiation. If theluminescence persists after the source ofexcitation is removed it is called PHOSPHO-RESCENCE; if not, it is called FLUORESCENCE.

The excitation of the particles mayoccur by a variety of mechanisms. Absorp-tion of other electromagnetic radiationgives photoluminescence. If the original ex-cited states are produced by bombardmentwith electrons the phenomenon is electro-luminescence. Chemiluminescence is lumi-nescence produced by chemical reactions.Bioluminescence occurs in natural systems,e.g. glowworms and fireflies. Radiolumi-nescence occurs in radioactive materials.

Luminescence produced in materials byfriction is called triboluminescence.

luminosity /loo-mă-noss-ă-tee/ See bright-ness; luminous intensity.

luminous exitance See exitance.

luminous flux Symbol: Φv The rate offlow of energy of visible radiation. It is theradiant flux corrected for the fact that thesensitivity of the eye is different for differ-ent wavelengths. The unit is the lumen(lm).

luminous intensity Symbol: Iv The lumi-nous flux from a point source per unit solidangle. The unit is the candela (cd).

lunar eclipse /loo-ner/ See eclipse.

lunar time See time; year.

lutetium /loo-tee-shee-ŭm/ A silvery ele-ment of the lanthanoid series of metals. Itoccurs in association with other lan-thanoids. It is rare and has few uses.

Symbol: Lu; m.p. 1663°C; b.p. 3395°C;r.d. 9.84 (25°C); p.n. 71; r.a.m. 174.967.

lux (pl. lux) /luks/ Symbol: lx The SI unitof illumination, equal to the illuminationproduced by a luminous flux of one lumenfalling on a surface of one square meter. 1lx = 1 lm m–2.

Lyman series /lÿ-măn/ A series of lines inthe ultraviolet spectrum emitted by excitedhydrogen atoms. They correspond to theatomic electrons falling into the lowest en-ergy level and emitting energy as radiation.The wavelength (λ) of the radiation in theLyman series is given by 1/λ = R(1/12 –1/n2), where n is an integer and R is the Ry-dberg constant. The series is named for theAmerican physicist Theodore Lyman(1874–1954). See also spectral series.

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machine A device for transmitting powerbetween one place and another. The userapplies a force (the effort) to the machine;the machine applies a force to a load ofsome kind. These two forces need not bethe same. In fact the purpose of the ma-chine may well be to overcome a large loadwith a small effort. For any machine thisrelationship is measured by the force ratio(or mechanical advantage): this is the forceapplied by the machine (load, F2) dividedby the force applied by the user (effort, F1).

The work done by the machine cannotexceed the work done to the machine.Therefore, for a 100% efficient machine:

if F2 > F1 then s2 < s1and if F2 < F1 then s2 > s1.

Here s2 and s1 are the distances moved byF2 and F1 in a given time.

The relationship between s1 and s2 in agiven case is measured by the distance ratio(or velocity ratio). This is the distancemoved by the effort (s1) divided by the dis-tance moved by the load (s2).

Neither distance ratio nor force ratiohas a unit; neither has a standard symbol.See also efficiency; hydraulic press; in-clined plane; lever; pulley; screw.

Mach number /makh/ The ratio of thespeed of a moving object (e.g. a high-speedaircraft) to the speed of sound in the air orother medium through which the object istraveling. An aircraft passes through the‘sound barrier’ as the Mach number ex-ceeds one; at this speed the air resistanceincreases sharply. The number is namedfor the Austrian physicist Ernst Mach(1838–1916).

magic number In nuclear physics, one ofseveral numbers of neutrons or protonsthat characterize especially stable atomic

nuclei. They are 2, 8, 20, 28, 50 and 82.The magic numbers in nuclei are the analogof closed electron shells in atoms.

magnesium /mag-nee-zee-ŭm, -seee-ŭm/A light metallic element. It has the elec-tronic configuration of neon with two ad-ditional outer 3s electrons. The elementaccounts for 2.09% of the Earth’s crustand is eighth in order of abundance. Mag-nesium metal is industrially important as amajor component in lightweight alloys(with aluminum and zinc). The metal sur-faces develop an impervious oxide filmwhich protects them from progressive dete-rioration.

Symbol: Mg; m.p. 649°C; b.p. 1090°C;r.d. 1.738 (20°C); p.n. 12; r.a.m. 24.3050.

magnet /mag-nĕt/ See permanent magnet.

magnetic bottle /mag-net-ik/ A magneticforce field used to contain charged parti-cles as in nuclear fusion experiments(where it contains the plasma). The plasmatemperature may exceed 100 million de-grees Celsius and any material containerwould vaporize instantly. The temperatureis so high that all the electrons are strippedfrom the atoms and the matter consists en-tirely of charged particles, which can be re-strained by a suitably arranged magneticfield.

magnetic circuit A closed path formedby magnetic lines of force. A simple exam-ple is given by a horseshoe magnet; its mag-netic circuit is improved by the use of akeeper.

The concept is very important in electri-cal engineering; it compares directly to anelectric circuit. Magnetomotive force F(unit – the ampere, A) compares to e.m.f.;

M

magnetic flux Φ (unit – the weber, Wb) isthe analog of current; reluctance R (unit –reciprocal henry, H–1) is like resistance.

magnetic compass See compass.

magnetic constant See permeability.

magnetic cooling A method of attainingvery low temperatures (well below 1 K). Asalt is magnetized isothermally and thendemagnetized adiabatically. See cryogen-ics.

magnetic declination See declination.

magnetic dip See inclination.

magnetic dipole A pair of north-seekingand south-seeking magnetic poles a dis-tance apart, as in a bar magnet. A loop car-rying an electric current also acts as amagnetic dipole, as do many atoms.

magnetic dipole moment See magneticmoment.

magnetic domain See domain.

magnetic elements The Earth’s magnet-ism at any point is defined by three mag-netic elements, which give the strength anddirection of the field at that point. They arethe horizontal component of the field andthe angles of inclination and declination.The horizontal intensity can be measuredby an Earth inductor, the inclination by aninclinometer, and the declination by acompass.

The elements change from place toplace and with time. See also magneticvariation.

magnetic equator See isoclinic line.

magnetic field A region in which a mag-netic force can be observed; i.e. a smallmagnet or a small loop of wire carrying acurrent will experience a force. Thestrength and direction of a field can be rep-resented by lines of force. The number oflines per unit cross-sectional area is a mea-

sure of magnetic field strength – the mag-netic flux density B.

magnetic field strength (magnetic inten-sity) Symbol: H The force that would beexerted on a unit N-pole at a given point ina magnetic field. The unit is the ampere permeter (A m–1).

magnetic flux Symbol: Φ The strength ofa magnetic field through an area, based onthe idea of the number of lines of forcepassing through the area. It is given by theproduct of magnetic flux density (B) andarea. The unit is the weber (Wb).

magnetic flux density (magnetic induc-tion) Symbol: B The flux per unit perpen-dicular area of a magnetic field; it issometimes thought of as the number oflines of force per unit area. It is defined bythe effect on a current-carrying conductorin the field. For a field B:

B = F/Qvwhere F is the force on a charge Q movingperpendicular to the field with velocity v.

The unit of magnetic flux density is thetesla (T). It is equivalent to the weber persquare meter (Wb m–2) since

B = ΦAwhere Φ is magnetic flux and A is area. InSI the relationship between magnetic fluxdensity and magnetic field strength is:

B = µrµ0Hwhere µr is the relative permeability of themedium and µ0 the permeability of freespace.

magnetic focusing The use of shapedmagnetic fields to focus beams of chargedparticles. Applications of the technique arefound in cathode-ray tubes, accelerators,and electron microscopes.

magnetic hysteresis See hysteresis.

magnetic induction 1. The magnetiza-tion of a substance by an external magneticfield. If a sample of magnetic material isplaced near a strong magnet N- and S-polesare induced in it. The sample will then actas an induced magnet and be attracted tothe other. See also induction.

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2. See magnetic flux density.

magnetic meridian An imaginary line onthe Earth’s surface joining the two mag-netic poles, and passing through the ob-server’s position. It is the line along whicha compass needle comes to rest at thatpoint. The angle between the magnetic andgeographic meridians is the declination atthat point, one of the three magnetic ele-ments.

See also Earth’s magnetism.

magnetic moment (magnetic dipole mo-ment) Symbol: m A measure of thestrength of a magnet or current-carryingcoil. It relates to the turning effect (mo-ment) on it when in a given field. It is de-fined as the torque T observed in a unitfield at 90° to the magnetic axis:

m = T/BThe unit is ampere meters-squared (A m2).For a coil with N turns and area A carryinga current I:

m = NIAIn this case m is often called the electro-magnetic moment of the coil.

magnetic monopole An elementary par-ticle postulated but not discovered, equiva-lent to an isolated N- or S-pole. Themonopole was postulated to provide sym-metry between theories of electricity andmagnetism.

magnetic north The location of the northmagnetic pole, the direction toward whicha magnetic compass needle points. Its posi-tion varies from year to year and also fromtime to time during the year. See poles;magnetic.

magnetic permeability See permeability.

magnetic pole See poles; magnetic.

magnetic pole strength See polestrength.

magnetic potential See magnetomotiveforce.

magnetic resistance See reluctance.

magnetic resonance imaging (MRI) Atechnique used in medicine for producingimages of the human body (or parts of thebody) which makes use of nuclear mag-netic resonance. In MRI the sample isplaced in a strong magnetic field and irra-diated with radiofrequency electromag-netic radiation, causing hydrogen nuclei tobe raised to a higher spin energy state. Re-version of these to the ground state emitsradiation, which is detected and analyzedto give a three-dimensional picture of in-ternal structures. MRI is less dangerousthan x-ray diagnosis, but is also better forinvestigating soft tissues.

magnetic susceptibility See susceptibil-ity.

magnetic variation 1. Various changeswith time of the magnetic elements at apoint on the Earth’s surface. Secularchanges are slow continuous changes.Thus the angle of declination at Londonhas changed from zero in 1659 to 8° in1960; the inclination at the same place haschanged from 74° in 1700 to 66° in 1960.Abrupt changes in the magnetic elementsare due to magnetic storms, which are re-lated to solar activity. See also annual vari-ation.2. A term still widely used in navigation in-stead of declination.

magnetism /mag-nĕ-tiz-ăm/ The study ofthe nature and cause of magnetic forcefields, and how different substances are af-fected by them. Magnetic fields are pro-duced by moving charge – on a large scale(as with a current in a coil, forming an elec-tromagnet), or on the small scale of themoving charges in the atoms. It is generallyassumed that the Earth’s magnetism andthat of other planets, stars, and galaxieshave the same cause. Substances may beclassified on the basis of how samples in-teract with fields. Different types of mag-netic behavior result from the type of atom.Diamagnetism, which is common to allsubstances, is due to the orbital motion ofelectrons. Paramagnetism is due to electron

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spin, and is a property of materials con-taining unpaired electrons. Ferromagnet-ism, the strongest effect, also involveselectron spin and the alignment of mag-netic moments in domains. Anti-ferromag-netism and ferrimagnetism are rarer effectsinvolving antiparallel alignment of spinmagnetic moments.

magnetism, terrestrial See Earth’s mag-netism.

magnetocaloric effect /mag-nee-toh-kă-lor-ik, -loh-rik/ The change of temperatureof a sample as the external magnetic fieldchanges. In particular, energy is stored inferromagnetic domains; as these appear ordisappear, energy is absorbed or released.A use of the effect is in adiabatic demagne-tization for the production of very lowtemperatures (close to absolute zero).

magnetohydrodynamics /mag-nee-toh-hÿ-droh-dÿ-nam-iks/ (MHD) The study ofhow magnetic fields interact with conduct-ing fluids (e.g. plasmas or liquid metals).

magnetometer /mag-nĕ-tom-ĕ-ter/ Aform of compass used for comparing mag-netic field strengths. The deflection magne-tometer consists of a very small barmagnet, pivoted so that it is free to move ina horizontal plane. A circular scale, gradu-ated in degrees, is placed below the magnetand a long light pointer is attached over itat 90°. The magnetometer is rotated in amagnetic field, H1, so that the reading is360. When another field, H2, is placed atright angles to H1, the needle is deflectedby an angle θ. Then:

tanθ = H1/H2The vibration magnetometer makes use ofthe (simple harmonic) vibration of a mag-netic needle to measure the horizontalmagnetic field strength at the needle. Thefield strength is inversely proportional tothe square of the period.

magnetomotive force /mag-nee-toh-moh-tiv/ (magnetic potential; m.m.f.) Sym-bol: F The integral of the magnetic fieldstrength around a closed path; i.e.

ʃΟHdl

The unit is the ampere (A). Magnetomotiveforce is analogous to electromotive force inelectric circuits. See also magnetic circuit.

magneton /mag-nĕ-ton/ See Bohr magne-ton.

magneto-optical effects /mag-nee-toh-op-ti-kăl/ Changes of the optical behaviorof matter when the external magnetic fieldchanges. Examples are the Faraday effectand the Kerr effect. See Faraday effect;Kerr effect.

magnetoresistive effect /mag-nee-toh-ri-zis-tiv/ The change of electrical resistanceof a sample when the external magneticfield changes.

magnetosphere / mag-nee-tŏ-sfeer/ A re-gion of space surrounding a planet with amagnetic field. The size and nature of themagnetosphere depends on the magneticfield in the body. In the case of the Earth,the magnetosphere is the region in whichthe motion of electrically charged particlesfrom the Sun is dictated by the magneticfield of the Earth. It is a pear-shaped regionextending to a distance of about 60 000km on the side of the Earth nearest the Sun,and to a much greater distance on the sideopposite the Sun.

magnetostatics /mag-nee-toh-stat-iks/ Adevelopment of magnetic theory analogousto electrostatics but based on magneticpoles rather than electric charges. Al-though free poles are not known, the re-sults of assuming their existence have somevalidity.

magnetostriction /mag-nee-toh-strik-shŏn/ The change in length (and sectionarea) of a ferromagnetic rod with change inexternal magnetic field. The effect is the re-sult of domain boundary changes. Such arod will vibrate longitudinally in an alter-nating field (particularly at the natural fre-quency); magnetostriction is a commontechnique for producing ultrasonic radia-tion.

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magnetron /mag-nĕ-tron/ A type ofthermionic tube used for producing pulsedmicrowaves. A steady magnetic field is ap-plied from outside the tube. The electronsemitted from a hot cathode circle under theinfluence of the field and generate electro-magnetic oscillations in resonant cavities inthe surrounding anode. Magnetrons areused in radar sets and microwave ovens.See also klystron.

magnification /mag-nă-fă-kay-shŏn/Symbol: m The extent to which an opticalsystem changes the apparent size of an ob-ject; i.e. the image size in comparison withthe object size. It is measured by the heightsperpendicular to the axis: m = y/x, where yis the image height and x the object height.It also depends on the distances of imageand object from the center of the system: m= v/u, where v is the image distance and uthe object distance. If the image is smallerthan the object the value of m is less than1; a negative value of m means that theimage (or object) is virtual. This is for the‘real is positive, virtual is negative’ signconvention; in the New Cartesian conven-tion a negative value of m denotes aninverted image. See also angular magnifica-tion.

magnifying glass /mag-nă-fÿ-ing/ See mi-croscope; simple.

magnifying power See angular magnifi-cation.

magnitude A logarithmic scale used tomeasure the brightness of celestial objects,ranging from minus values for the brightestobjects to positive values for the faintest.For example, Sirius, the brightest star, hasa magnitude of –1.4, while the faintest ob-jects visible to the Hubble Space Telescopehave magnitudes of +28. Absolute magni-tude refers to the actual brightness a celes-trial object would have at a distance of 10parsecs (308.57 petameters in SI units)from Earth. Apparent magnitude refers tothe perceived brightness of an object froma vantage point on Earth, and as such de-pends on both the object’s luminosity andits distance.

magnox /mag-noks/ A type of alloy con-taining magnesium (88%), aluminum(11%), and traces of other elements. It isused for canning the uranium rods in sometypes of nuclear reactors.

majority carrier See semiconductor.

make-and-break An arrangement bywhich a circuit is alternately opened andclosed; for instance by movement of an ar-mature. See electric bell.

malleability /mal-ee-ă-bil-ă-tee/ Theproperty of a substance that allows it to bebeaten or rolled into thin sheets. Compareductility.

Malus’s law /ma-lyoos, mah-/ A law de-scribing the intensity of polarized light in apolarizing apparatus consisting of a polar-izer and an analyzer. It states that when θis the angle between the transmission axesof the polarizer and the analyzer, i.e. the di-rections along which light can pass unaf-fected, the intensity of polarized light isproportional to cos2θ. This law was firststated by the French engineer ÉtienneMalus (1775–1812) in 1809.

manganese /mang-gă-neez, -nees/ A tran-sition metal occurring naturally as oxides.Nodules found on the ocean floor areabout 25% manganese. Its main use is inalloy steels made by adding pyrolusite toiron ore in an electric furnace.

Symbol: Mn; m.p. 1244°C; b.p.1962°C; r.d. 7.44 (20%C); p.n. 25; r.a.m.54.93805.

manometer /mă-nom-ĕ-ter/ A device formeasuring pressure. A simple type is a U-shaped glass tube containing mercury orother liquid. The pressure difference be-tween the arms of the tube is indicated bythe difference in heights of the liquid.

maser /may-zer/ (microwave amplificationby stimulated emission of radiation) A de-vice for producing an intense source of co-herent microwave radiation. Masers, likelasers, operate by population inversion andstimulated emission.

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mass Symbol: m A measure of the quan-tity of matter in an object. Mass is deter-mined in two ways: the INERTIAL MASS of abody determines its tendency to resistchange in motion; the GRAVITATIONAL MASS

determines its gravitational attraction forother masses. The SI unit of mass is thekilogram. See also weight.

mass, center of See center of mass.

mass defect The mass equivalent of theBINDING ENERGY of a nucleus.

mass density See density.

mass-energy equation The equation E =mc2, where E is the total energy (rest massenergy + kinetic energy + potential energy)of a mass m, c being the velocity of light.The equation is a consequence of Einstein’sspecial theory of relativity; mass is a formof energy and energy also has mass. Con-version of rest-mass energy into kinetic en-ergy is the source of power in radioactivesubstances and the basis of nuclear-powergeneration.

mass number See nucleon number.

mass spectrograph See mass spectrome-ter.

mass spectrometer An instrument forproducing ions in a gas and analyzing themaccording to their charge/mass ratio. Theearliest experiments by Francis Aston useda stream of positive ions from a dischargetube, which were deflected by parallel elec-tric and magnetic fields at right angles tothe beam. Each type of ion formed a para-bolic trace on a photographic plate (a massspectrograph).

In modern instruments, the ions areproduced by ionizing the gas with electronsfrom an electron gun. The positive ions areaccelerated out of this ion source into ahigh-vacuum region. Here, the stream ofions is deflected and focused by a combi-nation of electric and magnetic fields,which can be varied so that different typesof ion fall on a detector. In this way, theions can be analyzed according to their

mass, giving a mass spectrum of the mate-rial. Mass spectrometers are used for accu-rate measurements of relative atomicmasses, for analysis of isotope abundance,and for chemical identification of com-pounds and mixtures.

mass spectrum See mass spectrometer.

matrix /may-triks, mat-riks/ A set of quan-tities arranged in rows and columns toform a rectangular array. The common no-tation is to enclose these in parentheses.Matrices do not have a numerical value,like determinants. They are used to repre-sent relations between the quantities. Forexample, a plane vector can be representedby a single column matrix with two num-bers, a 2 × 1 matrix, in which the uppernumber represents its component parallelto the x-axis and the lower number repre-sents the component parallel to the y-axis.Matrices can also be used to represent, andsolve, simultaneous equations. In general,an m × n matrix – one with m rows and ncolumns – is written with the first row:

A = a11a12 … a1nThe second row is:

a21a22 … a2nand so on, the mth row being:

am1am2 … amnThe individual quantities a11, a21, etc., arecalled elements of the matrix. The numberof rows and columns, m × n, is the order ordimensions of the matrix. Two matricesare equal only if they are of the same orderand if all their corresponding elements areequal. Matrices, like numbers, can beadded, subtracted, multiplied, and treatedalgebraically according to certain rules.However, the commutative, associative,and distributive laws of ordinary arith-metic do not apply. Matrix addition con-sists of adding corresponding elementstogether to obtain another matrix of thesame order. Only matrices of the sameorder can be added. Similarly, the result ofsubtracting two matrices is the matrixformed by the differences between corre-sponding elements.

Matrix multiplication also has certainrules. In multiplication of an m × n matrixby a number or constant k, the result is an-

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other m × n matrix. If the element in the ithrow and jth column is aij then the corre-sponding element in the product is kaij.This operation is distributive over matrixaddition and subtraction, that is, for twomatrices A and B,

k(A + B) = kA + kBAlso, kA = Ak, as for multiplication ofnumbers. In the multiplication of two ma-trices, the matrices A and B can only bemultiplied together to form the product ABif the number of columns in A is the sameas the number of rows in B. In this casethey are called conformable matrices. If Ais an m × p matrix with elements aij and Bis a p × n matrix with elements bij, thentheir product AB = C is an m × n matrixwith elements cij, such that cij is the sum ofthe products

aijbij + ai2b2j + ai3b3j + … + aipbpj

Matrix multiplication is not commutative,that is, AB ≠ BA.

matter The term matter is commonly usedvery loosely and was formerly regarded assynonymous with substance. Since MASS isdefined as the quantity of matter, strictlythe term should be used to mean anythingthat has mass. It has been found necessaryto define a distinct concept, substance,measured in terms of the number of parti-cles in a system. The measured mass of abody depends on the relative motion of thebody and the observer but substance is in-variant. See also mole; relativistic mass.

maximum-and-minimum thermome-ter A thermometer designed to record themaximum and minimum temperaturesduring a period of time. It usually consistsof a graduated capillary tube at the base ofwhich is a bulb containing ethanol. Withinthe capillary is a thin thread of mercurywith a steel index at each end. When thetemperature rises, the alcohol expands,thus forcing the mercury up the tube, car-rying the upper steel index. Therefore theposition of the upper index marks the max-imum temperature reached, and similarlythe position of the lower index, the mini-mum temperature attained.

maxwell /maks-wĕl/ Symbol: Mx A unitof magnetic flux used in the c.g.s. system. Itis equal to 10–8 weber (Wb). The unit isnamed for the British physicist James ClerkMaxwell (1831–79).

Maxwell–Boltzmann statistics /maks-wĕl bohlts-măn, -mahn/ The statisticalrules for studying systems of identical par-ticles in classical physics. It was tacitly as-sumed that particles, although identical,could be distinguished in principle. It canbe shown that, for low concentrations ofparticles, especially at high temperatures,the classical statistics gives results similarto the more exact Fermi–Dirac andBose–Einstein statistics. It was the failureof classical statistics to predict results inagreement with experiment in certain caseswhich led to the development of quantumtheory. The statistics are named forMaxwell and the Austrian theoreticalphysicist Ludwig Edward Boltzmann(1844–1906). See Maxwell distribution;ultraviolet catastrophe.

Maxwell corkscrew rule A rule devisedby James Clerk Maxwell (1831–79) to re-member the direction of magnetic fieldlines associated with the electric currentproducing the magnetic field. If acorkscrew is being driven in the directionof the current then the direction of the linesof force is the same direction as the direc-tion that the corkscrew is being rotated.

Maxwell distribution The laws for thedistribution of speeds or kinetic energiesamong the molecules of a gas in equilib-rium. The number of molecules per unitrange of speed at speed v is given by

Nv = Av2 exp (–mv2/2kT)where m is the mass of a molecule, T is thekelvin temperature, k is the Boltzmannconstant, and A is a constant. The numberof molecules per unit range of kinetic en-ergy at kinetic energy E is given by

NE = √(BE)exp(–E/kT)where B is a constant.

This distribution is very closely obeyedby gases at ordinary pressures. For largeconcentrations of particles more exact laws

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are needed, particularly for the valenceelectrons in a solid.

See Bose–Einstein statistics; Fermi–Dirac statistics; Maxwell–Boltzmann sta-tistics.

Maxwell equations A set of four equa-tions that together form the basis of classi-cal electrodynamics. They are: (1)Coulomb’s law, (2) a statement of the non-existence of magnetic monopoles, (3) Fara-day’s law of electromagnetic induction, (4)a modification of Ampère’s law. It has be-come customary to express these laws interms of vector calculus.

Maxwell’s demon A hypothetical beingin a thought experiment that was used byJames Clerk Maxwell in a discussion of thesecond law of thermodynamics. Maxwellconsidered a container of gas, with the gasbeing divided into two volumes by a parti-tion. A small being (named a ‘demon’ byLord Kelvin) is able to distinguish individ-ual molecules in the gas and to open thepartition when a molecule with a fasterthan average speed approaches it on oneside and when a slower than average speedmolecule approaches it from the other side.Eventually, one side would have a higherproportion of fast molecules while theother side would have a higher number ofslow molecules. The side with the fast mol-ecules would thus become hotter than theside with the slow molecules in contraven-tion of the speed of law of thermodynam-ics. It is thought that the resolution of thisparadox involves the relations between en-tropy and information theory, with the re-alization that identifying the correctmolecules and operating the partitionwould generate entropy.

mean free path Symbol: λ 1. The averagedistance traveled by the particles of a fluidbetween collisions. It is given by

λ = 1/πr2nwhere r is the particle radius and n the den-sity of particles.2. The average distance traveled by elec-trons between collisions with the lattice inconduction.

mean free time For gas atoms or mol-ecules in a container, or electrons and im-purity atoms in a semiconductor, theaverage time between particle collisions.See also mean free path.

mean life Symbol: T The average time forwhich a radioactive nucleus exists before itdisintegrates. It is the reciprocal of thedecay constant.

mean solar day See day.

mechanical advantage See force ratio.

mechanical equivalent of heat SeeJoule’s equivalent.

mechanics The study of forces and theireffect on objects. If the forces on an objector in a system cause no change of momen-tum the object or system is in equilibrium.STATICS is the study of such cases. If theforces acting do change momentum, dy-namics is used. The ideas of DYNAMICS re-late the forces to the momentum changesproduced. KINEMATICS is the study of mo-tion without consideration of its cause.

medium (pl. mediums or media) The na-ture of the space through which somethingis transmitted or propagated. It may besolid, liquid, gas, or a vacuum (althoughsome people do not class a vacuum as amedium).

medium frequency (MF) A radio fre-quency in the range between 3 MHz and0.3 MHz (wavelength 100–1000 m).

mega- Symbol: M A prefix denoting 106.For example, 1 megahertz (MHz) = 106

hertz (Hz).

megaton /meg-ă-tun/ A unit used to ex-press the explosive power of nuclearweapons. One megaton is an explosivepower equivalent to that of one milliontonnes of TNT. This is equivalent to 4.2exajoules.

Meissner effect /mÿss-ner/ The exclusionof magnetic flux from a substance when it

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Meissner effect

is in the superconducting state. It is thenperfectly diamagnetic except for the pene-tration of flux into a thin surface layer.When an external magnetic field becomessufficiently intense it penetrates throughthe specimen, destroying its SUPERCONDUC-TIVITY. The effect is named for the Germanphysicist Fritz Walther Meissner (1882–1974). See diamagnetism.

meitnerium /mÿt-neer-ee-ŭm/ A radioac-tive metallic element not found naturallyon Earth. Only a few atoms of the elementhave ever been detected; it can be made bybombarding a bismuth target with iron nu-clei. The isotope 266Mt has a half-life ofabout 3.4 × 10–3s. The element is namedfor the Austrian physicist Lise Meitner(1878–1968).

Symbol: Mt; p.n. 109.

melting (fusion) The change from thesolid to the liquid state. For a pure crys-talline substance this happens at a charac-teristic temperature – the melting point (orfreezing point). This temperature dependson pressure, but is usually quoted at stan-dard atmospheric pressure. The meltingpoint of a substance is lowered by the pres-ence of impurities.

melting point See melting.

membrane See supermembrane.

mendelevium /men-dĕ-lee-vee-ŭm/ A ra-dioactive transuranic element of the acti-noid series, not found naturally on Earth.Several short-lived isotopes have been syn-thesized. The element is named for theRussian chemist Dimitrii Mendeleyev(1834–1907).

Symbol: Md; p.n. 101; most stable iso-tope 258Md (half-life 57 minutes).

meniscus (pl. menisci or meniscuses) /mĕ-niss-kŭs/ The curved surface of a columnof liquid in a tube or other container. Itsshape depends on contact angle. See alsocapillary action.

meniscus lens See concavo-convex.

mercury /mer-kyŭ-ree/ A transition metalthat is liquid at room temperatures(bromine is the only other element withthis property). The vapor is very poiso-nous. Mercury is used in thermometers,special amalgams for dentistry, scientificapparatus, and in mercury cells.

Symbol: Hg; m.p. –38.87°C; b.p.356.58°C; r.d. 13.546 (20°C); p.n. 80;r.a.m. 200.59.

mercury barometer See barometer.

mercury cell A voltaic or electrolytic cellin which one or both of the electrodes con-sists of mercury or an amalgam. Amalgamelectrodes are used in the Daniell cell andthe Weston cadmium cell.

mercury thermometer A liquid-in-glassthermometer that uses mercury as its work-ing substance. It consists of a thin capillarytube graduated in degrees, at the base ofwhich is a bulb containing mercury. Whenthe temperature rises, the mercury expandsalong the tube. The position indicates thetemperature.

meridian, magnetic See magnetic merid-ian.

meson /mee-zon, -son, mess-on, mez-on/ Atype of ELEMENTARY PARTICLE. Mesons aremore massive than muons but lighter thanprotons. They are bosons and form a sub-class of the hadrons. Yukawa predicted(1935) that such particles would be in-volved in the exchange forces between nu-cleons, and the subsequently discoveredmesons appear to conform to his theory.See also kaon; pion.

metallurgy /met-ă-ler-jee/ The branch ofscience devoted to the study of metals. Thebehaviour of metals and their alloys is theconcern of physical metallurgy while theextraction of metals from their ores andtheir purification are the concerns ofprocess metallurgy.

metastable state A condition of a systemor body in which it appears to be in stableequilibrium but, if disturbed, can settle

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154

into a lower energy state. For example, su-percooled water is liquid at below 0°C (atstandard pressure). When a small crystal ofice or dust (for example) is introducedrapid freezing occurs.

meter /mee-ter/ Symbol: m The SI baseunit of length, defined as the length of thepath traveled by light in a vacuum in a timeof 1/299 792 458 second. The meter hasnot always been defined in terms of time.As originally proposed by the FrenchAcademy of Sciences in 1791, the meterwas to be one ten-millionth of the distancerunning from the North Pole through Paristo the equator. Part of this distance wasmeasured over six arduous years, and thebalance extrapolated. However, becausethe Earth is not a perfect sphere, the ex-trapolated distance was eventually foundto be inaccurate. Subsequently the meterwas defined in 1889 as the length betweentwo fine lines on an international proto-type platinum–iridium alloy bar keptunder specified conditions in a vault atSèvres, in France. Due to the increasingneed for accuracy in scientific measure-ment the meter was again redefined in1960, this time as 1 650 763.73 wave-lengths in vacuum corresponding to thetransition between the levels 2p10 and 5d5

of the krypton –86 atom.

meter bridge A meter length of uniformresistance wire mounted above a scalemarked in millimeters, with suitable termi-nal points added to make the device adapt-able either as a WHEATSTONE BRIDGE or aPOTENTIOMETER. As a Wheatstone bridgethe wire acts as two arms of the bridge re-sistors; and as a potentiometer the poten-tial drop along the wire is proportional tothe length of wire.

metric horsepower See horsepower.

metric system A system of units based onthe meter and the kilogram and using mul-tiples and submultiples of 10. SI units,c.g.s. units, and m.k.s. units are all scien-tific metric systems of units.

metric ton See tonne.

MF See medium frequency.

MHD See magnetohydrodynamics.

mho /moh/ See siemens.

Michelson–Morley experiment /mÿ-kĕl-sŏn mor-lee/ A famous experiment car-ried out by the American physicists AlbertAbraham Michelson (1852–1931) andDayton Miller (1866–1941) in 1887 in anattempt to detect the ether, the mediumthat was supposed to be necessary for thetransmission of electromagnetic waves infree space.

In the experiment, two light beamswere combined to produce interferencepatterns after traveling for short equal dis-tances perpendicular to each other. The ap-paratus was then turned through 90° andthe two interference patterns were com-pared to see if there had been a shift of thefringes. If light has a velocity relative to theether and there is an ether ‘wind’ as theEarth moves through space, then the timesof travel of the two beams would change,resulting in a fringe shift. No shift was de-tected, not even when the experiment wasrepeated six months later when the etherwind would have reversed direction. Seealso relativity.

micro- Symbol: µ A prefix denoting 10–6.For example, 1 micrometer (µm) = 10–6

meter (m).

microelectronics /mÿ-kroh-i-lek-tron-iks/The branch of electronics that deals withvery small electronic circuits, components,and devices, such as silicon chips and othermicrominiature devices.

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microelectronics

••

•• ••

•terminals

uniform resistance wiremm scale

conductor

Meter bridge

micron /mÿ-kron/ Symbol: µm A unit oflength equal to 10–6 meter.

microphone A device for convertingsound signals into electrical signals. Thepressure variations of the sound wave areconverted into variations in an electricalsignal. There are various methods of doingthis. A ribbon microphone has a thin metalribbon held between the poles of a magnet.The sound waves vibrate this and a varyinge.m.f. is induced, which can be amplified.A moving-coil microphone has a di-aphragm connected to a small coil, whichmoves in a stationary magnetic field. Ane.m.f. is induced in the coil. A crystal mi-crophone depends for its action on thepiezoelectric effect; an e.m.f is induced bystress produced by sound waves hitting asuitable crystal of quartz or Rochelle salt.A carbon microphone has two blocks ofcarbon in contact. Pressure changes pro-duced by the sound waves cause corre-sponding changes in the resistance of thecarbon blocks. See also condenser micro-phone.

microscope, compound A device forproducing large images of close small ob-jects with a combination of lenses. In thenormal two-lens microscope each lens isconverging. In practice, except in verycheap instruments, both object lens andeye lens are replaced by compound lenssystems. Lighting is extremely important;

light is directed onto the object by a mirroror condenser lens.

The magnifying power of the com-pound microscope is the product of the lin-ear magnifications produced by objectiveand eyepiece.

See also blink microscope; electron mi-croscope.

microscope, simple The magnifyingglass, or simple magnifier. The small objectis viewed between the lens and its focalpoint; an upright virtual image is obtained.In this case the image is placed at the nearpoint of the eye – the magnifying power isthen given by (D/f) + 1, where D is thenear-point distance and f the lens focal dis-tance. The lens can also be used to give animage at infinity; the image is then viewedwith the relaxed eye, but the magnifyingpower is only D/f.

microwaves /mÿ-kroh-wayvz/ A form ofelectromagnetic radiation, ranging inwavelength from about 1 mm (where itmerges with infrared) to about 120 mm(bordering on radio waves). Microwavesare produced by various electronic devicesincluding the KLYSTRON; they are often car-ried over short distances in tubes of rectan-gular section called waveguides.

Microwave communication was untilrecently the most efficient form of elec-tronic telecommunication. Since the devel-opment of cheap lasers and optical fibers,telecommunication at visible wavelengthsis developing rapidly. Radar systems gener-ally use microwaves, while their ability to

micron

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objectimage (virtual)| |

F F

Microscope, simple

| | | |

observer

Fe

first image(real)

eye lens(converging)

object

final image(virtual)

object lens(converging)

Fo FoFoFo Fe

Microscope, compound

carry energy has a number of applications,including microwave cookers. See alsoelectromagnetic spectrum; magnetron.

mil 1. A unit of length in f.p.s. systems,equal to 0.001 inch or 0.02554 millimetrein SI units.2. A unit of area in f.p.s. systems, alsoknown as the circular mil, used especiallyfor wire sizes. It is based on the area of acircle having a diameter of 0.001 inch, andis equal in SI units to 506.7075 square mi-crometers.3. A colloquial term for the milliliter.

mile A unit of length equal to 1760 yards(equal to 1.60934 km).

milli- Symbol: m A prefix denoting 10–3.For example, 1 millimeter (mm) = 10–3

meter (m).

milliammeter /mil-ee-am-mee-ter/ An in-strument for measuring electric currents ofa few milliamperes. See also ammeter; gal-vanometer.

millibar See bar.

millimeter of mercury See mmHg.

minority carrier See semiconductor.

minor planet See asteroid.

minute 1. A unit of time equal to 60 sec-onds.2. Symbol: ′ A unit of angle; 1/60 of a de-gree.

mirage An optical illusion caused by totalinternal reflection in the air. It is commonwhen the ground is strongly heated by theSun so that the air in contact with theground is much warmer than the air above.Light from an object above the ground (in-cluding the sky) is refracted and totally in-ternally reflected by the warm air toproduce an image. Mirages are also some-times observed next to very warm verticalsurfaces.

mirror (reflector) An optical componentthat reflects incident rays. A mirror is bestdescribed by its effect on a parallel beam.Plane mirrors reflect it parallel; converingmirrors reflect it convergent; divergingmirrors make it diverge. Focal distance isthe usual measure of the power of a mirror

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mirror

axis F P

convergingreflector

FPaxis

divergingreflectorP = pole

F = focal point

Paths of light reflected from converging and diverging mirrors

to converge a parallel beam. Parallel raysare reflected by converging and divergingmirrors as shown in the diagram. Strictlysuch focusing occurs only with rays paral-lel and close to the principal axis. With aparabolic mirror, wide parallel beamsfocus at the focal point. Rays from an ob-ject will be reflected so that they appear tocome from somewhere else – the image.Two examples are given here to show howray diagrams are drawn.

For a diverging reflector, a virtualimage appears at F when the incident rayscome from infinity; radiation from an ob-ject anywhere between infinity and P willform a virtual image between F and P.

Object distance (u) and image distance(v) relate to the focal distance (f) of the re-flector as follows:

1/f = 1/v + 1/u(real is positive, virtual is negative sign con-vention).

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158

OBJECT AND IMAGE POSITIONS FOR CONVERGING MIRROR

Object position Image nature Image positioninfinity real Fbeyond C real between F and CC real Cbetween C and F real beyond CF virtual infinitybetween F and P virtual between infinity and P

| |

observer convergingreflector

C F O P I

C = center of curvatureobject O is between F and Pimage I is virtual, upright, magnified, andbehind the mirror

Formation of a virtual image by a convergingmirror

| |

observer

axis

divergingreflector

O P I F C

C = center of curvatureobject O is anywhereimage I is between F and P, virtual, upright,and diminished

Formation of a virtual image by a real object ata diverging mirror

converging mirror (concave) plane mirror (flat) diverging mirror (convex)

silvering

Types of mirror

The formula applies to real or virtualfocal points, objects, and images. All theabove can be adapted for use with reflec-tors of non-visible radiations such as in-frared and ultraviolet.

mirror image A shape that is identical toanother except that its structure is reversedas if viewed in a mirror, so that the twocannot be superimposed. For example, aleft hand is the mirror image of a righthand.

m.k.s.a. system A coherent metric systemof units for mechanics and electromagnet-ics based on the meter, the kilogram, thesecond, and the ampere. It superseded them.k.s. system and was in turn supersededby the SI in 1960.

m.k.s. system A system of units based onthe meter, the kilogram, and the second. Itsuperseded the c.g.s. system and was inturn superseded by the m.k.s.a. system in1946.

mmHg (millimeter of mercury) A formerunit of pressure defined as the pressure thatwill support a column of mercury one mil-limeter high under specified conditions. Itis equal to 133.322 4 Pa. It is equivalent tothe torr.

moderator /mod-ĕ-ray-ter/ Material usedin the cores of some nuclear reactors toslow down fast-moving neutrons so thatthey will be more easily captured by fissilenuclei. The most effective speeds are abouttwo thousand meters per second. Such neu-trons are called thermal neutrons becausethe distribution of their speeds is such thatthey are in thermal equilibrium with (i.e. atthe same temperature as) the surroundingmaterials. To achieve this slowing down inas few collisions as possible, moderatorsare substances of low relative atomic mass.Carbon, in the form of graphite, was usedin early experimental reactors and is stillused in Magnox reactors. Water – in somereactor designs, heavy water – is used andmay also serve as the coolant. Paraffin andberyllium are also suitable moderators.

modulation /moj-ŭ-lay-shŏn/ The super-imposition of a (video or audio) signal ontoa CARRIER WAVE so that the informationcontained in the signal can be transmittedwith the carrier wave. See amplitude mod-ulation; frequency modulation; phasemodulation. See also demodulation.

modulus (pl. moduli) /moj-ŭ-lŭs/ 1. Themagnitude of a vector quantity.2. The absolute value of a number or quan-tity. For example, the modulus of –4 is 4.3. A quantity that defines some property ofa material or of some other system. Seeelastic modulus.

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moiré fringes

moiré fringes /mwah-ray, mwa-ray/ Thepattern obtained when two regular sets oflines or points overlap. The effect can beseen through folds in netting drapes. Moirépatterns can be used as models of interfer-ence patterns Another application is incomparing two diffraction gratings by su-perimposing them and observing the moirépattern produced.

molar /moh-ler/ 1. Denoting a physicalquantity divided by the amount of sub-stance. In almost all cases the amount ofsubstance will be in moles. For example,volume (V) divided by the number of moles(n) is molar volume:

Vm = V/n.2. A molar solution contains one mole ofsolute per cubic decimeter of solvent.

molar gas constant See gas constant.

molar thermal capacity Symbol: Cm Thethermal capacity per unit amount of sub-stance; i.e. the energy required to raise unitamount of substance (1 mol) by unit tem-perature (1 K). It is measured in J mol–1

K–1. For a gas, it is common to specify twoprincipal molar thermal capacities: onemeasured at constant pressure and theother measured at constant volume. Therelationship between them are as for spe-cific thermal capacities.

mole Symbol: mol The SI base unit ofamount of substance, defined as theamount of substance that contains as manyelementary entities as there are atoms in0.012 kilogram of carbon-12. The elemen-tary entities may be atoms, molecules, ions,electrons, photons, etc., and they must bespecified. One mole contains 6.022 142 ×1023 entities One mole of an element withrelative atomic mass A has a mass of Agrams (this was formerly called one gram-atom). One mole of a compound with rel-ative molecular mass M has a mass of Mgrams (this was formerly called one gram-molecule).

molecular orbital See orbital.

molecular sieve A method used for sepa-rating similar substances by adsorbing themolecules of one substance within thestructural cavities of another, such as a nat-ural or synthetic zeolite.

molecular spectrum The absorption oremission spectrum that is characteristic ofa molecule. Molecular spectra are usuallyband spectra.

molecular weight See relative molecularmass.

molecule /mol-ĕ-kyool/ A single atom or agroup of atoms joined by chemical bonds.It is the smallest unit of a chemical com-pound that can have an independent exis-tence. Water, for instance has moleculesmade up of two hydrogen atoms and one

oxygen atom (H2O). Ionic compounds,such as sodium chloride, do not have dis-tinct molecules. Sodium chloride is usuallywritten NaCl, but crystals of sodium chlo-ride are, in fact, a regular arrangement ofsodium ions (Na+) and chloride ions (Cl–).Similarly, metals and certain covalentlybonded solids do not have discrete mol-ecules. In boron nitride, for instance, thecovalent bonds hold the atoms together ina giant molecule.

molybdenum /mŏ-lib-dĕ-nŭm/ A transi-tion element used in alloy steels, lampbulbs and catalysts.

Symbol: Mo; m.p. 2620°C; b.p.4610°C; r.d. 10.22 (20°C); p.n. 42; r.a.m.95.94.

moment The moment of a force about apoint is the product of the force and theperpendicular distance from the point tothe line of action of the force. It can be ex-pressed as the vector product of the forcetimes the displacement of this point fromthe point where the force acts. The resul-tant moment of the forces acting on a bodyis found by vector addition. If the forcesare coplanar, clockwise and anticlockwisemoments are given opposite signs. For abody in equilibrium, the sum of the clock-wise moments equals the sum of the anti-clockwise ones (the law of moments). If theresultant moment is non-zero the body hasan angular acceleration. See also couple;torque.

moment, magnetic See magnetic mo-ment.

moment of inertia Symbol: I The rota-tional analog of mass. The moment of in-ertia of an object rotating about an axis isgiven by I = Σmr2, where m is the mass ofan element distant r from the axis. Someimportant cases are listed in the table. Seealso radius of gyration; theorem of parallelaxes.

momentum, conservation of /mŏ-men-tŭm/ See constant (linear) momentum (lawof).

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160

momentum, linear (pl. momenta or mo-mentums) Symbol: p The product of anobject’s mass and velocity: p = mv. The ob-ject’s momentum cannot change unless anet outside force acts. This relates to New-ton’s laws and to the definition of force. Italso relates to the principle of constant mo-mentum. See also angular momentum.

monatomic /mon-ă-tom-ik/ Describing amolecule that consists of a single atom. Therare gases are monatomic gases.

monochord /mon-ŏ-kord/ See sonometer.

monochromatic radiation /mon-ŏ-kroh-mat-ik/ Electromagnetic radiation of anextremely narrow range of wavelengths.(The word means ‘of one color’.) It is im-possible to produce completely monochro-matic radiation, although the output ofsome lasers is not far off. The ‘lines’ in linespectra produced even in the most ideal cir-cumstances have some width in wave-length terms. The half-width is the measureused. It is the range of wavelengths definedin the figure, and contains almost 90% ofthe energy emitted. The half-width of asharp line in an optical spectrum is typi-cally 10–6 to 10–7 of the wavelength (λ).Using lasers, half-widths of the order 10–12

λ can be obtained. Low-quantum-energygamma rays emitted by atoms bound incrystals may have values of the order 10–13

λ.Simple quantum theory leads one to ex-

pect perfectly sharp lines in a line spectrum– the energies of the levels concerned ap-pear to be exactly defined, so that λ =hc/∆E. However, because of the uncer-tainty principle, no energy level or transi-tion can be defined exactly; this means thatany line is naturally broadened rather thanbeing sharp. A second broadening influ-

ence is the Doppler effect, which is relevantas the radiating particles are always in mo-tion. Thirdly, collisions between emittingparticles will broaden the emitted line.

Compare polychromatic radiation.

monochromator /mon-ŏ-kroh-mă-ter/ Adevice for providing monochromatic radi-ation from a polychromatic source. In thecase of light, for example, a prism or grat-ing disperses the light and slits are used toselect a small wavelength range.

monolithic IC /mon-ŏ-lith-ik/ See inte-grated circuit.

monomode fiber A type of optical fiberthat has a narrow core of glass with a di-ameter of about 5 µm surrounded by alarge coating (cladding) of glass with asmaller refractive index than the core. Seealso multimode fibre.

monostable circuit /mon-ŏ-stay-băl/ Anelectronic circuit, usually a MULTIVIBRATOR,that has one stable state but can change to

161

monostable circuit

MOMENTS OF INERTIAThe value given is that for a perpendicular axis through the center of mass.

Object Dimensions Moment of inertiathin rod length l ml2/12thin disk radius r mr2/2thin ring radius r mr2

solid sphere radius r 2mr2/5

relativeintensity

half-width

λ1 λ2 λ

1.0

0.5

0

Monochromatic radiation

another state for a time after the applica-tion of a trigger pulse. Monostable circuitscan be used for generating single pulses ofa fixed duration, for shortening or length-ening pulses, or to delay pulses in computerlogic circuits. In a monostable multivibra-tor the input pulse is fed to the base termi-nal of one transistor (TR1) and through aresistor R to the collector terminal of theother (TR2). The base of TR2 and the col-lect of TR1 are connected through a capac-itor C. The output voltage at the collectionof TR2 is a pulse with a duration that de-pends on the values of R and C.

Moseley’s law Lines in the x-ray spectraof elements have frequencies that dependon the proton number of the element. Fora set of elements, a graph of the square rootof the frequency of x-ray emission againstproton number is a straight line (for spec-tral lines corresponding to the same transi-tion). The law is named for the Britishphysicist Henry Gwyn Jeffreys Moseley(1887–1915).

Mössbauer effect /mohs-bow-er, moss-/After an atomic nucleus has emitted agamma-ray photon (during radioactivedecay), the absorption of the momentumof the atom by the whole of its crystal lat-tice because it is so firmly bound that itcannot recoil. The same effect occurs withabsorption of gamma rays. The effect isnamed for the German physicist RudolphLudwig Mössbauer (1929– ).

Moseley’s law

162

mirror

coil

wiresuspension

Moving-coil instrument

coil

soft iron

Moving-iron instrument

moving-coil instrument An electricmeasuring instrument that depends on thecouple on a small vertical rectangular coilcarrying direct current in a magnetic field.A cylindrical soft-iron core is fitted be-tween the concave pole pieces of a strongpermanent magnet, giving a radial mag-netic field. The coil is supported either by afine wire suspension or by needle points onbearings. When the current flows, there isa couple that moves the coil until torsion inthe suspension or the resistance of a hairspring brings it to rest. The equilibriumangle, which is proportional to the current,is measured by a pointer or (for sensitiveinstruments) by reflecting a beam of lightfrom a small mirror attached to the coil.

The torque on the coil is equal toBIAN, where B is magnetic flux density, Icurrent, A coil area, and N the number ofturns. The current depends on the angle oftwist (θ) according to I = kθ/BAN, where kis a constant of the spring or torsion wire.Typically, currents of the order of mil-liamps can be measured, and some instru-ments can measure microamps.

moving-coil microphone See micro-phone.

moving-iron instrument An electricalmeasuring instrument in which the currentis passed through a fixed coil. The mag-netic field produced attracts a piece of softiron on a pivot. The iron is restrained by aspring and the movement detected by apointer. Moving-iron instruments are lesssensitive than moving-coil instruments, but

can be used for alternating-currents with-out a rectifier (the attraction does not de-pend on the direction of current flow). Themovement of the iron is roughtly propor-tional to the square of the current.

MRI See magnetic resonance imaging.

M theory See superstring theory.

multimeter /mul-tim-ĕ-ter/ An electricalmeasuring instrument designed to measurevoltage and current over a number ofranges. It is a moving-coil instrument witha switch enabling various resistors to beconnected in series with the coil (for differ-ent voltage ranges) or various shunt resis-tances to be connected in parallel (forcurrent ranges). Usually, an internal drycell is incorporated so that direct measure-ments can also be made of resistances.

multimode fiber A type of optical fiberthat has a relatively large core of glass witha diameter of about 50 µm surrounded bya relatively small amount of cladding. Seealso monomode fibre.

multiple capacitor A capacitor consist-ing of a series of parallel plates with a di-electric between each plate. Thecapacitance of such a device is N times thecapacitance between two consecutiveplates of the series, where N is the numberof successive pairs of parallel plates.

multiplication factor Symbol: k In a nu-clear chain reaction, the ratio of the rate ofproduction of neutrons to the rate of ‘loss’of neutrons (by absorption and leakage).For subcritical reactions k < 1For supercritical reactions k > 1For critical reactions k = 1

multiplier One of a set of resistors thatare used in series with a VOLTMETER toallow it to measure a wide range of volt-ages. See also photomultiplier; shunt.

multistable circuit /mul-ti-stay-băl/ Anelectronic circuit that has more than onestable state. See multivibrator.

multivibrator /mul-ti-vÿ-bray-ter/ Abasic electronic circuit consisting of twotransistors and other components, such asresistors and capacitors. Its main propertyis that it can switch its output instanta-neously from one voltage level to another.Multivibrators are used to generate conti-nous streams of voltage pulses (squarewaves), to store information in the form ofbinary digits (0 and 1) in a computer, andto form part of a logic circuit.

The transistors are connected in thecommon-emitter mode with the collectorof each joined through other componentsto the base of the other. If one transistor isin the cut-off state, that is with almost zerobase current and collector current, theother is saturated, that is the collector cur-rent will not increase with collector-emittervoltage. A sufficiently high voltage pulse atthe base of one transistor will change itsstate from cut-off to saturation and viceversa. The second transistor will thenchange state in the other direction. Abistable multivibrator circuit has two over-all stable conditions and has the two tran-sistors connected to each other throughresistors only. In the astable multivibratorthe coupling is capacitive and the circuitswitches continuously from one state toanother. The monostable multivibrator hasa coupling that is both resistive and capac-itive and has only one stable state. See alsoastable circuit; bistable circuit; monostablecircuit.

mu-meson /myoo/ See muon.

muon /myoo-on/ A type of lepton with amass 207 times that of the electron. Thereare two types, having positive or negativecharge. Originally the muon was classifiedas a meson and called a mu-meson. See alsoelementary particles.

mutual inductance See mutual induc-tion.

mutual induction The production ofe.m.f. in one circuit by change in the cur-rent in, and therefore the magnetic fieldaround, a second nearby circuit. For exam-ple, in a transformer, an e.m.f. is induced in

163

mutual induction

one coil by a changing current in the other.Mutual induction is greatly increased bythe presence of an iron core that links thetwo coils. The mutual inductance (M) be-tween two conductors is defined (in freespace) by the equation E = M(dI/dt), whereE is the induced e.m.f. and dI/dt is the rateof change of current. The SI unit is thehenry (H). Compare self-induction.

myopia /mÿ-oh-pee-ă/ Short sight, nor-mally caused if the distance between thelens and the back of the eyeball is too long.Light from distant objects is focused at apoint in front of the retina, and thus distantobjects cannot be accommodated. Onlyclose objects can be seen clearly. The prob-lem may be corrected by use of divergingspectacle or contact lenses.

myopia

164

NAND gate See logic gate.

nano- Symbol: n A prefix denoting 10–9.For example, 1 nanometer (nm) = 10–9

meter (m).

nanotechnology /nan-oh-tek-nol-ŏ-jee/The branch of technology that is concernedwith the production and behavior of verysmall components, especially electronic de-vices, that have a size of a few nanometers(1 nm = 10–9m). Electronic devices of thistype may use the movement of only a fewelectrons in their action. The fabrication ofnanocomponents may be effected by me-chanical means or by carefully controlledchemical reactions, particularly varioustypes of etching process.

natural abundance See abundance.

natural convection See convection.

natural frequency The frequency atwhich an object or system will vibratefreely. A free vibration occurs when there isno external periodic force and little resis-tance. The amplitude of free vibrationsmust not be too great. For instance, a pen-dulum swinging with small swings underits own weight moves at its natural fre-quency. Normally, an object’s natural fre-quency is its fundamental frequency.

near point The closest point to the eye atwhich an object can clearly be seen withoutexcessive strain. The eye is then fully ac-commodated, and has maximum power. Inthe normal eye, the distance to the nearpoint increases with age, as the eye’s abilityto accommodate decreases. For many pur-poses it is convenient to take a standardnear-point distance, D, to be 250 mm.

near sight Short sight. See myopia.

Néel temperature /nay-ĕl/ See antiferro-magnetism.

negative See charge; electric.

negative feedback See feedback.

negative lens A lens with a negativepower. See diverging lens.

negative mirror A mirror with a negativepower. See diverging mirror.

negative pole A south pole of a magnet.See pole.

neodymium /nee-ŏ-dim-ee-ŭm/ A toxicsilvery element belonging to the lanthanoidseries of metals. It occurs in associationwith other lanthanoids. Neodymium isused in various alloys, as a catalyst, in com-pound form in carbon-arc searchlights,etc., and in the glass industry.

Symbol: Nd; m.p. 1021°C; b.p.3068°C; r.d. 7.0 (20°C); p.n. 60; r.a.m.144.24.

neon /nee-on/ An inert colorless odorlessmonatomic element of the rare-gas group.

165

N

THE VARIATION OF NEAR-POINTDISTANCE WITH AGE

Age (years) Distance (mm)10 7020 10030 14040 22050 40060 2000

neper

166

Neon forms no compounds. It occurs inminute quantities (0.0018% by volume) inair and is obtained from liquid air. It isused in neon signs and lights, electricalequipment, and gas lasers.

Symbol: Ne; m.p. –248.67°C; b.p.–246.05°C; d. 0.9 kg m–3 (0°C); p.n. 10;r.a.m. 20.18.

neper /nay-per, nee-/ Symbol: Np A unit ofrelative difference in power or field levelsexpressed logarithmically, equal to 8.686decibels (dB). Two powers P1 and P2 differby n neper, where

n = ½ln(P2/P1)The neper is probably most commonlyused as the unit of radiation attenuation;here the radiation powers P1 and P2 areusually given as intensities I1 and I2. It isalso used in acoustics, electricity, and mag-netism.

neptunium /nep-tew-nee-ŭm/ A toxic ra-dioactive silvery element of the actinoid se-ries of metals that was the first transuranicelement to be synthesized (1940). Foundon Earth only in minute quantities in ura-nium ores, it is obtained as a by-productfrom uranium fuel elements.

Symbol: Np; m.p. 640°C; b.p. 3902°C;r.d. 20.25 (20°C); p.n. 93; most stable iso-tope 237Np (half-life 2.14 × 106 years).

Nernst calorimeter /nernst/ An appara-tus for determining the specific thermal ca-pacity of a metal. A piece of the metal(mass m) is wound with a coil of insulatedplatinum wire and suspended in an evacu-ated container. Aluminum foil is wrappedaround the coil to reduce radiation loss. Acurrent (I) is passed through the coil atmeasured voltage V for a time (t). The coilis also used as a resistance thermometer(with the heating current off) to measurethe temperature rise (θ) in the metal. Then

IVt = (mc + C)θwhere c is the specific thermal capacity ofthe specimen and C the thermal capacity ofthe coil and foil (this is found by a separatemeasurement). The calorimeter is namedfor the German chemist Walther HermannNernst (1864–1941).

Nernst effect When a magnetic field isapplied at right angles to a conductorthrough which heat is flowing, an electricpotential develops transversely across theconductor. The direction of heat flow,magnetic field, and potential gradient areall mutually perpendicular. Compare Halleffect.

Neumann’s law /noi-mănz, noi-mahnz/See electromagnetic induction.

neutral Having neither negative nor posi-tive net charge. This will be when the bodyis at earth potential.

neutral equilibrium EQUILIBRIUM suchthat if the system is disturbed a little, thereis no tendency for it to move further nor toreturn. See stability.

neutral point A point where two fields ina region are equal and opposite, so thatthere is no resultant force. The situation ismost often met in the case of magneticfields. Thus magnetic neutral points arefound near a permanent magnet in theEarth’s field.

neutrino /new-tree-noh/ An ELEMENTARY

PARTICLE with zero charge and very smallrest mass having only weak INTERACTIONS.Neutrinos are classified as LEPTONS and areFERMIONS with spin ½. There are threetypes of neutrino (each with a correspond-ing antiparticle); one type is emitted in betadecay, another in the decay of muons, anda third is associated with the tau particle.

The existence of neutrinos was postu-lated by Pauli (1930) and was shown to ac-count for the continuous energy spectrumof beta radiation. Later it was found thatthe conservation of momentum and angu-lar momentum, as well as energy conserva-tion in beta decay, required the neutrinohypothesis. The development of the theoryof beta radioactivity led to the concept thatthe particle emitted with an electron in betadecay is an antineutrino while that emittedwith positrons is the neutrino.

In 1956 the antineutrinos produced byshort-lived beta emitters in a nuclear reac-tor were detected by the reaction

11H + ν

_; → 1

0n + e+

Because of the lack of electromagnetic andstrong interactions these particles have anextremely low probability of reacting withmatter. For hydrogen at the density of theSun the mean free path for the nuclear re-actor antineutrinos is millions of times thesolar diameter.

Thermonuclear fusion in the Sun is ex-pected to cause the emission of neutrinos.Attempts have been made to detect theseby the reaction

3717Cl + νν

_→ 37

18Ar + e–

These experiments have failed to detectneutrinos with the intensity predicted bytheories based on the assumption that theSun is in a steady state.

See also neutrino oscillations; solar neu-trino problem.

neutrino oscillation An oscillation be-tween the different species of neutrinos as-sociated with electrons, muons, and tauleptons; i.e. a reversible change betweenone species and another. Neutrino oscilla-tions can only occur if neutrinos have non-zero masses. There are several independentsources of evidence showing that neutrinooscillations actually occur, and they arepredicted to happen in most GRAND UNIFIED

THEORIES.

neutron /new-tron/ An ELEMENTARY PAR-TICLE with zero charge and a rest mass of1.674 92 × 10–27 kg. Neutrons are nucle-ons, found in all nuclides except 1H. Iso-lated neutrons are unstable and decay witha half-life of about 12 minutes. Neutronsare fermions with spin ½. They arestrongly interacting particles. As they areuncharged, they interact with nuclei moreeasily than do protons and other chargedparticles, especially at low energies. Neu-trons are made up of more fundamentalparticles called quarks.

neutron capture The capture by anatomic nucleus of a neutron, often accom-panied by the emission of gamma radia-tion. See also electron capture.

neutron diffraction The diffraction ofneutrons by matter. The technique of neu-

tron diffraction to investigate crystals de-pends on the fact that neutrons have an as-sociated wavelength and, at a suitableenergy, can be diffracted just as x-rays arediffracted. The technique is more difficultthan x-ray diffraction because a suffi-ciently intense neutron source has to beavailable. However, neutron diffractionhas certain advantages over x-ray diffrac-tion. In particular, x-rays are scattered byelectrons in atoms and consequently aremore useful in investigating heavier atomswith many electrons. They do not detectthe position of the hydrogen atoms presentin all atomic molecules. Neutrons are scat-tered by atomic nuclei and are particularlyuseful for investigating the positions of hy-drogen atoms in molecules. Also, becauseof their magnetic moment, neutrons areuseful in studying various types of mag-netic crystal.

neutron number Symbol: N The numberof neutrons in the nucleus of an atom; i.e.the nucleon number (A) minus the protonnumber (Z).

neutron–proton ratio The ratio of thenumber of neutrons to the number of pro-tons in an atomic nuclide. This ratio is im-portant in the consideration of whichnuclei are stable. For light nuclei, the moststable are those in which the ratio has thevalue of one. For nuclei heavier than thoseof calcium the neutron–proton ratio in-creases, finishing at a value of about 1.6 foruranium.

neutron star A very dense star that is pro-tected from gravitational collapse to aBLACK HOLE by the DEGENERACY PRESSURE ofthe neutrons of which it is composed. Neu-tron stars are thought to have been formedby the collapse of stars several times moremassive than the Sun in supernova explo-sions. See also pulsar.

New Cartesian convention See signconvention.

newton Symbol: N The SI unit of force,equal to the force needed to accelerate onekilogram by one meter second–2.

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newton

1 N = 1 kg m s–2

The unit is named for the English scien-tist Sir Isaac Newton (1642–1727).

Newtonian fluid A fluid in which thestress at any point is proportional to therate of change of strain with respect to timeat that point, with the constant of propor-tionality being called the coefficient of vis-cosity. Many liquids are Newtonian fluids.Examples of non-Newtonian fluids includenon-drip paints, lubricating oils, and poly-mer solutions and melts. See also thix-tropy.

Newtonian mechanics /new-toh-nee-ăn/The system of mechanics that applies NEW-TON’S LAWS OF MOTION, as they relate tostationary objects and those that are mov-ing much slower than the speed of light(relative to the observer). See also relativity(theory of).

Newtonian telescope The earliest typeof reflecting telescope; the system is stilloften used. Light from the converging mir-ror is reflected back onto an angled planemirror, and from there into the eyepiece.See also reflector.

Newton’s formula For a simple lens, thedistance between two CONJUGATE POINTS (pand q) and their respective FOCAL POINTS (f)are related by the equation:

pq = f2

Newton’s law of cooling When a hotbody is cooling in air, the rate of transfer ofheat is proportional to the temperature dif-ference between the body and its surround-ings. This is strictly true only for forcedconvection. See convection.

Newton’s law of universal gravitationThe force of gravitational attraction be-tween two point masses (m1 and m2) is pro-portional to the product of the massesdivided by the square of the distance (r) be-tween them. The law is often given in theform F = Gm1m2/r2, where G is a constantof proportionality called the gravitationalconstant. The law can also be applied toextended bodies by integrating the infini-tesimal forces acting on each element. Inthe case of spherically symmetrical bodies,the force is the same as if the whole masswere concentrated at the center. To a firstapproximation, bodies such as the Earthare regarded as spherically symmetrical. Itwas unchallenged for over 200 years untilAlbert Einstein put forward his theory ofrelativity. See also Kepler’s laws; relativity.

Newton’s laws of motion Three laws ofmechanics formulated by Sir Isaac Newtonin 1687. They can be stated as:(1) An object continues in a state of rest orconstant velocity unless acted on by an ex-ternal force.(2) The resultant force acting on an objectis proportional to the rate of change of mo-mentum of the object, the change of mo-mentum being in the same direction as theforce.(3) If one object exerts a force on anotherthen there is a simultaneous equal and op-posite force on the first object exerted bythe second. The first law was discovered byGalileo, and is both a description of inertiaand a definition of zero force. The secondlaw provides a definition of force based onthe inertial property of mass. The secondand third laws combined give the law ofconservation of momentum.

See also reaction.

Newton’s rings INTERFERENCE patternsproduced by placing a lens (with very largeradius of curvature) on a reflecting surface

Newtonian fluid

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to eye lensand observer

curvedmirror

planemirror

Newtonian telescope

and illuminating it with monochromaticlight from above. Usually a plano-convexlens is used with the curved surface in con-tact. If the arrangement is observed fromabove with a microscope, light and darkrings are seen concentric with the contactpoint. A dark spot occurs in the center. Theradius of a bright ring is given by:

r2 = a(m + ½)λwhere a is the radius of curvature of theconvex surface and m = 0, 1, 2, etc. For thefirst bright ring m = 0, for the second m =1, etc. Newton’s original experiments(1704) were with white light so coloredrings were produced.

Nichrome /nÿ-krohm/ (Trademark) Analloy of about 62% nickel, 15%chromium, and 23% iron, used for makingelectric heating elements and resistors. Ithas a high resistivity and a high meltingpoint.

nickel /nik-ăl/ A transition metal that oc-curs naturally as the sulfide and silicate. Itis used as a protective coating (on othermetals) and in the manufacture of variousalloys, such as Nichrome and stainlesssteel.

Symbol: Ni; m.p. 1453°C; b.p. 2732°C;r.d. 8.902 (25°C); p.n. 28; r.a.m. 58.6934.

nickel–iron accumulator (Edison cell;Nife or NIFE cell) A type of secondary cellin which the electrodes are formed by steelgrids. The positive electrode is impreg-nated with a nickel-nickel hydride mixture.The negative electrode is impregnated withiron oxide. Potassium hydroxide solutionforms the electrolyte. The nickel-iron cell islighter and more durable than the lead ac-

cumulator, and it can work with highercurrents. Its e.m.f. is approximately 1.3volts. Modern forms of this cell use cad-mium or cadmium-iron alloy for the nega-tive electrode. It is also named the Edisoncell for the American scientist and inventorThomas A. Edison (1847–1931).

Nicol prism /nik-ŏl/ A device for produc-ing plane polarized light, consisting of acrystal of calcite cut with a 68° angle,cleaved along the optic axis, and stuck to-gether with a thin layer of Canada balsam.The Canada balsam, which is not birefrin-gent, has the same refractive constant forboth ordinary and extraordinary rays (n =1.66). The latter ray passes through theprism (in calcite n = 1.66). However, theordinary ray in calcite has a lower refrac-tive constant (n = 1.48) than in the Canadabalsam, and suffers total internal reflectionat the interface. Nicol prisms are moretransparent than Polaroid. It is named forthe Scottish physicist William Nicol(1768–1851).

NIFE cell See nickel-iron accumulator.

niobium /nÿ-oh-bee-ŭm/ A soft silverytransition element used in welding, specialsteels, and nuclear reactor work.

Symbol: Nb; m.p. 2468°C; b.p.4742°C; r.d. 8.570 (20°C); p.n. 41; r.a.m.92.90638.

Nipkow disk /nip-koff/ A primitive me-chanical scanning device consisting of a ro-tating disk with radial notches or a spiralof small holes. It was employed in the earlydevelopment of television. It is named forthe German physicist Paul Nipkow(1860–1940).

nit Symbol: nt A unit of luminance, equalto the luminance produced by one candelaper square meter (cd m–2).

nitrogen /nÿ-trŏ-jĕn/ A nonmetallic ele-ment; nitrogen accounts for about 78% ofthe atmosphere (by volume) and it also oc-curs as sodium nitrate in various mineraldeposits. It is separated for industrial useby the fractionation of liquid air. Nitrogen

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nitrogen

path difference = 2t + λ /2

interferingwave trains

ttt

Newton’s rings

has two isotopes; 14N, the common iso-tope, and 15N (natural abundance0.366%), which is used as a marker inmass spectrometric studies.

Symbol: N; m.p. –209.86°C; b.p.–195.8°C; d. 1.2506 kg m–3 (0°C); p.n. 7;r.a.m. 14.

NMR See nuclear magnetic resonance.

nobelium /noh-bel-ee-ŭm/ A radioactivetransuranic element of the actinoid series,not found naturally on Earth. Several veryshort-lived isotopes have been synthesized.The element is named for the Swedishchemist Alfred Nobel (1833–96).

Symbol: No; p.n. 102; most stable iso-tope 259No (half-life 58 minutes).

node A place in a stationary wave whereone of the two kinds of disturbance haszero (or minimum) value. Nodes occur atdistances apart equal to half the wave-length of the corresponding progressiveWAVE.

The nodes for one disturbance are nor-mally antinodes (i.e. places of maximumamplitude) for the other. Thus, in station-ary electromagnetic waves, electric nodesare magnetic antinodes and vice versa. Instationary sound waves the pressure nodesare antinodes for particle velocity and viceversa. Similar rules apply to other types ofwave. Generally energy oscillates longitu-dinally between the nodes for one variableand the adjacent antinodes. See also inter-ference.

noise 1. Sound composed of a randommix of different frequencies. White noise isa completely random mix over a wide fre-quency range; it has a confusing effect onthe listener. Pink noise – random frequen-cies in a selected range – is often used as abackground to mask other sounds.2. A general term describing any signal thatimpairs the efficient working of an elec-tronic device. There are two principaltypes: white noise and impulse noise. Theunwanted energy of white noise is distrib-uted across a wide frequency band, in thesame way that the energy of white light isdistributed across a band according to

color. Impulse noise is a consequence ofone or more momentary electrical im-pulses. There are numerous types of whitenoise: thermal noise is caused by the ran-dom thermal motion of electrons superim-posed on a steady current flow; randomnoise can also be caused by an irregularmomentary disturbance originating in anatmospheric electrical disturbance or asimilar disturbance in the Sun, etc.

Noise results in undesirable sounds in aloudspeaker, which mask the desired ef-fect, and, in television, results in ‘snow’, anunwanted pattern on a TV screen similar tofalling snow.

non-equilibrium statistical mechanicsThe branch of statistical mechanics con-cerned with systems that are not in ther-modynamic equilibrium. Non-equilibriumstatistical mechanics is used to calculatetransport coefficients such as electrical andthermal conductivity. For systems that arefar from thermodynamic equilibrium it candescribe such behavior as chaos, self-orga-nization, and turbulence.

non-equilibrium thermodynamics Thebranch of thermodynamics concerned withsystems which are not in equilibrium. Non-equilibrium thermodynamics is used todescribe such phenomena as self-organiza-tion. It is not known whether general lawsexist, analogous to the well-establishedthree laws of thermodynamics, for systemsthat are far from thermodynamic equilib-rium.

non-inductive Describing a circuit com-ponent that has a low inductance. Non-in-ductive coils are made by doubling backthe wire on itself before making the coil.The current then flows in both sensesthrough the coil and a negligible magneticfield is produced.

non-ohmic Describing a substance or cir-cuit component that does not obey Ohm’slaw; i.e. the current passed is not directlyproportional to the potential differenceacross the circuit.

NMR

170

no parallax See parallax.

NOR gate See logic gate.

normal The perpendicular to a reflectingor refracting surface at the point of inci-dence of the ray concerned. Angles of inci-dence, reflection, and refraction aremeasured between the normal and the inci-dent ray, reflected ray, and refracted ray re-spectively. A normal ray is one incidentperpendicularly on a surface – the angle ofincidence is zero.

normal adjustment An image formed byan optical system is in normal adjustment ifit is in a similar viewing position to the ob-ject. The term really refers to the adjust-ment of the system. Thus, normaladjustment of a telescope gives the image atinfinity; normal adjustment of a micro-scope puts the image at the viewer’s nearpoint. Other adjustments are quite possi-ble, and may be preferred in some cases.

normal ray See normal.

normal temperature and pressure(NTP) See STP.

north pole See poles; magnetic.

note (tone) A sound that has a single fun-damental frequency. A pure note (or puretone) has a simple harmonic waveform(approximately). Such a note can be pro-duced by a tuning fork. Musical instru-ments produce complex notes, which canbe analyzed into a single fundamental fre-quency mixed with higher frequency over-tones. See quality of sound.

NOT gate (inverter gate) See logic gate.

n-p-n transistor See transistor.

N-pole See poles; magnetic.

NTP Normal temperature and pressure.See STP.

n-type conductivity See semiconductor;transistor.

nuclear energy /new-kee-er/ Energy de-rived from nuclear reactions either by thefission of heavy nuclei into lighter ones orby fusion of light nuclei into heavier ones.

Nuclear energy is exploited both forweapons construction and for civil powersupplies. Both fission and fusion processeshave been used in weaponry but, so far, ithas not proved possible to exploit fusionprocesses for power production. See alsofusion; nuclear reactor; nuclear weapon.

nuclear fission The disintegration of anatomic nucleus into two or more large frag-ments. Fission may be spontaneous or in-duced. Spontaneous fission is a rare formof radioactivity shown by a few heavy nu-clides. Induced fission is the instantaneousdisintegration of a heavy nucleus on irradi-ation, usually by neutrons. In fission, nu-clei usually disintegrate to form twofragments of roughly comparable massnumber along with a few neutrons. For ex-ample, the neutron-induced fission of235uranium could yield 90krypton and143barium as follows: 2

932

5U + 01n → 3

960Kr +

15

463Ba + 30

1nThe energy made available will be about 30petajoules (pJ) per fission. Nuclear fissionis exploited for the production of nuclearpower and for nuclear weapons.

nuclear force A very strong short-rangeattractive force acting between nucleons.Nuclear forces act over a range up to about2 × 10–15 m and are much stronger thanelectromagnetic forces, so are able to over-come the electrostatic repulsion betweenprotons in the nucleus. They are thus re-sponsible for holding the nucleus together.See also exchange force; interaction.

nuclear fusion See fusion.

nuclear isomers A pair of isotopes of thesame proton and neutron numbers, but indifferent quantum states. They thus havediffering stability, and behave as differentnuclides having different half-lives. For ex-ample, the beta decay of 234Th yields twoisomers of 234Pa with half-lives of about 70seconds and about 6.7 hours respectively,which may both undergo beta decay to

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nuclear isomers

form 29304U. About 1 in 700 nuclei of the less

stable isomer (that with the shorter half-life) may emit a gamma photon and makea transition to the more stable isomer.

nuclear magnetic resonance (NMR) Aneffect that results when waves of radio fre-quency are absorbed by the nuclei of mat-ter in a strong external magnetic field. Ithas various applications in chemistry(NMR spectroscopy,), medicine, andphysics.

nuclear physics The branch of physicsthat is concerned with nuclear structure,properties, and reactions, and their appli-cations (e.g. in producing nuclear power orusing radioisotopes).

nuclear power The use of nuclear reac-tions for power generation (usually by gen-eration of electricity but nuclear poweredships use the heat generated to raise steamto power the turbines directly without con-version to electricity). The reactions con-cerned are usually restricted to fission andfusion reactions; some people, however, in-clude the use of energy from radioisotopedecay.

nuclear reaction A reaction involvingnuclei. Such reactions include the sponta-neous disintegration of a single nucleus (ra-dioactive decay or fission); the formationof a new nucleus from two smaller nuclei(fusion); or absorption of a photon, neu-tron, proton, or other particle. An equa-tion for a nuclear reaction shows thenuclides and particles involved by theirsymbols. For example:

28

120Pb → 2

813

0Bi + –10e

represents the beta decay of lead-210 toform bismuth-210.

nuclear reactor A device in which nu-clear reactions take place on a large scale.A reactor may be built for the purpose ofproviding useful energy, producing newnuclides, or research. Present designs arefission reactors that depend on the con-trolled fission of uranium or plutonium. Ingeneral, they are constructed of a core con-taining the fuel (uranium); control rods to

absorb surplus neutrons; a reflector tobounce straying neutrons back into thecore; coolant to carry the energy from thecore; containment – a barrier to prevent theescape of radioactive material; and shield-ing to protect workers from the intense ra-diation generated.

In thermal reactors a moderator is usedto slow the neutrons so that a chain reac-tion can be sustained. Fast reactors do nothave a moderator, and use fast neutrons. Inthis case the fuel has to be enriched (so thatit contains more 235U isotope). This type ofreactor uses a blanket of natural uranium,which is converted to plutonium by neu-trons. Some fast reactors produce more fis-sile 239Pu from the nonfissile 238U than theamount of fissile material used up. Theseare called BREEDER REACTORS if the originalfuel is mainly plutonium and converter re-actors if it is mainly 235U. Thermal breederreactors are possible using 233U as fuel andgenerating more of this fissile material bycapturing neutrons in nonfissile 232Th. Sofar, this type has been little developed.

Fusion reactors are reactors for produc-ing energy by nuclear fusion. They are po-tentially important because the fuel(hydrogen isotopes) is available in unlim-ited quantities. However, there are im-mense practical problems in sustaining acontrolled fusion reaction, and these reac-tors are still in the development stage. Seealso boiling-water reactor; gas-cooled reac-tor; pressurized water reactor; Tokamak.

nuclear waste The unwanted radioactiveby-products of the nuclear industry, partic-ularly from the mining, extraction, and re-processing of nuclear fuels and fromdecommissioned nuclear reactors. Theirdisposal presents an environmental (andpolitical) problem. Methods of treatmentinclude storage of highly radioactive wasteuntil its activity is reduced enough toprocess it, containment in concrete of in-termediate-level waste and burial under-ground or below the seabed, and storage oflow-level waste in steel drums at specialsites.

nuclear weapon An explosive device inwhich the energy release results either from

nuclear magnetic resonance

172

the fission of heavy nuclei (such as 235U or239Pu) in a rapidly built up chain reactionor from the fusion of light nuclei such asdeuterium and tritium to form helium andneutrons. This latter type of device isknown as a ‘hydrogen bomb’. See also crit-ical mass; mass defect.

nucleon /new-klee-on/ A particle found inthe nucleus of atoms; i.e. a proton or a neu-tron. Nucleons are classified as baryons.See also elementary particles.

nucleon number (mass number) Symbol:A The number of nucleons (protons plusneutrons) in an atomic nucleus.

nucleosynthesis /new-klee-oh-sin-th’ĕ-siss/ The synthesis of the nuclei of thechemical elements in nuclear reactions.The term is often used in the context of thecreation of chemical elements in the Uni-verse. Nucleosynthesis can occur in severaldifferent ways. In primordial nucleosyn-thesis, which occurred very soon after theBIG BANG when the Universe was very hot,the light elements such as helium weremade. Nearly all other elements have beenmade in stellar nucleosynthesis, i.e. nuclearreactions occurring inside stars. In particu-lar, most of the elements heavier than ironare made in SUPERNOVA explosions. Somelight elements, particularly beryllium andboron, were produced by spallation, i.e.nuclear reactions in interstellar space oc-curring when cosmic rays hit the nuclei ofinterstellar matter.

nucleus, atomic (pl. nuclei or nucleuses)The compact, comparatively massive, pos-itively charged center of an atom made upof one or more nucleons (protons and neu-

trons) around which is a cloud of electrons.The density of nuclei is about 1015 kg m–3.The number of protons in the nucleus de-fines the element, being its atomic number(or proton number). The nucleon number,or atomic mass number, is the sum of theprotons and neutrons. The simplest nu-cleus is that of a hydrogen atom, 1H, beingsimply one proton (mass 1.67 × 10–27 kg).The most massive naturally occurring nu-cleus is 238U of 92 protons and 146 neu-trons (mass 4 × 10–25 kg, radius 9.54 ×10–15 m). Only certain combinations ofprotons and neutrons form stable nuclei.Others undergo spontaneous decay.

A nucleus is depicted by a symbol indi-cating nucleon number (mass number),proton number (atomic number), and ele-ment name. For example, 1

213Na represents

a nucleus of sodium having 11 protons andmass 23, hence there are (23 – 11) = 12neutrons.

nuclide /new-klÿd/ A nuclear species witha given number of protons and neutrons;for example, 23Na, 24Na, and 24Mg are alldifferent nuclides. Thus:12

13Na has 11 protons and 12 neutrons

12

14Na has 11 protons and 13 neutrons

12

24Mg has 12 protons and 12 neutrons

The term is applied to the nucleus andoften also to the atom.

nutation /new-tay-shŏn/ A periodicchange in the inclination of the axis in themotion of a spinning body with respect tosome reference axis. For example, the mainnutation in the precessional motion of theEarth occurs because of periodic changesin the orbit of the Moon. This gives a nu-tation with a period of 19 years.

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nutation

174

object A real or apparent source of rays inan optical system, perhaps incident on alens or a reflector. After refraction or re-flection, the rays appear to come fromsome other place – the image.

An object need not be real. The dia-grams show how the real image I1, pro-duced by the lens, becomes a virtual objectO2 when the mirror is introduced. Thisnow gives a real image I2. Just as with realobjects, virtual objects can appear as realor virtual images.

objective The lens or combination oflenses nearest the object in an optical in-strument. The nearest lens to the object ina compound objective is often called theobject lens. The large converging mirror ina reflecting telescope can also be describedas the objective.

object plane The plane that is perpendic-ular to the axis and centered on the objectin an optical system.

octave /ok-tiv/ The interval between awaveform and another of twice the fre-quency. An octave in sound corresponds toeight notes on the diatonic musical scale.

octet /ok-tet/ (electron octet) For an atom,an outer shell containing eight electrons,which confers stability. For example, thevery unreactive rare gases have an octet ofelectrons in their outer shell. See also elec-tron shell.

ocular /ok-yŭ-ler/ See eyepiece.

oersted Symbol: Oe A unit of magneticfield strength in the c.g.s. system. It is equalto 79.578 A m–1. The unit is named for theDanish physicist Hans Christian Oersted(1777–1851).

ohm /ohm/ Symbol: Ω The SI unit of elec-trical resistance, equal to a resistance thatpasses a current of one ampere when thereis an electric potential difference of one

O

| |I1

O1

converginglens

Formation of a real image from a real object

divergingmirror

O2

O1

real image I2

converginglens

Formation of a real image involving a virtualobject

volt across it. 1 Ω = 1 V A –1. The unit isnamed for the German physicist GeorgSimon Ohm (1787–1854).

ohmic /oh-mik/ Describing a substance orcircuit component that obeys Ohm’s law.

Ohm’s law The current (I) in a conductoris proportional to the potential difference(V) between its ends. This leads to V = IR,where R is the conductor’s resistance. R isconstant provided the physical conditionsin the conductor are unaltered. If V is involts and I in amperes, R is in ohms. Com-ponents that conduct in accordance withOhm’s law (e.g. metal resistors) are said tobe ohmic.

oil-drop experiment An experiment car-ried out by Millikan in 1913 to determinethe charge on an electron. He deduced thecharge by measuring the rate of descent ofa charged oil drop in an electric field. Seeelectron charge.

oil-immersion objective See immersionobjective.

omega particle /oh-meg-ă, -mee-gă, -may-gă/ See elementary particles.

opaque /oh-payk/ Not able to pass radi-ant energy. A substance that is opaque toone type of electromagnetic radiation maybe transparent to another. Thus glasspasses visible radiation very well, but isopaque to most thermal (infrared) radia-tion. Compare translucent.

opaque projector (episcope) An opticalinstrument for projecting an image of anopaque object (e.g. a diagram or picture)onto a screen. High-intensity illuminationis used and the image is projected by acombination of mirrors and lenses.

open circuit See circuit; electrical.

open pipe A pipe that is open at bothends. When stationary waves are set up inan open pipe the ends of the pipe have to beantinodes.

opera glasses See binoculars; Galileantelescope.

optical activity /op-tă-kăl/ The ability ofcertain crystals or compounds in solutionto rotate the plane of polarization of planepolarized light. Compounds that are opti-cally active have an asymmetric molecularstructure such that their molecules canexist in left- and right-handed forms (theforms are mirror images of each other; theproperty of having such forms is called chi-rality). Particular forms of the compoundare classified as dextrorotatory (right turn-ing) or levorotatory (left turning). Levoro-tatory compounds rotate the plane ofpolarization to the left; i.e. anticlockwiseas viewed facing the oncoming light. Dex-trorotatory compounds rotate the plane tothe right (i.e. in the opposite sense). Manynaturally occurring substances (e.g. sugars)are optically active.

optical axis The principal axis of an op-tical system, i.e. the path of rays passingalong the principal axes of the lenses ormirrors.

optical center (optic center) See pole.

optical density A measure of the extentto which a transluscent material preventsthe passage of light through it. It is definedas log10I0/I, where I0 is the intensity of theincident light and I is the transmitted in-tensity.

optical fiber See fiber optics.

optical glass A type of glass with proper-ties suitable for making lenses, prisms, etc.There are two major groups: the crownglasses and the flint glasses, differing intheir density and refractive constants. Op-tical glasses are fairly hard yet easily pol-ished and highly transparent to light.

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optical glass

OPTICAL GLASS

Glass Density (kg m–3) Refractiveconstant

crown 2500–2600 1.51–1.61flint 2700–4800 1.53–1.75

optical lever A device for measuring an-gular displacement. A small mirror is at-tached to the rotating body and a narrowfixed beam of light directed onto it. The re-flected beam is directed onto a screen, pro-ducing a spot of light. Movement of thisspot shows small angular movements ofthe mirror. The angle turned through bythe reflected beam is twice that turned bythe mirror. The device is commonly used intorsion balances, as in the mirror gal-vanometer.

optical path Symbol: d The product ofdistance (l) traveled in a medium and therefractive constant (n) of the medium; i.e. d= nl. Phase difference (∆φ) relates to pathdifference (∆d) thus:

∆φ = 2π∆d/λ

optical pyrometer (disappearing-fila-ment pyrometer) A type of pyrometer usedto measure the temperature of incandes-cent sources. Light from the source is fo-cused onto a tungsten filament, and thefilament and the image of the source areviewed through a red filter and an eyepiece.The current in the filament, measured byan ammeter, is varied until this has thesame brightness as the body (i.e. it cannotbe seen against the background of thesource). The ammeter is calibrated directlyin degrees Celsius, with the assumptionthat the source emits black-body radiation.A correction can be made for the spectralemissivity of the source. See also total-radi-ation pyrometer.

optical rotary dispersion (ORD) Thephenomenon in which the amount of rota-tion of plane-polarized light of an opticallyactive substance depends on the wave-length. Optical rotary dispersion is an im-portant technique in chemistry. Plots ofrotation against wavelength can be used togive information on the molecular struc-ture of optically active compounds.

optical telescope A TELESCOPE using vis-ible light from a distant object to producea magnified image.

optic axis The direction in a BIREFRIN-GENT CRYSTAL along which the ordinaryand extraordinary rays travel at the samespeed. Uniaxial crystals have one such axis;biaxial crystals have two.

optics /op-tiks/ The study of the natureand behavior of light and other radiations.The reflection of ultraviolet radiation andthe refraction of sound (pressure) wavesalso follow the laws of optics. Electron dif-fraction and the electron microscope arebranches of electron optics.

Where the wave nature of the radiationneed not be considered, situations can bediscussed in terms of rays. That study istraditionally called geometrical optics.Physical optics is the field of optics inwhich wave properties are important. Thusthe use of lenses is part of geometrical op-tics, while the diffraction grating comesinto physical optics.

optoelectronics /op-toh-i-lek-tron-iks/ Abranch of electronics based on light beamsrather than electric currents. The main ad-vantage is that light frequencies are farhigher than radio frequencies so that muchmore information can be carried in a suit-ably treated light beam than in an elec-tronic (radio) signal. Optical fibers, of verycheap very transparent glass, carry thelight beams, produced by semiconductorlasers and detected by photocells.

orbit The curved, usually closed, path, ortrajectory along which a moving objecttravels. Examples include the ellipticalorbit of a planet in the solar system, the cir-cular orbit of an electron in a magneticfield, and the parabolic trajectory of a pro-jectile under gravity.

orbital 1. Pertaining to an orbit. For ex-ample, an orbital electron is one that isbonded around the nucleus of an atom.2. According to quantum theory, the elec-trons in an atom do not have fixed orbitsaround the nucleus. Instead, there is a finiteprobability of finding the electron in agiven volume at any distance from the nu-cleus. The region in space in which there isa high probability of finding an electron is

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176

an atomic orbital. Orbitals are usuallythought of as three-dimensional states cen-tered on the nucleus. For a hydrogen atomin its ground state the electron occupies anorbital that has a spherical distributionaround the nucleus. This is known as an s orbital. Other types of orbital have dif-ferent shapes: for example, p orbitals havetwo lobes extending out from the nucleus;d orbitals have four lobes. Similarly, inmolecules, electrons move in molecular or-bitals around the nuclei of the atoms.

order 1. A specific pattern in a system. Forexample, there is order in a perfect crystalbecause of the lattice structure. In a ferro-magnet there is order in the form of all themagnetic moments of the atoms beingaligned in the same direction.2. An integer (m) associated with a giveninterference fringe or diffraction pattern.In interference a bright fringe occurs for apath difference mλ; a dark fringe is pro-duced if the path difference is (m + ½)λ. Abright fringe is first order if it arisesthrough a path difference of one wave-length (m = 1). Similarly, second order cor-responds to m = 2, etc.

ordinary ray See birefringent crystal.

OR gate See logic gate.

oscillation /os-ă-lay-shŏn/ A regularly re-peated motion or change. See vibration.

oscillator /os-ă-lay-ter/ A device that gen-erates an alternating current signal ofknown frequency from a direct currentinput. The output is usually in the form ofa sine wave or a square wave. A sinusoidaloscillation can be produced by combiningan inductor and a capacitor in a resonantcircuit. The frequency is dependent on thevalues of the inductance and the capaci-tance. A square wave is produced in a MUL-TIVIBRATOR by the alternate charge anddischarge of a capacitor, the frequencybeing dependent on the resistance and ca-pacitance. See also crystal oscillator.

oscilloscope /ŏ-sil-ŏ-skohp/ See cathode-ray oscilloscope.

osmium /oz-mee-ŭm/ A transition metalthat is found associated with platinum. Os-mium is the most dense of all metals. Themetal is used in catalysts and in alloys forpen nibs, pivots, and electrical contacts.

Symbol: Os; m.p. 3054°C; b.p. 5027°C;r.d. 22.59 (20°C); p.n. 76; r.a.m. 190.23.

Otto cycle The idealized reversible cycleof four operations occurring in a perfectfour-stroke (spark ignition) gasoline en-gine. The cylinder is filled with atmos-pheric air containing gasoline vapor(intake stroke); with valves closed, the air-vapor mixture is compressed adiabatically(compression stroke); the spark ignites themixture, which burns rapidly, increasingthe temperature at nearly constant volume;the hot mixture of air and combustionproducts expands adiabatically doingwork (power stroke); a valve opens and thepiston expels the gas (exhaust stroke). Thecycle is then repeated.

Assuming ideal reversible processes andperfect thermal insulation, the ideal cyclegives the maximum conceivable EFFICIENCY

for this type of engine. In practice, it will beconsiderably less efficient. The cycle isnamed for the German engineer NikolausAugust Otto (1832–91). See also Carnotcycle.

overdamping See damping.

overhead projector A type of PROJECTOR

able to project, on a screen, large bright im-ages of slides or transparent objects placedon a horizontal table.

overtone A component of a note that hashigher frequency and (usually) lower inten-sity than the fundamental. The overtoneshave frequencies that are simple multiplesof the fundamental frequencies. The wordis a musical term best avoided in physics.See partials; quality of sound.

oxygen /oks-ă-jĕn/ A colorless odorless di-atomic gas. It has the electronic configura-tion [He]2s22p4. Oxygen is the mostplentiful element in the Earth’s crust ac-counting for over 40% by weight. It is pre-sent in the atmosphere (20%) and is a

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oxygen

constituent of the majority of minerals androcks as well as the major constituent ofthe sea.

Oxygen is an essential element for al-most all living things. Elemental oxygenhas two forms: the diatomic molecule O2and the less stable molecule trioxygen(ozone), O3, which is formed by passing anelectric discharge through oxygen gas. In-dustrially oxygen is obtained by the frac-

tionation of liquid air. The element occursin three natural isotopic forms, 16O(99.76%), 17O (0.0374%), 18O(0.2039%); the rarer isotopes are used indetailed studies of the behavior of oxygen-containing groups during chemical reac-tions (tracer studies).

Symbol: O; m.p. –218.4°C; b.p.–182.962°C; d. 1.429 kg m–3 (0°C); p.n. 8;r.a.m. 15.99.

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178

packing fraction The difference betweenthe actual mass of a nuclide and the near-est whole number (i.e., the mass defect) di-vided by the mass number. See also bindingenergy.

pain threshold The intensity of sound atwhich sound is painful to the ear. It corre-sponds to about 120 decibels.

pair production The production of anelectron and its antiparticle (a positron)from a photon (according to the equationE = mc2). The process can occur in the fieldof an atomic nucleus. Since the mass of anelectron or positron is equivalent to 0.511MeV, the minimum energy of a photonthat can promote pair production is 1.022MeV. Any surplus energy becomes kineticenergy of the products.

palladium /pă-lay-dee-ŭm/ A silverywhite ductile transition metal occurring inplatinum ores. It is used in electrical relaysand as a catalyst in hydrogenationprocesses. Hydrogen will diffuse through ahot palladium barrier.

Symbol: Pd; m.p. 1552°C; b.p. 3140°C;r.d. 12.02 (20°C); p.n. 46; r.a.m. 106.42.

parabola /pă-rab-ŏ-lă/ A conic with an ec-centricity of 1. The curve is symmetricalabout an axis through the focus at right an-gles to the directrix. This axis intercepts theparabola at the vertex. A chord throughthe focus perpendicular to the axis is thelatus rectum of the parabola.

In Cartesian coordinates a parabola canbe represented by an equation:

y2 = 4axIn this form the vertex is at the origin andthe x-axis is the axis of symmetry. Thefocus is at the point (0,a) and the directrix

is the line x = –a (parallel to the y-axis).The latus rectum is 4a.

If a point is taken on a parabola andtwo lines drawn from it – one parallel tothe axis and the other from the point to thefocus – then these lines make equal angleswith the tangent at that point. This isknown as the reflection property of theparabola, and is utilized in parabolic re-flectors and antennas.

The parabola is the curve traced out bya projectile falling freely under gravity. Forexample, a tennis ball projected horizon-tally with a velocity v has, after time t, trav-eled a distance d = vt horizontally, and hasalso fallen vertically by h = gt2/2 because ofthe acceleration of free fall g. These twoequations are parametric equations of theparabola. Their standard form, corre-sponding to y2 = 4ax, is

x = at2

y = 2atwhere x represents h, the constant a is g/2,and y represents d. See also conic.

parabolic mirror /pa-ră-bol-ik/ A reflec-tor with a parabolic section. The converg-ing type can converge wide parallel beamsaccurately into its focal point (and is thus

179

P

F

F = focal point

Parabolic mirror

parallax

180

used for reflection telescopes and solarpower applications). On the other hand,radiation from a source at the focal pointwill be reflected into a parallel beam (asused in various lighting systems).

parallax /pa-ră-laks/ The apparent differ-ence in an object’s position relative to thatof another when viewed from two differentplaces. If there is no parallax between twoobjects, they must be at effectively the sameplace. Often in experiments with light, no-parallax methods are used to locate im-ages. When there is no parallax betweenthe image and the object used to find it, thetwo are in the same position.

parallel Elements in an electrical circuitare in parallel if connected so that the cur-rent divides between them and rejoins atthe other side. The word ‘shunt’ is some-times used.

For resistors in parallel, the resulting re-sistance R is given by:

1/R = 1/R1 + 1/R2 + 1/R3 + …For capacitors in parallel, the capacitanceof the combination is given by:

C = C1 + C2 + C3 + …Compare series.

parallel axes, theorem of See theorem ofparallel axes.

parallel forces When the forces on an ob-ject pass through one point, their resultantcan be found by using the parallelogram ofvectors. If the forces are parallel the resul-tant is found by addition, taking sign intoaccount. There may also be a turning effectin such cases, which can be found by theprinciple of moments.

parallelogram (law) of forces See par-allelogram of vectors.

parallelogram (law) of velocities Seeparallelogram of vectors.

parallelogram of vectors A method forfinding the resultant of two vectors actingat a point. The two vectors are shown astwo sides of a parallelogram: the resultantis the diagonal through the starting point.The technique can be used either with care-ful scale drawing or with trigonometry.The trigonometrical relations give:

F = √(F12 + F2

2 + 2F1F2cosθ)α = sin–1[(F1/F)sinθ]

paramagnetism /pa-ră-mag-nĕ-tiz-ăm/The magnetic behavior of substances witha small susceptibility; this often varies withtemperature according to Curie’s law. Therelative permeability of a paramagneticsubstance is slightly greater than one. Para-magnetism results from unpaired electron

• •

R1

R3

C2

C3

C1

capacitors in parallel

resistors in parallel

R2

Parallel circuits

(a) F = F1 + F2 + F3

(b) F = F1 – F2 + F3

M is the center of mass

M

M

F1F2

F3

F2

F1

F3

Parallel forces

spins. In an external field, a piece of para-magnetic material will slightly concentrate,and thus increase, the field; this is becausethe magnetic moments of the particles alignthemselves in the same direction. As a re-sult, the sample itself will align parallel tothe field. Above its Curie temperature, aferromagnetic material will have no do-mains and will show only paramagneticbehavior. See also magnetism.

paraxial /pă-raks-ee-ăl/ Describing raysincident on a surface close and parallel tothe axis. Only paraxial rays pass or appearto pass through the focal point of a spheri-cal reflecting or refracting surface. See alsomirror; parabolic mirror.

parent A nuclide that undergoes radioac-tive decay to another specified nuclide (thedaughter).

parity (pl. parities) /pa-ră-tee/ A propertyof the wave functions that describe physi-cal systems in quantum mechanics. If allthree space coordinates are reversed themagnitude of the wave function does notchange. If the sign is unchanged the func-tion is said to have even parity (or +1); ifthe sign is reversed it has odd parity (or–1).

Each quantum state of a body has evenor odd parity and the various interactionsare subject to rules related to changes ofparity. For example, the more usualprocesses of emission or absorption of elec-tromagnetic radiation occur only between

states of opposite parity. The parity of asystem is the product of the parities of theparts. The parity of a system of interactingbodies is conserved in strong and electro-magnetic interactions, but not in weak in-teractions such as beta decay.

parking orbit (synchronous orbit) Anorbit of a satellite round the Earth in whichthe period of the orbiting satellite is 24hours, i.e. the same as the period of the ro-tation of the Earth about its axis of rota-tion. A satellite in a parking orbit is alwayspositioned above the same point on theEarth. A parking orbit is about 36 000 kmabove the surface of the Earth. Such orbitsare used for communication satellites.

parsec /par-sek/ Symbol: pc A unit of dis-tance used in astronomy and defined asthat at which the angle subtended by oneASTRONOMICAL UNIT equals one second ofone degree of arc, or 1/3600 of a degree ofarc. The parsec is used with SI units, inwhich it is equal to approximately 30.857petameters.

partial eclipse See eclipse.

partial pressure See Dalton’s law.

partials Components of a sound wavewith frequencies above the fundamentalfrequency. The partials include the over-tones together with non-harmonic compo-nents.

particle An abstract simplification of areal object – the mass is concentrated atthe object’s center of mass; its volume iszero. Thus relational aspects can be ig-nored.

particle, elementary See elementary par-ticle.

particle accelerator See accelerator.

particle physics The branch of physicsthat deals with elementary particles, theirproperties and interactions.

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F2

F

α

F1

Parallelogram of vectors

partition coefficient The ratio of theequilibrium concentrations of a solute dis-solved in two specified immiscible solvents.It is independent of the actual concentra-tions.

pascal /pas-kăl/ Symbol: Pa The SI unit ofpressure and stress, equal to a pressure ofone newton per square meter (1 Pa = 1 Nm–2). The unit is named for the Frenchmathematician, physicist, and religiousphilosopher Blaise Pascal (1623–62).

Paschen series /pash-ĕn/ A series of linesin the infrared spectrum emitted by excitedhydrogen atoms. The lines correspond tothe atomic electrons falling into the thirdlowest energy level and emitting energy asradiation. The wavelength (λ) of the radia-tion in the Paschen series is given by

1/λ = R(1/32 – 1/n2)where n is an integer and R is the Rydbergconstant. The series is named for the Ger-man physicist Louis Paschen (1865–1947).See also spectral series.

Pauli exclusion principle /pow-lee/ Seeexclusion principle.

p.d. See potential difference.

peak value The maximum value attainedby an alternating quantity (e.g. an alternat-ing current).

Peltier effect /pel-tyay/ The change intemperature produced at a junction be-tween two different metals or semiconduc-tors when electric charge is passed throughit. If the current direction is reversed then aheating effect becomes a cooling one orvice versa. The temperature change is di-rectly proportional to the current. The ef-fect is named for the French physicist JeanCharles Athanase Peltier (1785–1845).Compare Seebeck effect.

pencil A narrow beam of rays from a sin-gle point. See beam.

pendulum A simple pendulum consists ofa small mass oscillating to and fro at theend of a very light string. If the amplitude

of oscillation is small (less than about 10°),it moves with simple harmonic motion.The period does not depend on amplitudeor mass; there is a continuous interchangeof potential and kinetic energy. The periodis given by

T = 2π√(l/g)Here l is the length of the pendulum (fromsupport to center of the mass) and g is theacceleration of free fall.

A compound pendulum is a rigid bodyswinging about a point. The period de-pends on the radius of gyration. For smalloscillations it is given by the same relation-ship as that of the simple pendulum with lreplaced by [√(k2 + h2)]/h. Here, k is the ra-dius of gyration about an axis through thecenter of mass and h is the distance fromthe pivot to the center of mass.

pentode /pen-tohd/ A thermionic tubewith three GRIDS, one grid more than theTETRODE. The extra grid, called the sup-pressor grid, is placed between the screengrid and the anode. It is held at cathode po-tential, which suppresses by repulsion theloss of secondary electrons ejected by theanode. Thus the disadvantage of thetetrode is overcome. See also thermionictube.

penumbra (pl. penumbrae or penumbras)/pi-num-bră/ Partial shadow. See shadow.

perfect gas See gas laws; kinetic theory.

period Symbol: T The time for one com-plete cycle of an oscillation, wave motion,or other regularly repeated process. It is thereciprocal of the frequency, and is relatedto pulsatance, or angular frequency, (ω) byT = 2π/ω.

periodic motion Any kind of regularlyrepeated motion, such as the swinging of apendulum, the orbiting of a satellite, the vi-bration of a source of sound, or an electro-magnetic wave.

If the motion can be represented as apure sine wave, it is a simple harmonic mo-tion. Harmonic motions in general aregiven by the sum of two or more pure sinewaves. See simple harmonic motion.

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182

periodic table A table of the chemical el-ements arranged in order of increasingatomic number. The table is usually orga-nized in rows and columns and shows therelation between chemical properties of el-ements and their electron configurations.

periscope /pe-ră-skohp/ An optical instru-ment enabling the user to see over or roundan obstacle. The simplest version is themirror periscope, which has two mirrors,each at 45° to the viewed direction. Rathermore effective types use internally reflect-ing prisms. In submarines, telescopic lensesare fitted.

permanent gas A gas that cannot be liq-uefied by increasing its pressure at roomtemperature, but must also be cooled. Sucha gas has a critical temperature belowroom temperature. See critical state.

permanent magnet A sample of a sub-stance that retains its magnetism when theexternal magnetic field is removed. Perma-nent magnets are often made from steel,other alloys, or ferrites; they have manyuses. Permanent magnetism is mainly aproperty of ferromagnetic materials thathave high coercivity. Materials like this areoften said to be magnetically ‘hard’. Com-pare temporary magnetism

permeability /per-mee-ă-bil-ă-tee/ Sym-bol: µ A measure of the tendency of a sub-stance to develop magnetic lines of fluxwhen exposed to an external source ofmagnetomotive force. Absolute permeabil-ity is the ratio of the magnetic flux density(B) in a substance to the external magneticfield strength (H); i.e.

µ = B/HThe unit is the henry per meter (H m–1).The permeability of free space (i.e. a vac-uum) has a value of 4π × 10–7 H m–1, andis given the symbol µ0. The relative perme-ability (µr) of a substance is the ratio of itsabsolute permeability to the permeabilityof free space; i.e.

µr = µ/µ0Note that relative permeability, being a

ratio, has no units. It is related to suscepti-bility (χ) by:

µr = 1 + χ

permittivity /per-mă-tiv-ă-tee/ Symbol: εThe mutual force between two charges Q1and Q2 a distance r apart is given by theequation:

F = Q1Q2/4πεr2

The constant ε is the permittivity of themedium. The unit is the coulomb2 new-ton–1 metre–2 (C2 N–1 m–2), or faradmetre–1 (F m–1). The permittivity of freespace, ε0, (also called the electric constant)has the value 8.854 × 10–12 F m–1. The ab-solute permittivity of a material is equal toε0εr, where εr is the relative permittivity.See also Coulomb’s law.

perpetual motion Constant motion oc-curring without any external energy sup-ply. Perpetual-motion machines areimpossible to construct because of fric-tional and other forces dissipating the orig-inal energy.

perversion (lateral inversion) The effectproduced by a mirror in reversing imagesapparently left to right. Thus writing ap-pears backwards when reflected; the imageof a person raising the right hand appearsto raise the left hand.

Perversion is not of unusual signifi-cance. In the case of a plane mirror it fol-lows directly from the fact that each pointof the object produces an image point thatis directly opposite it behind the mirror.

peta- Symbol: P A prefix denoting 1015.For example, 1 petameter (Pm) = 1015

meter (m).

phase /fayz/ 1. A homogeneous part of amixture distinguished from other parts byboundaries. A mixture of ice and water hastwo phases. A mixture of ice crystals andsalt crystals also has two phases. A solutionof salt in water is a single phase.2. The stage in a cycle that a WAVE (or otherperiodic system) has reached at a particulartime (taken from some reference point).Two waves are in phase if their maximaand minima coincide.

For a simple wave represented by theequation

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phase

y = asin2π(ft – x/λ)the phase of the wave is the expression2π(ft – x/λ). The phase difference betweentwo points distances x1 and x2 from theorigin is 2π(x1 – x2)/λ.

A more general equation for a progres-sive wave is

y = asin2π(ft – x/λ – φ)Here, φ is the phase constant – the phasewhen t and x are zero. Two waves that areout of phase have different phase constants(they ‘start’ at different stages at the ori-gin). The phase difference is |φ1–φ2|. It isequal to 2πx/λ, where x is the distance be-tween corresponding points on the twowaves. It is the phase angle between thetwo waves; the angle between two rotatingvectors (phasors) representing the waves.

See also beats; interference.

phase angle See phase.

phase constant See phase.

phase difference The difference in thephases of two coherent radiations travelingin the same direction in a superposition re-gion. If the phase difference (∆φ) is 0, 2π,4π, etc., the two are in phase and will in-terfere constructively. If ∆φ is π, 3π, 5π,etc., the two are in anti-phase and will in-terfere destructively. See interference.

phase modulation A type of modulationin which a CARRIER WAVE is made to carrythe information in a signal (audio or visual)by fluctuations in the phase of the carrier.The difference in phases between the mod-ulated and the unmodulated carrier is pro-portional to the amplitude of the signal.The carrier remains at the same frequency.The carrier amplitude is constant. See alsomodulation.

phase rule (Gibbs phase rule) For anyequilibrium system, the expression

P + F = C + 2which relates the number of DEGREES OF

FREEDOM, F, to the number of phases, P,and the number of components, C. Seephase.

phase space A multi-dimensional spacethat can be used to define the state of a sys-tem. Phase space has coordinates (q1, q2,…p1, p2,…), where q1, q2, etc., are degrees offreedom of the system and p1, p2, are themomenta corresponding to these degreesof freedom. For example, a single particlehas three degrees of freedom (correspond-ing to the three coordinates defining its po-sition). It also has three components ofmomentum corresponding to these degreesof freedom. This means that the state of theparticle can be defined by six numbers (q1,q2, q3, p1, p2, p3) and it is thus defined by apoint in six-dimensional phase space. If thesystem changes with time (i.e. the particlechanges its position and momentum), thenthe point in phase space traces out a path(known as the trajectory). The system mayconsist of more than one particle. Thus, ifthere are N particles in the system then thestate of the system is specified by a point ina phase space of 6N dimensions. The ideaof phase space is useful in CHAOS THEORY.See also attractor.

phase transition A change in a systemfrom one phase to another phase. Exam-ples of phase transitions including melting,freezing, boiling, sublimation, going froma ferromagnetic to a paramagnetic stateand going from a superconducting to anon-superconducting state. A phase transi-tion involves a change in the order in a sys-tem. Phase transitions can be describedtheoretically using techniques in statisticalmechanics.

phase velocity The velocity with whichthe phase in a traveling wave is propa-gated. It is equal to λ/T, where T is the pe-riod. Compare group velocity.

phasor /fay-zer/ A rotating vector used torepresent a sinusoidally varying quantity(e.g. an alternating current). The projec-tion of the vector on a fixed axis representsthe amplitude variation with time. A phaseangle between two quantities (e.g. currentand voltage) is represented by the angle be-tween their phasors.

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phi particle /fÿ/ See elementary particles.

phon /fon/ Symbol: p A unit for measur-ing the loudness of sounds on a sound-levelscale. Noises of the same intensity soundlouder or softer, depending on the fre-quency. The phon is defined using a stan-dard reference source of 1000 hertz, withwhich other sounds are compared. A loud-ness of n phons is the same as that of astandard source with an intensity of n deci-bels above the threshold of hearing, whichfor the average person is 2 × 10–5 pascal or0 decibels at 1000 hertz..

phonon /foh-non/ A quantized lattice vi-bration in a crystal. The concept ofphonons is essential in the quantum theoryof solids for analyzing thermal conductiv-ity, electrical conductivity, and supercon-ductivity. In electrical conductivity andsuperconductivity it is necessary to takeelectron–phonon interactions into account.

phosphor /fos-fer/ A substance thatshows luminescence or phosphorescence.

phosphorescence /fos-fŏ-ress-ĕns/ 1. Theabsorption of energy by molecules fol-lowed by emission of electromagnetic radi-ation. Phosphorescence is a type ofLUMINESCENCE, and is distinguished fromfluorescence by the fact that the emitted ra-diation continues for some time after thesource of excitation has been removed. Inphosphorescence the excited moleculeshave relatively long lifetimes before theymake transitions to lower energy states.However, there is no defined time distin-guishing phosphorescence from fluores-cence. The process by which moleculesreturn to the ground state in phosphores-cence is a different process from fluroes-cence and usually takes longer.2. In general usage the term is applied tothe emission of ‘cold light’ – light producedwithout a high temperature. The namecomes from the fact that white phosphorusglows slightly in the dark as a result of achemical reaction with oxygen. The lightcomes from excited atoms produced di-rectly in the reaction – not from the heatproduced. It is thus an example of chemi-

luminescence. There are also a number ofbiochemical examples (bioluminescence);for example, phosphorescence is some-times seen in the sea from marine organ-isms, or on rotting wood from certain fungi(known as ‘fox fire’).

phosphorus /fos-fŏ-rŭs/ A reactive solidnon-metallic element. There are three com-mon allotropes of phosphorus and severalother modifications of these, some ofwhich have indefinite structures.

Symbol: P; m.p. 44.1°C (white) 410°C(red under pressure); b.p. 280.5°C; r.d.1.82 (white) 2.2 (red) 2.69 (black) (all at20°C); p.n. 15; r.a.m. 30.973762.

phot /foht, fot/ A unit of illumination inthe c.g.s. system, equal to an illuminationof one lumen per square centimeter. It isequal to 104 lux.

photocathode /foh-toh-kath-ohd/ Acathode that emits electrons by the photo-electric effect.

photocell /foh-tŏ-sell/ Any device for pro-ducing an electric signal from electromag-netic radiation. Originally, photocells werephotoelectric cells – i.e. devices in which acurrent was produced between two elec-trodes by the photoelectric effect. The pre-sent common type depends onphotoconductivity. A piece of semiconduc-tor material is held between two contactsand a voltage applied. In the absence of ra-diation the current is very small; when ra-diation falls on the sample, its resistance isreduced and the current increases. Photo-conductive cells, unlike photoelectric cells,can be used in the infrared region. Othertypes of photocell are photodiodes or de-pend on the photovoltaic effect. See alsophotoelectric cell.

photoconductivity /foh-toh-kon-duk-tiv-ă-tee/ The increase of electrical conductiv-ity in certain materials, produced byincident electromagnetic radiation. Thephotons absorbed by the solid give up en-ergy to electrons, freeing them and thus in-creasing the number of electrons in theconduction band. See energy bands.

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photodiode /foh-toh-dÿ-ohd/ A semicon-ductor diode that is sensitive to electro-magnetic radiation. The p-n junction isreverse biased. When radiation falls on it,electron-hole pairs are created. Some ofthese additional charge carriers are imme-diately swept across the junction beforethey recombine, constituting a current thatdepends on the illumination. See also pho-totransistor.

photodisintegration /foh-toh-dis-in-tĕ-gray-shŏn/ The ejection of particles fromatomic nuclei on absorption of electromag-netic radiation. Most commonly a neutronis ejected.

photoelasticity /foh-toh-ĕ-las-tis-ă-tee/The double refraction observed in certainmaterials only when stressed. A number ofsynthetic materials are photoelastic, exam-ples being Perspex and Cellophane. Polar-ized white light passed through a stressedsample shows colored fringes relating tothe stress pattern. This is a very useful en-gineering test technique. Glass also showsinterference fringes and the method is usedfor locating strains in glass laboratory ap-paratus.

photoelectric cell /foh-toh-i-lek-trik / Adevice in which an electric current is pro-duced by electromagnetic radiation (visibleor ultraviolet) by the photoelectric effect. Alight-sensitive cathode (photocathode) andan anode are placed in an evacuated glassenvelope. The photosurface contains mat-erial with low work function (e.g. potas-sium or cesium) and emits electrons whenirradiated. A positive potential on theanode causes a current to flow between theelectrodes and in an external circuit. Thedevice used to be called a PHOTOCELL. Inmost applications it has been supersededby the photoconductive cell.

photoelectric effect The ejection of elec-trons from the surface of substances by ul-traviolet radiation (or occasionally light oreven infrared), or from atoms within a sub-stance by x- or gamma radiation. The num-ber of electrons emitted is proportional tothe intensity of radiation at a given fre-

quency. There is normally no emissionbelow a certain threshold, and above thisthe amount depends in a complicated wayupon frequency. The maximum kinetic en-ergy (W) of the ejected electrons is given byEinstein’s equation: W = hν – φ where h isthe Planck constant and φ is the minimumenergy required to remove an electron. Inthe case of the emission of valence elec-trons from solids and liquids by optical ra-diations φ is called the work function. Forthe removal of electrons from individualatoms by high quantum energy radiationsφ is the binding energy of the electron. Thethreshold frequency ν0 is given by: hν0 = φ.

For ultraviolet and visible light, only avery small proportion of the incident radi-ation causes photoelectric emission. For x-rays the probability of the effect isproportional to the fourth power of theproton number, hence the use of lead (Z =82) in shielding.

Einstein (1905) proposed his equationas an example of the concept that electro-magnetic radiation interacts with matter asquanta (photons) with energy hν. At nor-mal intensities one photon ejects an elec-tron. It is now possible to eject electrons byradiation with quantum energy far belowν0 using the great intensities obtainable byfocusing laser radiation. In this case onemay suppose that many photons interactwith one electron. See duality; photoion-ization; quantum theory.

photoelectricity /foh-toh-i-lek-tris-ă-tee/A group of phenomena in which electric ef-fects are produced by electromagnetic radi-

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frequency νν00

Wm

threshold frequency

maximumphotoelectron

energy

Photoelectric effect

ation. See photoconductivity; photoelectriceffect; photoionization; photovoltaic ef-fect.

photoelectron /foh-toh-i-lek-tron/ Anelectron ejected from a solid, liquid, or gasby the photoelectric effect or by photoion-ization.

photoemission /foh-toh-i-mish-ŏn/ Theemission of photoelectrons by the photo-electric effect or by photoionization.

photography The production of a per-manent record of an image on suitablepaper or film. Normally the image is pro-duced by the optical system of some type ofcamera on the light-sensitive surface of anemulsion. This is usually a layer of gelatinecontaining grains of silver bromide coatedon a sheet of glass, paper, or plastic. Expo-sure to radiation releases minute quantitiesof silver in some of the grains forming a la-tent image. The material is placed in a de-veloper, that is a solution containing aweak reducing agent. The silver of the la-tent image acts as a catalyst, promoting thereduction of the grains to particles of silver.The remaining silver salt is then dissolvedby a fixing solution and the material iswashed and dried giving the permanentphotograph.

Photographic emulsions are ‘sensitive’to electromagnetic radiations of wave-lengths less than around 1.5 micrometers.They are also sensitive to other energeticionizing radiations, and are important in x-ray investigations and in nuclear physics.Color photography involves mixing speci-fied dyes into the silver halide–gelatineemulsion.

photoionization /foh-toh-ÿ-ŏ-ni-zay-shŏn/ The ionization of atoms or mol-ecules by electromagnetic radiation.Photons absorbed by an atom may havesufficient photon energy to free an electronfrom its attraction by the nucleus. Theprocess is M + hν → M+ + e–. As in the pho-toelectric effect, the radiation must have acertain minimum threshold frequency. Theenergy of the photoelectrons ejected isgiven by W = hν – I, where I is the ioniza-

tion potential of the atom or molecule. Seephotoelectric effect.

photoluminescence /foh-toh-loo-mă-ness-ĕns/ See luminescence.

photometer /foh-tom-ĕ-ter/ An instru-ment for determining illumination or lumi-nous intensity by comparisons made withthe eye. There are various types. The gen-eral principle is to compare a source with astandard source. The two sources each illu-minate a screen, and the positions of thesources are adjusted until both give equalillumination. The illumination (E) is re-lated to luminous intensity by E = (Icosi)/d2, where I is the luminous intensity,d the distance from the source to surface,and i the angle of incidence.

photometry /foh-tom-ĕ-tree/ The branchof physics concerned with measuring inten-sity, illumination, etc., for visual radiation.

There are two basic types of measure-ment. ‘Luminous’ quantities, such as lumi-nous flux, luminous intensity, andillumination, are based on measurementsmade with the eye (e.g. by comparing theillumination of two surfaces). They thusdepend on the sensitivity of the eye to dif-ferent wavelengths. ‘Radiant’ quantities(e.g. radiant flux, radiance, and irradiance)depend on absolute measures of energyflow made by photocells. See also Lam-bert’s law.

photomultiplier /foh-toh-mul-tă-plÿ-er/A device in which electrons originally emit-ted from a photocathode initiate a cascadeof electrons by secondary emission in anelectron multiplier. It is much more sensi-tive as a radiation detector than a singlephotoelectric cell. See also photoelectriccell.

photon /foh-ton/ See duality.

photonics /foh-tonn-niks/ The study anddevelopment of devices that use lightrather than electrons in circuits. An exam-ple is the use of light transmission throughoptical fibers in telecommunications.

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photopic vision /foh-top-ik/ Vision atnormal levels of light intensity (as in nor-mal daylight). Under such conditions thecones in the retina are the main receptors.Compare scotopic vision.

photosphere /foh-tŏ-sfeer/ The visiblesurface layer of a star. In the Sun this layerconsists of gas at an average temperature ofabout 5750 K. It extends this layer for afew hundred kilometres from the surfaceand radiates a continuous spectrum.

phototransistor /foh-toh-tran-zis-ter/ Atransistor that is sensitive to electromag-netic radiation. When radiation falls on theemitter part of the device, more charge car-riers are produced in the base region andthe collector current increases. A photo-transistor acts like a photodiode with anamplifier. See also photodiode.

photovoltaic effect /foh-toh-vol-tay-ik/The effect in which irradiation of a p-njunction or the junction of a metal and aSEMICONDUCTOR by electromagnetic radia-tion (ultraviolet to infrared) generates ane.m.f., which can be used to deliver powerto an external circuit. A solar cell consistsof such a p-n junction.

physical change A reversible change in asubstance’s properties (such as melting), asopposed to a chemical change, which re-sults in a change in composition that is dif-ficult to reverse.

physical constants See fundamental con-stants.

physical optics See optics.

physisorption /fiz-ă-sorp-shŏn, -zorp-/See adsorption.

pico- /pÿ-koh/ Symbol: p A prefix denot-ing 10–12. For example, 1 picofarad (pF) =10–12 farad (F).

piezoelectric effect /pee-ay-zoh-i-lek-trik,pÿ-ee-zoh-/ The generation of a small po-tential difference across certain materialswhen they are subjected to a stress. The ef-

fect is used in devices for pressure and vi-bration measurement, in gas lighters, incrystal microphones, in strain gauges, andin oscillators. Compare magnetostriction.

pi-meson See pion.

pin-hole camera A box into which lightcan enter only through a very small hole.Because light rays travel in straight lines ina given medium (air in this case), an in-verted image is formed on the wall of thebox opposite the pin hole. The wall maycarry a photographic plate, or be made ofa diffusing material such as tissue paper orground glass.

Because the hole is small, the image isvery faint – a long exposure is needed tomake a photograph. However the image isin sharp focus, whatever the distance of theobject. This is because the rays passthrough the hole without deviation. Unlikethe lens of a lens camera, the pin hole givesno image aberrations. If the hole is madelarger, the image becomes brighter – butmore blurred. A large hole can be thoughtof as a set of pin-holes – each pin hole givesa faint image, but the images are in slightlydifferent positions.

pink noise See noise.

pion /pÿ-on/ (pi-meson) A type of MESON.There are three types of pion, having posi-tive, negative, or zero charge. The chargedpions have rest energy 139.6 MeV andmean life 2.6 × 10–8 s. Each decays to givea muon and a neutrino. The neutral pionhas a rest energy 135 MeV and has meanlife 8 × 10–17 s. It decays by emitting elec-tromagnetic radiation. Pions are stronglyinteracting bosons with zero spin. See alsoelementary particle.

pitch The sensation that a sound producesin a listener as a result of its frequency(though other factors are involved). High-pitched notes are high-frequency vibra-tions and low-pitched notes arelow-frequency vibrations.

Pitot tube /pee-toh/ A double tube placedwith one end in a stream of fluid, parallel

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to the flow, to measure fluid pressure. Ithas two openings. One is usually at theside, in the outer section of a double-walledtube, and measures static pressure, p. Theother, in the inner section, faces the fluidflow and registers the total pressure (thesum of p and dynamic pressure). The otherends are connected to pressure-measuringdevices. Pitot tubes can be used to measurefluid velocity. The tube is named for theFrench physicist Henri Pitot (1695–1771).See Bernoulli effect.

Planck constant /plank/ Symbol: h Afundamental constant; the ratio of the en-ergy (W) carried by a photon to its fre-quency (v). A basic relationship in thequantum theory of radiation is W = hv.The value of h is 6.626 069 3 × 10–34 joulesecond. The Planck constant appears inmany relationships in which some observ-able measurement is quantized (i.e. cantake only specific separate values ratherthan any of a range of values). The con-stant is named for the German physicistMax Planck (1858–1947).

Planck’s formula See Planck’s radiationlaw.

Planck’s radiation law The energy radi-ated per unit area per unit time per unitwavelength range at wavelength λ from ablack body at kelvin temperature T is givenby

Eλ = 2πhc2λ–5/[exp (hc/λkT) – 1]where h is the Planck constant, k the Boltz-mann constant and c the speed of light in avacuum.

This law was first proposed by Planck(1900). The problem of the energy distrib-ution in black-body radiation had beenstudied for many years. The physical sys-tem considered is of extreme simplicity,and the failure of the existing statisticalsystem of Maxwell and Boltzmann to solvethe problem was rightly considered to bevery significant (see ultraviolet catastro-phe). Planck deduced his equation by as-suming that electromagnetic radiation wasnot emitted and absorbed continuously aspreviously supposed but in quanta of en-ergy hc/λ.

Planck’s formula was found to be ingood agreement with experiment and itpermitted the first reasonably accuratemeasurement of the Boltzmann constant,and hence of related quantities such as thecharge of the electron and the masses ofatoms. Little progress however was madewith developing the ideas until Einstein(1905) argued that the quantum hypothe-sis would explain the photoelectric effectand Stokes’ law of fluorescence, and laterproposed other applications. This work ledeventually to the development of quantummechanics.

See Bose–Einstein statistics.

plane of polarization For historical rea-sons, this is defined as the plane containingincident and reflected rays in cases of po-larization by reflection. It is therefore theplane containing the magnetic vector B,rather than the electric vector E.

plane polarization A type of POLARIZA-TION of electromagnetic radiation, nor-mally described with reference to a ray. Inplane-polarized radiation, the magnetic os-cillations are all parallel and occur in oneplane containing the ray. The electric oscil-lations are all parallel and occur in a planecontaining the ray and at right angles to theplane containing the magnetic oscillations.The electric and magnetic fields are bothperpendicular to the direction of propaga-tion. Plane polarization can be producedby reflection or by transmission through aNicol prism or Polaroid. See also circularpolarization.

planetoid See minor planet.

plano-concave lens /play-noh-kon-kayv/A diverging LENS with one plane face andonce concave face.

plano-convex lens /play-noh-kon-veks/A converging LENS with one plane face andone convex face.

plasma /plaz-mă/ A mixture of free elec-trons and ions or atomic nuclei. Plasmasoccur in thermonuclear reactions, as in theSun. The glowing region of ions and elec-

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trons in a discharge tube is also a plasma.Sometimes plasmas are referred to as afourth state of matter.

plasticity /plas-tis-ă-tee/ The tendency ofa material to suffer a permanent deforma-tion; i.e. not to return to its original di-mensions after a deforming stress has beenremoved. An elastic material becomes plas-tic above its yield point. See elasticity.

platinum /plat-ă-nŭm/ A silvery-whitemalleable ductile transition metal. It occursnaturally either free or in association withother platinum metals. Platinum is used asa catalyst for ammonia oxidation (to makenitric acid) and in catalytic converters. It isalso used in jewelry.

Symbol: Pt; m.p. 1772°C; b.p. 3830 ±100°C; r.d. 21.45 (20°C); p.n. 78; r.a.m.195.08.

platinum black A finely divided blackform of platinum produced, as a coating,by evaporating platinum onto a surface inan inert atmosphere. Platinum-black coat-ings are used as pure absorbent electrodecoatings in experiments on electric cells.They are also used, like carbon-black coat-ings, to improve the ability of a surface toabsorb radiation.

plutonium /ploo-toh-nee-ŭm/ A radioac-tive silvery element of the actinoid series ofmetals. It is a transuranic element found onEarth only in minute quantities in uraniumores but readily obtained, as 239Pu, by neu-tron bombardment of natural uranium.The readily fissionable 239Pu is a major nu-clear fuel and nuclear explosive. Plutoniumis highly toxic because of its radioactivity;in the body it accumulates in bone.

Symbol: Pu; m.p. 641°C; b.p. 3232°C;r.d. 19.84 (25°C); p.n. 94; most stable iso-tope 244Pu (half-life 8.2 × 107 years).

p-n-p transistor See transistor.

point defect See defect.

point source A source of exactly spheri-cal wave fronts. All sources can be consid-ered to be point-like if viewed from a large

enought distance. The stars provide an ob-vious example.

In a number of practical situations,sources that are effectively point sourcesare required. Normally a small hole in anotherwise opaque illuminated surface isused. Holes can be made as small as 100µm; the main problem is to arrange ade-quate illumination of the hole by the realsource.

poise Symbol: P A c.g.s. unit of dynamicviscosity. It is equal to 0.1 pascal second. Itis named for the French physician andphysicist Jean Léonard Marie Poiseuille(1797–1869).

Poiseuille’s formula /poi-zew-eelz, pwa-ză-eelz/ (Hagen’s formula) An equationthat describes the laminar flow of liquidthrough a pipe. The volume flow per sec-ond in a circular pipe of radius r and lengthl is given by:

πr4∆p/8ηlwhere ∆p is the fluid pressure differenceand η is its viscosity. It is named forPoiseuille (see poise) and for the Germanphysicist Gotthilf Heinrich Ludwig Hagen(1797–1884).

Poisson equation /pwass-awn/ The fun-damental equation of POTENTIAL THEORY.In the case of electrostatics it states that∇2V = ρ/ε, where ∇2 is the Laplacian oper-ator, V is the electric potential, ρ is the elec-tric charge density, and ε is the electricpermittivity. There is an analogous equa-tion in the case of the gravitational poten-tial. When the right hand of the Poissonequation is zero the Poisson equation be-comes the LAPLACE EQUATION. The equationwas first put forward by the French math-ematician and physicist Siméon-DenisPoisson in 1813.

Poisson ratio Symbol: v A measure ofhow a material changes shape when it isstretched. It is equal to minus the fractionalchange in cross-sectional area (∆a/a) di-vided by the fractional change in length(∆l/l). For many solids, including manymetals, the value is about 0.3. It cannot ex-ceed 0.5 for any material. The ratio is

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named for the French mathematician andphysicist Siméon-Denis Poisson (1781–1840).

Poisson’s spot A bright spot observed inthe middle of the shadow of a circularopaque obstacle. This spot was shown tobe a consequence of the wave theory oflight by Siméon-Denis Poisson in 1818. Itwas discovered experimentally by his col-league Dominique François Jean Arago(and is sometimes known as Arago’s spot).

polar coordinates A method of definingthe position of a point by its distance anddirection from a fixed reference point(pole). The direction is given as the anglebetween the line from the origin to thepoint, and a fixed line (axis). On a flat sur-face only one angle, θ, and the radius, r, areneeded to specify each point. For example,if the axis is horizontal, the point (r,θ) =(1,π/2) is the point one unit length awayfrom the origin in the perpendicular direc-tion. Conventionally, angles are taken aspositive in the anticlockwise sense.

In a rectangular Cartesian coordinatesystem with the same origin and the x-axisat θ = 0, the x- and y-coordinates of thepoint (r,θ) are

x = rcosθy = rsinθ

Converselyr = √(x2 + y2)

andθ = tan–1(y/x)

In three dimensions, two forms of polarcoordinate systems can be used. See cylin-drical polar coordinates; spherical polarcoordinates. See also Cartesian coordi-nates.

polarimeter /poh-lă-rim-ĕ-ter/ (saccha-rimeter) A device for measuring the angleof rotation of a plane-polarized beamcaused by an optically active sample. Typ-ically, light from a source is passed througha Nicol prism (the polarizer) to plane-po-larize it, then through the sample. Theamount of rotation is measured by a sec-ond prism (the analyzer), which can beturned on an angular scale. The position ofminimum transmission is observed. As this

angle depends, among other things, on theconcentration of an active solute, po-larimeters are used to measure this. Seealso optical activity.

polarization /poh-lă-ri-zay-shŏn/ Restric-tion of the vibrations in a transverse wave.Normally in a transverse wave the vibra-tions can have any direction in the planeperpendicular to the direction of propaga-tion. If the directions of the vibrations arerestricted in any way the radiation is saidto be polarized. The simplest case is that ofPLANE POLARIZATION. In a plane-polarizedtransverse acoustic wave in a solid, all thevibrations are parallel to each other. Inplane-polarized electromagnetic radiation,all the electric oscillations are parallel toeach other and at right angles to the mag-netic oscillations.

Light can be plane-polarized by reflec-tion or on passing through certain sub-stances (e.g. Polaroid). Light polarized in acertain plane by passing through one po-larizer is totally absorbed by a second po-larizer set to polarize at right angles.Electromagnetic waves such as light andthose of shorter wavelength generally in-teract with matter by means of their elec-tric fields (although energy is transferredequally by both). Thus, for example, thedirections in which photoelectrons areejected may depend upon the plane of po-larization.

Radio waves are normally emittedplane-polarized. Thus if the electric vibra-tions are vertical a rod-shaped antenna,which responds to these vibrations, mustbe set vertically to detect them. An antennaconsisting of a coil with ferrite core willhave to be set so that the magnetic vibra-tions are perpendicular to its plane.

See also circular polarization; ellipticalpolarization; birefringent crystal; Nicolprism; optical activity; plane of polariza-tion.

polarization, angle of See Brewsterangle.

polarization, electric The separation ofthe charges in the molecules of an insulatoras an effect of an electric field. One face of

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an insulator in a field gains a net positivecharge with the other becoming negative.

polarization, electrolytic Changes in thecharacteristics of a voltaic cell when it pro-duces large currents. Generally the e.m.f. isreduced while the internal resistance mayincrease (or in certain cases, decrease). Inextreme cases a layer of bubbles of hydro-gen may form on the cathode. Many cellscontain a depolarizer such as man-ganese(IV) oxide to reduce this effect. Po-larization usually disappears on resting thecell.

polarized light See polarization.

polarizer /poh-lă-rÿ-zer/ A device orarrangement producing plane-polarized ra-diation from incident unpolarized radia-tion. A Nicol prism or Polaroid sheets arenormally used.

polarizing angle See Brewster angle.

Polaroid (Trademark) A synthetic doublyrefracting substance, that strongly absorbspolarized light in one plane, while easilypassing polarized light in another plane atright angles. Unpolarized light passedthrough a sheet of Polaroid is plane-polar-ized. Spectacle lenses made of this materialnormally absorb light vibrating horizon-tally – as produced by reflection from hor-izontal surfaces. They thus reduce reflectedglare.

The first type was announced by Landin 1934. The modern form is made from aplastic sheet, highly strained to align themolecules and make it birefringent, thenstained with iodine to make it dichroic.

pole (optical center; optic center) The geo-metric center of a surface or lens. In ray di-agrams rays can be drawn undeviatedthrough the pole of a LENS. At the pole of aMIRROR the incident and reflected raysmake equal angles with the principal axis.All distances from a refracting surface, re-flector, or lens – object and image dis-tances, focal distances, radii of curvature,etc. – are measured from the pole.

poles, magnetic The regions of a mag-netic field where the forces appearstrongest. Thus, in a bar magnet, the linesof force appear to diverge from and con-verge to two small regions near the ends,these being the poles of the magnet. Theconcept of magnetic ‘pole’, however, hasno more reality than that of ‘regions in thefield’, as in the first sentence above.

A north-seeking pole (north pole or N-pole) is attracted approximately in the di-rection of geographical North; asouth-seeking pole (south pole or S-pole)tends to move toward geographical South.Magnetic poles can be found only in oppo-site (unlike) pairs. The Earth’s magneticpoles – regions where the Earth’s field isstrongest – are close to the geographicalpoles.

pole strength The force exerted by agiven magnetic pole when it is one meterfrom a unit pole in a vacuum. A unit poleis defined as that pole which, when placedone meter from a similar pole in a vacuum,exerts a force of one newton. It is equal to125.663 7 microweber (µWb). See alsopoles, magnetic.

polonium /pŏ-loh-nee-ŭm/ A radioactivemetallic element belonging to group 16 ofthe periodic table. It occurs in very minutequantities in uranium ores. Over 30 ra-dioisotopes are known, nearly all alpha-particle emitters. Polonium is a volatilemetal and evaporates with time. It is alsostrongly radioactive; a quantity of polo-nium quickly reaches a tempertaure of afew hundred degrees C because of thealpha emission. For this reason it has beenused as a lightweight heat supply in spacesatellites.

polarization, electrolytic

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P P

P= pole, or optic center

Pole of a lens

Symbol: Po; m.p. 254°C; b.p. 962°C;r.d. 9.32 (20°C); p.n. 84; stablest isotope209Po (half-life 102 years).

polyatomic /pol-ee-ă-tom-ik/ Describinga molecule that consists of several atoms(three or more). Examples are benzene(C6H6) and methane (CH4).

polychromatic radiation /pol-ee-krŏ-mat-ik/ Electromagnetic radiation that hasa mixture of different wavelengths. Com-pare monochromatic radiation.

polygon of vectors A closed polygonthat represents a set of vectors in equilib-rium. Each vector is represented, both insize and direction, by an arrow, with thearrows being arranged head to tail. If thearrows did not close to form a completepolygon then there would be a net forceand the forces would not be in equilibrium.The TRIANGLE OF VECTORS is a special case.

polymer A compound consisting of largemolecules in which basic molecular unitsare repeated. A common example is thesynthetic plastic polythene, which is apolymer of the compound ethylene (CH2 =CH2). Many similar synthetic polymershave been produced, but natural polymersare of fundamental importance in bio-chemistry. In physics, the physical proper-ties of polymers can be analyzedtheoretically using the methods of statisti-cal mechanics.

population inversion See laser.

positive See charge.

positive column A luminous area in anelectrical discharge in a gas, occurring nearthe positive electrode.

positive feedback See feedback.

positive lens A lens with a positivepower. See converging lens.

positive mirror A curved mirror with apositive power. See converging mirror.

positive pole A magnetic N-pole. Seepole.

positive rays Streams of positive ions inan electrical discharge.

positron /poz-ă-tron/ The antiparticle ofthe electron; a particle with the same massas the electron but with a positive charge.Positrons are found in cosmic-ray showers,where they result from pair production.They are also produced by a type of betadecay. They are annihilated when they en-counter an electron, so have a short sepa-rate existence. Positrons can be detected bytheir tracks in cloud or bubble chambers,where they show the opposite deflection toelectrons in a magnetic field. See elemen-tary particles.

positronium /poz-ă-troh-nee-ŭm/ A fleet-ing combination of an electron and apositron to form an analog to a hydrogenatom. When the two particles have theirspins parallel the half-life is about 1.5 ×10–7 s; when they are antiparallel the half-life is shortened to 10–10 s. A positronium‘atom’ decays to form two photons by an-nihilation. A combination of two electronsand two positrons also appears to exist,and is known as a positronium ‘molecule’,analogous to a hydrogen molecule.

Post Office box A box containing resis-tances that can be switched into the circuit,suitable for use as a WHEATSTONE BRIDGE orpotentiometer.

potassium /pŏ-tass-ee-ŭm/ A soft reactivemetal. The atom has the argon electronicconfiguration plus an outer 4s1 electron.

Symbol: K; m.p. 63.65°C; b.p. 774°C;r.d. 0.862 (20°C); p.n. 19; r.a.m. 39.0983.

potassium–argon dating A method ofradioactive dating used for estimating theage of certain rocks. It is based on thedecay of 40K to 40Ar (half-life 1.28 × 109

years). The technique is useful for time pe-riods from 105 years ago back to the age ofthe Earth (4.6 × 109 years).

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potassium–argon dating

potential difference (p.d.) Symbol: VThe difference in electric potential betweentwo points; the work done per unit chargewhen a charge is displaced between thepoints, by any path. The SI unit is the volt.In a vacuum, the total energy of the chargeis constant; the change in potential energyis balanced by change of kinetic energy. Ina material the average kinetic energy of thedisplaced charges remains constant, be-cause of resistance, and energy is dissi-pated. Potential difference can also beexpressed as power divided by current. Seealso electromotive force.

potential divider See voltage divider.

potential energy Symbol: V The work anobject can do because of its position orstate. There are many examples. The workan object at height can do in falling is itsgravitational potential energy. The ENERGY

‘stored’ in elastic or a spring under tensionor compression is elastic potential energy.Potential difference in electricity is a simi-lar concept, and so on. In practice the po-tential energy of a system is the energyinvolved in bringing it to its current statefrom some reference state, or vice versa.

potential theory The theory of physicalfields, such as electric, gravitational, andmagnetic fields, in terms of the potentialsof these fields. In the cases of electric andgravitational fields, the potentials are de-scribed by the POISSON EQUATION and theLAPLACE EQUATION.

potentiometer /pŏ-ten-shee-om-ĕ-ter/ Aninstrument for measuring electrical poten-tial difference by balancing two opposingpotentials, so that no current flowsthrough a galvanometer. In a simple forma battery maintains a steady current in auniform resistance wire. A sliding contactconnected with a standard cell (as shown inthe diagram) is moved until the gal-vanometer is undeflected, the contact beingat distance Ls from the left-hand end. Theunknown p.d. V now replaces the standardcell, and the new distance Lv for zero cur-rent is found. Then V = ELv/Ls; where E isthe e.m.f. of the standard cell.

In more accurate instruments the resis-tance wire is replaced by a series of high-grade resistors. The instrument is thencapable of extremely high precision. Oneadditional advantage is that it draws verylittle current from the system under test. (Ifa galvanometer is not sensitive enough anelectrometer is used.)

Current can also be measured by find-ing the p.d. across a standard resistance.Also resistances can be compared by mea-suring the potential differences across themwhen connected in series.

pound 1. An f.p.s. unit of weight or massin the avoirdupois system, subdivided into16 ounces and equal to 0.453 592 37 kg inSI units.2. An f.p.s. unit of weight or mass in thetroy system, subdivided into 12 ounces andequal to 0.373 241 72 kg in SI units.

poundal Symbol: pdl The unit of force inthe f.p.s. system. It is equal to 0.138 255 N.

pound force Symbol: lbf An f.p.s. unit ofgravitational force, equal to the force ex-erted on a one-pound mass by gravity atsea level. It is equal to 9.806 65 meters persecond squared or, in SI derived units, to4.448 222 newtons.

power (focal power) Symbol: P A mea-sure of the ability of a lens or mirror toconverge a parallel beam, given by the rec-iprocal of the focal distance f.

potential difference

194

••

••

batterymeter bridge

mm scale

uniformresistancewire

variablepoints

standardcell

+ –

G

unknown p.d.

Potentiometer

P = 1/fGenerally, f is in meters in which case P isin DIOPTERS (D).

Strictly, power measures the ability of areflecting or refracting surface, or of a lens,to change the curvature of incident wavefronts..

power Symbol: P The rate of energytransfer (or work done) by or to a system.The unit of power is the watt – the energytransfer in joules per second. In an electri-cal system power is given by VI, where V isthe potential difference across a conductorand I the current through it. If V and I arenot in phase the power absorbed is IVcosφ,where φ, the phase angle, is known as the‘power factor’.

Poynting vector Symbol: S The vectorproduct of the electric field vector E andthe magnetic field vector H (= B0/µ0) in anelectromagnetic wave. The Poynting vectorgives, in magnitude and direction, thepower radiated through unit area at any in-stant. The unit is the watt per square meter.In a simple harmonic wave, the averagevalue is ½E0H0, where E0 and H0 are theamplitudes. The vector is named for theBritish physicist John Henry Poynting(1852–1914).

praseodymium /pray-zee-oh-dim-ee-ŭm/A soft ductile malleable silvery element ofthe lanthanoid series of metals. It occurs inassociation with other lanthanoids. Pra-seodymium is used in several alloys, as acatalyst, and in enamel and yellow glass foreye protection.

Symbol: Pr; m.p. 931°C; b.p. 3512°C;r.d. 6.773 (20°C); p.n. 59; r.a.m. 140.91.

precession /pri-sesh-ŏn/ If a body is spin-ning on an axis, the axis of rotation can it-self move around another axis at an angleto it. This occurs when a couple is appliedabout an axis which is always perpendicu-lar to the axis of rotation. For gyroscopesand tops this couple is caused by gravityand the support force. The gravitationalfields of the Moon and Sun acting on theequatorial bulge of the Earth causes theprecession of the equinoxes, that is the axis

of rotation of the Earth sweeps out a conewith semi-angle 23½° in a period of 26 000years. Similarly the planes of the orbits ofplanets and satellites precess. A normal tothe plane of the orbit of the Moon sweepsout a cone of semi-angle 5° and period 18.6years, causing the sequence of eclipses.

presbyopia /prez-bee-oh-pee-ă/ The nor-mal development with age of far sighted-ness. The distance to the eye’s near pointincreases as the eye’s ability to accommo-date is reduced (the lens becomes morerigid with age). See near point.

pressure Symbol: p A quantity that ex-presses the condition of a fluid such that itexerts a perpendicular force on any surfacein contact with it: pressure = force/area.Gases can only exert repulsive forces sotheir pressure is always positive. Liquidsalso normally have positive pressure, but insome circumstances liquids free from dis-solved gas can sustain a tension, that is anegative pressure. The SI unit of pressure isthe pascal.

Uniform isotropic solids within fluidsare compressed uniformly (without distor-tion) so the concept of pressure can be ex-tended to them. More usually, especiallywhen solids interact with each other, thebodies are distorted by uneven systems offorces. There is then a STRESS, which is dis-tinct from fluid pressure. When the pres-sure on a body is increased the distancesbetween the molecules all decrease in thesame proportion, whereas for stresses insolids, different separations change differ-ently. For example, when a heel thrustsdownward upon a floor the moleculesmove closer together in the vertical direc-tion and farther apart horizontally.Around the edge of the heel the floor mate-rial is in tension; it is here that damage isusually done. Similarly, the human body isinsensitive to changes in fluid pressure yetdetects slight local stresses caused by gentlecontact with a solid.

On going downward in a fluid the pres-sure increases by an amount equal to: in-crease in depth × mean density × g. Thedensity of a liquid can usually be assumedto be constant, but for gases it is necessary

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pressure

to integrate. At uniform temperature thisgives an exponential variation of pressurewith depth.

See also gas laws; pressure of the at-mosphere; upthrust.

pressure broadening The increase in thewidth of a spectral line resulting from col-lisions between atoms or molecules. It re-lates to pressure, as there are morecollisions at high pressure. See monochro-matic radiation.

pressure gauge An instrument for mea-suring fluid pressure, such as a BAROMETER

or MANOMETER. See Bourdon gauge.

pressure of the atmosphere The pres-sure at a point near the Earth’s surface dueto the weight of air above that point. Itsvalue varies around about 100 kPa(100 000 newtons per square meter).Barometers are used to measure atmos-pheric pressure, which is important be-cause the small changes relate to imminentweather changes.

Because the pressure at depth in a fluiddepends on depth, barometers can be usedas altimeters; they can be marked to indi-cate distance above or below sea level.

pressurized-water reactor (PWR) A nu-clear reactor in which water, used as mod-erator, coolant, and reflector, is kept underpressure to prevent it from boiling at theoperating temperature. The hot water isused to raise steam in a heat exchanger tooperate a steam turbine. This is by far themost common form of reactor used forelectricity generation and for nuclear sub-marines. The fuel is enriched, typicallycontaining a few percent of uranium–235in the form of UO2. Compare boiling-water reactor.

Prévost’s theory of exchanges /pray-vosts/ The theory that all bodies emit andabsorb radiation continuously. The rate ofemission depends on the body’s surfaceand its temperature. The rate of absorptiondepends on the surface and the tempera-ture of the surroundings. If there is noother process of energy transfer and the

temperature of the surroundings is uniformand constant, the body will eventually at-tain the same temperature as that of thesurroundings. The rates of emission andabsorption of radiation must then beequal. This shows that the absorptance ofa surface equals its emissivity. The theory isnamed for the Swiss physicist PierrePrévost (1751–1839). See also black body;Kirchhoff’s law of radiation.

primary cell A voltaic cell in which thechemical reaction that produces the e.m.f.is not reversible. This is not the case with asecondary cell (accumulator).

primary colors A set of three coloredlights (hues) that when mixed together inthe right proportions, give the sensation ofwhite. Normally the hues are chosen fromthe red, green, and blue regions.

An infinite number of sets of primaryhues exists. The standard choice is one ofconvenience. According to the trichromatictheory of color, any set of three primarycolors has only one requirement – no oneof them can be matched by mixing theother two. See also color.

primary winding See transformer (volt-age).

principal axis (axis) The line joining thecenters of curvature of the faces of a LENS,or the line normal to a reflector at the pole.See also mirror.

principal focus See focal point.

principal plane The plane perpendicularto the principal axis of a lens centered onthe pole (optical center). The pole isequidistant between the principal focalpoints. This is strictly true only for a thinlens. A thick lens has two principal planes;each is centered on a principal point. Thefocal distance of a thick lens is the distancebetween each focal point and the principalplane on that side of the lens.

principal points Two points of a thicklens corresponding to the single pole (opti-

pressure broadening

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cal center) of a thin lens. See principalplane.

principle of least action A VARIATIONAL

PRINCIPLE regarded as the fundamentalprinciple underlying Newtonian mechan-ics, stating that the integral over time of the

kinetic energy minus the potential energy(the action) for a system is always less forthe actual motion of the system than forany other possible motion.

principle of moments When an object orsystem is in equilibrium, the sum of themoments in any direction equals the sum ofthe moments in the opposite direction. Be-cause there is no resultant turning force,the moments of the forces can be measuredrelative to any point in the system or out-side it.

principle of superposition When two(or more) waves of the same type passthrough the same region, the amplitude ofvibration at any point is the algebraic sumof the individual amplitudes. Sign (crest ortrough, i.e. positive or negative) must betaken into account. The waves emergefrom the region of superposition unaf-fected. See also interference.

printed circuit A circuit that is con-structed as an entity on an insulating board

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printed circuit

wave 1

wave 2

wave 3

resultant

t

t

t

t

y1

0

y2

0

y3

0

y

0

Principle of superposition

thick converginglens

firstprincipal plane

secondprincipal plane

F2HHH222H1

F1

F1 first focal pointF2 second focal pointH1 first principal pointH2 second principal pointF1H1 first focal distanceF2H2 second focal distance

Principal plane

without the need for connecting wires, theconnections being incorporated on the sur-face of the board as a conducting film. Theboard is first completely coated with a con-ductor film, usually copper. The circuit isthen ‘printed’ on the board by a photo-graphic process that superimposes anotherfilm, this time of protective material in apredetermined pattern. The exposed con-ducting film is then removed by etching,and the remainder acts as a network ofconductors between components or ICsbuilt into the circuit.

Boards are often printed on both sides,and some have two or more conductinglayers, insulated from each other and sepa-rately etched. See also integrated circuit.

prism, optical An important componentof many optical systems: a block (usuallyof glass for work with visible radiation)with two nonparallel sides. Prisms areoften triangular in section. Prism action de-pends on two successive refractions, eachwith DEVIATION (bending) in the same di-rection. This is effective, for instance, inspreading different wavelengths into aspectrum. Many prisms have been de-signed for special purposes for use in opti-cal instruments. See binoculars; erectingprism.

prism binoculars See binoculars.

progressive wave See wave.

projectile An object falling freely in agravitational field, having been projectedat a speed v and at an angle of elevation θto the horizontal. In the special case that θ= 90°, the motion is linear in the vertical di-rection. It may then be treated using theequations of motion. In all other cases thevertical and horizontal components of ve-locity must be treated separately. In the ab-sence of friction, the horizontal componentis constant and the vertical motion may betreated using the equations of motion. Thepath of the projectile is an arc of aparabola. Useful relations are:time to reach maximum height

t = vsinθ/gmaximum height

h = v2sin2θ/2ghorizontal range

R = v2sin2θ/gNote that similar treatment can be ap-

plied to the case of an electric charge pro-jected into an electric field. See also orbit.

projectors Optical arrangements able toproduce a large bright real image on ascreen.

There are two main types of projector –those in which light from the source ispassed through the object, and those inwhich the light is reflected by the object.The opaque projector (episcope) is themain example of the latter. The formertype, the diascope, includes the overheadprojector and slide and film projectors.

Light from the source, concentrated bya converging mirror, passes through theslide (or is reflected by the opaque object).A condenser (condensing lens) produces animage; the converging projection lensforms an image of this on the screen.

promethium /prŏ-mee-th’ee-ŭm/ A ra-dioactive element of the lanthanoid seriesof metals. It is not found naturally on Earthbut can be produced artificially by the fis-sion of uranium. It is used in some minia-ture batteries.

Symbol: Pm; m.p. 1168°C; b.p. 2730°C(approx.); r.d. 7.22 (20°C); p.n. 61; sta-blest isotope 145Pm (half-life 18 years).

proof plane A small shaped piece of foilwith an insulating handle, used (often withan electroscope) to investigate the distribu-tion of charge on the surface of an object.

propagation /prop-ă-gay-shŏn/ Thetransmission of energy in the form ofwaves, such as light, radio waves, andother forms of electromagnetic radiation,and sound.

proportional counter A counter for ion-izing radiation in which the potential dif-ference applied is high enough formultiplication of ions, so that the height ofthe pulse is proportional to the number ofions produced by the particle, and thus toits energy loss. A counter used in this way

prism, optical

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199

proportional counter

single fixed pulley

force ratio = F2 /F1 = T/T = 1distance ratio =1

single moving pulley

force ratio = F2 /F1 = 2T/T = 2distance ratio = 2

multiple moving pulleys (example)

force ratio = F2 /F1 = 2T /T /2 = 4distance ratio = 4

block and tackle (simplified example)

force ratio = F2 /F1 = 4T/T = 4distance ratio = 4

T

load F2T

effort F1

F1

F2

T

T

F2

F1

TT

T

T

T /2T /2

fixed block

tackle

moving block

F2

F1T

T T

T

Pulley

its energy loss. A counter used in this wayis said to be in the proportional region.

proportional limit See elasticity;Hooke’s law.

proportional region See proportionalcounter.

proton An ELEMENTARY PARTICLE with apositive charge (+1.602 192 × 10–19 C) andrest mass 1.672 614 × 10–27 kg. Protons arenucleons, found in all nuclides. They arefermions with spin ½ showing strong inter-actions. Protons are made up of more fun-damental particles called quarks.

proton number (atomic number) Sym-bol: Z The number of protons in the nu-cleus of an atom. The proton numberdetermines the chemical properties of theelement because the electron structure,which determines chemical bonding, de-pends on the electrostatic attraction to thepositively charged nucleus.

proton–proton chain reaction A seriesof nuclear fusion reactions by which hy-drogen is converted into helium. It isthought that the reactions are responsiblefor energy production in the Sun and simi-lar stars. There are in fact three possible se-quences. The main one is:

1H + 1H → 2H + ν + e+

2H + 1H → 3He + γ3He + 3He → 4He + 21H

The two other sequences lead to 4He also,through 7Li and 8Be. See also carbon cycle.

psi particle /sÿ, psÿ/ See elementary parti-cles.

p-type conductivity See semiconductor;transistor.

pulley A class of machine. In any pulleysystem power is transferred through thetension in a string wound over one or morewheels. The FORCE RATIO and DISTANCE

RATIO depend on the relative arrangementof strings and wheels. Efficiency is not usu-ally very high as work must be done toovercome friction in the strings and thewheel bearings, and to lift any movingwheels. There are two types of single pulleysystem and two types of multiple pulleysystem. In the diagram, T is string tension;in each case it is assumed that efficiency is100%.

pulsar /pul-sar/ An astronomical bodythat emits electromagnetic radiation in theform of highly regular pulses. Pulsars arethought to be rotating neutron stars. Thepulses are due to a ‘lighthouse-beam’ effectcaused by synchrotron radiation from elec-trons in the very strong magnetic field ofthe neutron star.

pulsatance /pul-să-tăns/ See angular fre-quency.

pulse generator See astable circuit.

pupil /pyoo-păl/ The aperture of the eye,adjustable in size by the circular iris mus-cle. The pupil appears black as very littleincident light is reflected by the retina.

pure note (pure tone) See note.

PWR See pressurized-water reactor.

pyrolysis /pÿ-rol-ă-sis, pi-/ The decompo-sition of chemical compounds by subject-ing them to very high temperature.

pyrometer /pÿ-rom-ĕ-ter, pi-/ A device formeasuring very high temperatures (aboveabout 1000°C) by the radiation emitted bythe body. There are two main types. Seeoptical pyrometer; total-radiation pyrome-ter.

pyrometry /pÿ-rom-ĕ-tree, pi-/ The mea-surement of high temperatures using py-rometers.

proportional limit

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QCD See quantum chromodynamics.

quality of sound (timbre) The character-istic of a musical note that is determined bythe frequencies present. It enables a listenerto tell the difference between two notes ofthe same fundamental frequency played ondifferent musical instruments. A pure tonehas no overtones present and its waveformis a sine wave. Musical instruments pro-duce notes that have more complex wave-forms, and it can be shown that these areformed by mixing a pure tone (the funda-mental) with different higher frequencies.These frequencies are simple multiples ofthe fundamental frequency (f); i.e. 2f, 3f,and so on. The fundamental together withthe ‘overtones’ are harmonics of the note;the different contributions characterize itsquality.

quantized /kwon-tÿzd/ A physical quan-tity is said to be quantized when it canchange only in definite steps – it does nothave a continuous range of values. To ex-plain the photoelectric effect, for instance,the energy of the electromagnetic radiationmust be quantized. Angular momentum isquantized in atoms and molecules.

quantum /kwon-tŭm/ (pl. quanta) A defi-nite amount of energy released or absorbedin a process. Energy often behaves as if itwere ‘quantized’ in this way. The quantumof electromagnetic radiation is the photon.See also photoelectric effect.

quantum chromodynamics (QCD) AQUANTUM FIELD THEORY that describes thestrong nuclear interactions. The basic enti-ties in QCD are QUARKS and GLUONS. QCDis mathematically much more complicatedthan quantum electrodynamics.

quantum computer A computer that de-pends on quantum mechanics in the logicof its processing. There has been a lot of in-terest in the idea that the indeterminacy in-herent in quantum mechanics could beexploited to increase computing power. Sofar, these ideas are mainly theoretical.

quantum electrodynamics The use ofquantum mechanics to describe how parti-cles and electromagnetic radiation interact.

quantum entanglement See Bell’s para-dox.

quantum field theory A FIELD theorythat also involves QUANTUM MECHANICS.All the non-gravitational interactions ofmatter can be described by quantum fieldtheories, and these are also in accord withspecial relativity theory. Quantum fieldtheory can also be used to analyze many-body problems in quantum mechanics. Atpresent, it does not appear to be possible tohave a quantum field theory that unifies allthe INTERACTIONS known in Nature.

quantum Hall effect A version of theHall effect found at low temperatures inwhich it is found that the coefficient of theHall effect is quantized. In the integerquantum Hall effect the coefficient is quan-tized in integers. This can be explained interms of non-interacting electrons. In thefractional quantum Hall effect, fractionalnumber quantization for the coefficientcan occur. This can be explained in termsof interactions between electrons.

quantum mechanics See quantum the-ory.

quantum number An integer or half in-

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quantum state

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teger that specifies the value of a quantizedphysical quantity (energy, angular momen-tum, etc.). See atom; Bohr theory; spin.

quantum state A state of a physical sys-tem, such as a crystal or an ATOM, specify-ing the condition of its constituent particlesand defined by a unique set of quantumnumbers. In the case of bosons any numberof identical particles can occupy a givenstate whereas for fermions (including elec-trons) a state cannot contain more thanone particle of a given type.

A particular quantum state under de-fined conditions has a certain energy, butthe energy may be changed by externalelectric or magnetic fields. A number ofstates may have the same energy. For ex-ample, an atom has two quantum stateswith principal quantum number n = 1. Thenumbers l and m are both zero, but the spinquantum number ms can be +½ or –½ cor-responding to opposite orientations of thespin axis. A hydrogen atom is said to be inthe ground state if either of these states isoccupied by its one electron. There is aminute difference in energy caused by theinteraction between the electron’s intrinsicmagnetic moment and that of the nucleus.A helium atom normally has both thesestates occupied. As the nucleus has no mag-netic moment these states have exactly thesame energy unless the atom is in a mag-netic field.

When atoms are combined in a struc-ture such as a molecule or a crystal eachquantum state of each atom becomes astate of the system. Normally the energiesassociated with the states of the system aredifferent from those of the separate atoms.See energy bands.

quantum theory A mathematical theoryoriginally introduced by Max Planck(1900) to explain the black-body radiationfrom hot bodies. Quantum theory is basedon the idea that energy (or certain otherphysical quantities) can be changed only incertain discrete amounts for a given sys-tem. Other early applications were the ex-planations of the photoelectric effect andthe Compton effect, and the Bohr theory ofthe atom.

Quantum mechanics is a system of me-chanics that developed from quantum the-ory and is used to explain the behavior ofatoms, molecules, etc. In one form it isbased on de Broglie’s idea that particles canhave wavelike properties – this branch ofquantum mechanics is called wave me-chanics.

quark A type of elementary particle that isthought to be one of the fundamentalbuilding blocks of matter. There are six fla-vors of quark, with there being two flavorsin each of the three generations of elemen-tary particles. The quarks in the first gen-eration are called the up quark and thedown quark. Those in the second genera-tion are called the strange quark and thecharm quark, while those in the third gen-eration are called the bottom quark (some-times called beauty quark) and the topquark (sometimes called truth quark). Allquarks are spin 1/2 particles with an elec-tric charge which is either +2/3 or –1/3. AllHADRONS are made up of quarks. Quarkstake part in strong interactions, as gov-erned by QUANTUM CHROMODYNAMICS.This means that a quark is associated witha color charge. There are three types ofcolor charge: red, green, and blue.

Isolated quarks have never been ob-served. This has given rise to the hypothe-sis of QUARK CONFINEMENT. Nevertheless,there is still a great deal of experimental ev-idence in favor of quarks.

In the course of weak interactions ofhadrons one flavor of quark turns into an-other flavor of quark. For example, in thebeta decay of a neutron to a proton (withthe emission of an electron and an antineu-trino) a neutron, which has two downquarks and up quark, is converted into aproton, which has two up quarks and onedown quark. Since quarks are electricallycharged they take part in electromagneticinteractions and since they have nonzerorest masses they also take part in gravita-tional interactions.

quarter-wave antenna An antenna thathas a length of λ/4, where λ is the wave-length of the radio wave. Many aerials for

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medium-wavelength radio waves are quar-ter-wave aerials.

quarter-wave plate See retardationplate.

quasar /kway-zar/ Abbreviation for quasi-stellar object. Quasars are astronomicalobjects that have large gravitational red-shifts. It is thought that quasars are super-massive BLACK HOLES at the centers ofgalaxies, each having a mass of about 200million times the mass of the Sun and arapidly accreting mass.

quasicrystal /kway-sÿ-kriss-tăl, kway-zÿ-,kwah-see-, kwah-zee-/ A type of solid thatdoes not have the long-range order of a

true crystal but has orientational order in-volving shapes such as pentagons andicosahedra, which would normally be for-bidden in crystallography. The two-dimen-sional analog of a quasicrystal is called aPenrose pattern. For example, an alloy ofaluminum and manganese, Al Mn, canform a quasicrystal with icosahedral sym-metry.

quenching The rapid cooling of a hotmetal by immersion in a cold liquid.Quenching is sometimes used to improvethe properties of a metal. For example, de-fects in the crystal, occurring at high tem-perature, can be frozen in by rapid coolingto harden the metal.

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racemic mixture /ray-see-mik, ră-/ Amixture that contains equal amounts of thedextrorotatory and levorotatory forms ofan optically active substance; the mixtureis not optically active. See optical activity.

rad A m.k.s. unit of absorbed dose of ion-izing radiation, equal to 1/100 gray.

radar /ray-dar/ An acronym for radio di-rection and ranging. A system for the pre-cise location of distant objects (especiallyships and aircraft) by means of RADIO. Amicrowave radio beam is transmitted, re-flected by the distant object, and receivedon return to the transmitter. The direc-tional antenna points in the direction of theobject, the distance of which is calculatedfrom the time of travel of the wave at thespeed of electromagnetic waves, 3 × 108 ms–1. Alternatively the beam can be made toscan in continuous circles, and so locate allobjects in any direction, the result beingshown on a plan position indicator (PPI), acathode-ray tube with a rotating time base.

radial field A field in which the field linesare directed either towards or away fromthe source of the field, as along the radii ofa circle. The electric field of a single pointcharge is an example of a radial field.

radian Symbol: rad The SI unit of planeangle; 2π radian is one complete revolution(360°).

radiance Symbol: Le In a given direction,the radiant intensity of a source of radia-tion per unit area projected at right anglesto the direction. The unit is the watt persteradian per square meter (W sr–1 m–2).

radiant exitance See exitance.

radiant flux Symbol: Φe The rate of flowof radiant energy; the total power emittedor received in the form of electromagneticradiation. It is measured in watts.

radiant heat Heat emitted from a body inthe form of electromagnetic radiation. Atlow temperatures it is nearly all in the in-frared region but at a few thousand degreesthe amount of visible light becomes impor-tant, and at the radiating temperature ofthe Sun (6000 K) ultraviolet is becomingsignificant. The fact that sunlight was partof the heat radiation of the Sun was dis-covered by Herschel (1800). See also blackbody.

radiant intensity Symbol: Ie The radiantflux from a point source per unit solidangle. The unit is the watt per steradian (Wsr–1).

radiation /ray-dee-ay-shŏn/ Any particlesor waves emitted by a source. There aretwo main uses of the term: 1. Electromag-netic radiation produced by any mecha-nism. In particular the emission of radiantheat by hot bodies, in contrast to heattransfer by convection and conduction.2. The emission of particles (alpha or betaparticles) and electromagnetic radiation(gamma rays) by radioactive substances.

radiation formula See Planck’s radiationlaw.

radiation pressure Pressure exerted on asurface by electromagnetic radiation. Abeam of electromagnetic radiation of en-ergy E has momentum equal to E/c, wherec is the speed of light. Hence, if radiation ofintensity I is totally absorbed by a surfaceat perpendicular incidence, the force/area

R

is equal to I/c. For perfect specular reflec-tion, force/area is 2I/c. For example, solarradiation totally absorbed by a surface atthe distance of the Earth will exert a pres-sure of 4.5 × 10–6 N m–2.

There is an analogous phenomenon inacoustics.

radiator 1. An object that emits radiation.2. A heat exchanger. See heat exchanger.

radio /ray-dee-oh/ The process of commu-nication across space by the transmissionand reception of an electromagnetic waveof radiofrequency without the use of con-necting wires or other material link.

radioactive /ray-dee-oh-ak-tiv/ Describ-ing an element or nuclide that exhibits nat-ural radioactivity.

radioactive dating (radiometric dating)Any method of measuring the age of mate-rials that depends on radioactivity. See car-bon dating; dating; fission-track dating;potassium–argon dating; rubidium–stron-tium dating; thermoluminescent dating;uranium–lead dating.

radioactive series A series of radioactivenuclides, each being formed by the decay ofthe previous one. All such series terminatein the product of a stable nuclide. An ex-ample of a radioactive series is the thoriumseries, which starts with 232Th, and which,after six alpha decays and four beta decays,terminates in 208Pb. This series is known asthe 4n series because all its members havemass numbers that are multiples of 4. Theactinium series, passing from 235U to 207Pbis known as the 4n – 1 series. The uranium-radium series, starting with 238U and end-ing with 206Pb, is known as the 4n + 2series. The neptunium series, terminatingin 209Bi, is not found in nature as it con-tains no long-lived member.

radioactive waste See nuclear waste.

radioactivity /ray-dee-oh-ak-tiv-ă-tee/The spontaneous disintegration of certainunstable nuclides with emission of radia-

tion. There are various types classified asalpha, beta, and gamma decay, and fission.

radiocarbon dating /ray-dee-oh-kar-bŏn/See carbon dating.

radio frequency (RF) A frequency be-tween 3 KHz and 300 GHz (wavelength 1cm–100 km).

radiography /ray-dee-og-ră-fee/ The pro-duction of an image of an object usingshort-wavelength radiation. The term isfrequently taken to mean the production ofan image in medicine using x-rays. A pho-tograph or other image produced in thisway is called a radiograph.

radioisotope /ray-dee-oh-ÿ-sŏ-tohp/ Aradioactive isotope of an element. Tritium,for instance, is a radioisotope of hydrogen.Radioisotopes are extensively used in re-search as sources of radiation and as trac-ers in studies of chemical reactions. Thus, ifan atom in a compound is replaced by a ra-dioactive nuclide of the element (a label) itis possible to follow the course of thechemical reaction. Radioisotopes are alsoused in medicine for diagnosis and treat-ment.

radioluminescence /ray-dee-oh-loo-mă-ness-ĕns/ See luminescence.

radiometer /ray-dee-om-ĕ-ter/ An instru-ment for detecting and measuring radiant(i.e., electromagnetic) radiation. See actin-ometer; bolometer; thermopile.

radiometric dating /ray-dee-oh-met-rik/See radioactive dating.

radio telescope A telescope that detectsradiation in the radio region of the electro-magnetic spectrum from beyond the at-mosphere of the Earth. There are manytypes of radio source, both inside and out-side the Galaxy.

radio waves A form of electromagneticradiation with wavelengths greater than afew millimeters. There is no upper limit –

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radio waves

applications have been found for radiowaves tens of kilometers long.

Artificial radio waves of any frequencycan be produced when suitable electroniccircuits feed alternating signals to suitableantennas. They are generated by the oscil-lating motion of the electrons in the con-ductor.

The main application of radio waves isto carry information – for ‘wireless telegra-phy’ and television for instance. The infor-mation is used to modulate a carrier wave,suitably changing its amplitude, frequency,or phase during transmission. The receiveris able to separate the carried informationfrom the carrier.

See also electromagnetic spectrum.

radium /ray-dee-ŭm/ A white radioactiveluminescent metallic element of the alka-line-earth group. It has several short-livedradioisotopes and one long-lived isotope,radium-226 (half-life 1602 years). Radiumis found in uranium ores, such as the ox-ides pitchblende and carnotite. It was for-merly used in luminous paints andradiotherapy.

Symbol: Ra; m.p. 700°C; b.p. 1140°C;r.d. 5 (approx. 20°C); p.n. 88; r.a.m.226.0254 (226Ra).

radius of curvature Symbol: r The radiusof the sphere of which a MIRROR or LENS

surface is part. In the case of a reflector, theradius of curvature is twice the focal dis-tance, f.

r = 2fIn the case of a lens it is of value to use

the points at 2f and 2f′, twice as far fromthe pole as f and f′. The distance to eitherof these, double the focal distance, is the

nominal radius of curvature of the lens. Itcan be related to the radii of curvature ofthe two lens surfaces.

radius of gyration Symbol: k For a bodyof mass m and moment of inertia I aboutan axis, the radius of gyration about thataxis is given by k2 = I/m. In other words, apoint mass m rotating at a distance k fromthe axis would have the same moment ofinertia as the body.

radon /ray-don/ A colorless monatomicradioactive element of the rare-gas group,now known to form unstable compounds.It has 19 short-lived radioisotopes; themost stable, radon-222, is a decay productof radium-226 and itself disintegrates intoan isotope of polonium with a half-life of3.82 days. 222Rn is sometimes used in ra-diotherapy. Radon occurs in uraniummines and is also detectable in houses builtin certain areas of the country.

Symbol: Rn; m.p. –71°C; b.p. –61.8°C;d. 9.73 kg m–3 (0°C); p.n. 86.

rainbow The effect of refraction in, forexample, rain drops causing sunlight toseparate into the colors of the spectrum.The Sun is behind the observer as he or shefaces the rainbow.

The primary bow is formed by lightthat is partially internally reflected oncewithin each drop, and is refracted on en-tering and leaving. (The appearance maybe affected by diffraction, especially withvery small drops.) In good viewing condi-tions, a faint secondary bow with the col-ors in reverse order may be seen outside theprimary bow. This involves two partial in-ternal reflections in each drop. Sometimes

radium

206

FREQUENCY BANDS OF RADIO WAVES

Band Frequency range (Hz) Wavelength range (m)extremely low frequency (ELF) –3 × 103 105–very low frequency (VLF) 3 × 103–3 × 104 104–105

low frequency (LF) 3 × 104–3 × 105 103–104

medium frequency (MF) 3 × 105–3 × 106 102–103

high frequency (HF) 3 × 106–3 × 107 10 –102

very high frequency (VHF) 3 × 107–3 × 108 1 –10ultra high frequency (UHF) 3 × 108–3 × 109 0.1 –1

other bows (supernumary bows) can alsobe seen.

Raman effect /rah-măn/ The scattering ofmonochromatic light as it passes through atransparent medium. Interaction with themolecules of the medium cause the light tobe scattered, with some at wavelengthsabove and below that of the incident light.The Raman effect is used extensively in thedetermination of molecular structure. Theeffect is named for the Indian physicist SirChandrasekhara Venkata Raman (1888–1970).

random walk A concept applied toBrownian movement and diffusion basedon the idea of finding the distance a walkeris from a starting point if he or she canwalk forward or backward, making thechoices entirely randomly. After taking Nsteps, the average distance from the start-ing point is √N.

range 1. The length over which a force op-erates. For example, both strong and weaknuclear forces are short range since they donot extend outside a nucleus but electro-magnetic and gravitational forces are longrange since they extend over macroscopicdistances.2. The average distance that a particlecausing ionization in matter travels beforeit comes to rest.

Rankine scale /rank-in/ An absolute tem-perature scale on which a temperature in-terval of one degree Rankine (°R)corresponds to a temperature interval ofone degree Fahrenheit. On the Rankinescale absolute zero is 0°R (–273.15°C), thefreezing point of water is 491.67°R (0°C),and the boiling point of water is 671.67°R(100°C). The Rankine scale is named forthe Scottish engineer William John Mac-quorn Rankine (1820–72).

Raoult’s law /rah-oolz/ At a particulartemperature, the relative lowering in vaporpressure of a solution is proportional to themole fraction of the solute dissolved in it.The law is true only for ideal solutions. It is

named for the French chemist François-Marie Raoult (1830–1901).

raster /ras-ter/ The scanning-line patternon a visual display such as the screen of acathode-ray tube.

ratemeter /rayt-mee-ter/ An instrumentthat measures or indicates the rate of decayof a source of radioactivity. This rate canbe manifested as a reading in an electricalinstrument and/or a click in a loudspeaker.

ratio arms See Wheatstone bridge.

rationalized units A system of units inwhich the units are related to one anotherby only a few mathematical operations in-volving addition or multiplication. SI unitsform a rationalized system of units.

ray A very narrow beam of radiation. Byconsidering how selected rays behave, raydiagrams can be drawn to relate object andimage positions for any lens or mirror.

Theoretically a ray is infinitely narrow,like a mathematical line. Then, even if partof a convergent or divergent beam, it willnot converge or diverge itself. There is noevidence that beams are really formed ofrays in this way; however rays are ex-tremely useful in discussion and in ray dia-grams.

ray diagrams Accurate or approximatediagrams showing how selected rays passthrough an optical system (such as a lens,prism, or microscope). The rays are se-lected on the basis of known behavior.Suitable ray diagrams can show details ofthe image formed of any object by the op-tical system. They are also important insystem design. Many examples appear inthis book.

Rayleigh criterion /ray-lee/ See resolvingpower.

Rayleigh–Jeans law The law that de-scribes black-body radiation according toclassical physics. This law shows the neces-sity of quantum physics since it leads to theultraviolet catastrophe of infinity in the

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Rayleigh–Jeans law

limit of the wavelength of the radiationgoing to zero. The Rayleigh–Jeans law wasderived by the British scientist LordRayleigh (1842–1919) in 1900 and modi-fied by the British physicist and as-tronomer Sir James Jeans (1877–1946) in1905.

Rayleigh scattering The scattering ofelectromagnetic radiation, usually light, inwhich the wavelength of the electromag-netic radiation is not changed. Rayleighscattering involves no exchange of energybetween the radiation and the particles (al-though it does involve a change of phaseand direction). This type of scattering is re-sponsible for the blue color of the sky.

reactance /ree-ak-tăns/ Symbol: X A mea-sure of the opposition of inductance or ca-pacitance to alternating current. Reactanceis the ratio of the peak voltage to the peakcurrent. Like resistance it is measured inohms; it causes the current to become outof phase with the voltage. Reactance de-pends on the frequency of the supply.

For a pure capacitance (C), the currentleads the voltage by one quarter cycle. Thereactance is given by 1/2πfC, where f is thefrequency. For a pure inductance (L) thecurrent lags behind the voltage by onequarter cycle. The reactance is given by2πfL. See also alternating-current circuit;impedance; resonance.

reaction Newton’s third law of motionstates that whenever object A applies aforce on object B, B simultaneously appliesan equal force on A in the same line but theopposite direction. These forces arise froman interaction; neither should be consid-ered the cause or effect of the other force.Newton expressed this law in a Latinphrase translated as ‘to every action thereis an equal and opposite reaction’. Studentsvery often seriously misunderstand this.The words action and reaction are justnames given arbitrarily to the two forces ina third-law pair. Often it is wrongly sup-posed that the ‘reaction’ is a consequenceof the ‘action’, and comes afterwards.Sometimes ‘reaction’ is thought to mean

any effect of a force. It is advisable to avoidthe use of the word reaction in mechanics.

reactor See nuclear reactor.

real gas An actual gas, as opposed to a hy-pothetical ideal gas (see gas laws). In a realgas the molecules have non-zero sizes andthere are intermolecular forces between themolecules. The equation of state for a realgas is more complicated than for an idealgas. See van der Waals’ equation.

real image See image.

real is positive, virtual is negative Seesign convention.

Reaumur scale An obsolete temperaturescale in which water freezes at 0° and boilsat 80° at standard pressure. A temperatureinterval of 1 Reamur (Re) is equivalent to atemperature interval of 1.25 degrees Cel-sius. The scale is named for the Frenchphysicist René-Antoine de Réaumur(1683–1757).

rectifier /rek-tă-fÿ-er/ An electrical con-ductor that allows current to flow throughit in one direction only, thus enabling theconversion of a.c. to d.c. The commonesttype of rectifier is the semiconductor diode,which consists of a single p-n junction. Ametal rectifier, which is also a junction rec-tifier, consists of a metal in contact with asemiconductor or an oxide of the metal.Typical examples are copper-selenium andcopper-copper oxide rectifiers. Thethermionic diode is another type of recti-fier.

rectilinear propagation Passage of radi-ation in straight lines in a constantmedium.

red shift A displacement of lines in thespectra of certain celestial objects towardlonger wavelengths (i.e. toward the red endof the visible spectrum). The spectral linesappear at slightly longer wavelengths thanthey would under ‘normal’ laboratory con-ditions. It is caused by the Doppler effectand indicates that the observed galaxy is

Rayleigh scattering

208

moving away from the Earth. Some objectsshow a blue shift, indicating movement to-ward the observer. These shifts are knownas Doppler shifts.

Not all red shifts are thought to becaused by the Doppler effect. Some may re-sult from the source being at a very lowgravitational potential. These are ex-plained by the general theory of relativity,and are known as gravitational red shiftsor Einstein shifts. It is customary to expressa red shift as ∆λ/λ, where ∆λ is the changein the wavelength for an electromagneticwave with a wavelength λ.

reed switch A type of switch that is usedeither as a sensor or in the fast chargingand discharging of capacitors. It gets itsname because the simplest type of reedswitch consists of a glass capsule with threemetal strips. Two of these strips, includingthe one called the reed can become magne-tized. The third strip cannot become mag-netic. In the presence of a magnetic fieldthe reed moves from the strip which cannotbecome magnetic to the magnetized stripwhich attracts the reed.

reflectance /ri-flek-tăns/ (reflection factor)Symbol: ρ The fraction of incident radia-tion reflected by a surface; i.e. the ratio ofthe reflected flux to the incident flux. Foreach surface this will depend on wave-length; often too it depends on angle of in-cidence. There is no unit. If the material issufficiently thick, so that the reflectingproperties do not depend on thickness, it iscalled reflectivity.

reflecting telescope See reflector.

reflection /ri-flek-shŏn/ The process inwhich radiation meeting the boundary be-tween two media ‘bounces back’, to stay inthe first medium. Any kind of radiation –wave or stream of particles – can be re-flected. Whenever an incident ray is re-flected, the laws of reflection can be used tofind the direction into which the ray isturned (deviated). Reflection from a sourcemakes the radiation appear to come fromsomewhere else – the image of the source.For reflection by a plane surface:

1. The image is the same distance behindthe surface as the object is in front.

2. The line joining each object point withits image is normal (perpendicular) tothe surface.

3. The image is the same size as the object.4. The image is the same way up as the ob-

ject, but perverted (laterally inverted).5. The image is virtual (no light actually

passes through it).For reflection by a curved surface, the

relations between object and image dependon how far the object is from the surfacecompared with the focal distance (f) of thesurface. According to the real is positive,virtual is negative convention, the imagedistance (v) and object distance (u) are re-lated by:

1/f = 1/v + 1/uImage size (y) relates to object size (x) thus:

y = x(v/u)The focal distance of a curved reflector ishalf the radius of curvature (r).

Regular reflection (specular reflection)occurs from smooth surfaces. The beam isnot scattered on reflection and undistortedimages are formed. In diffuse reflection thereflecting surface is rough and the reflectedbeam is scattered randomly.

See also diffusion; mirror; reflection,laws of; total internal reflection.

reflection, angle of See angle of reflec-tion.

209

reflection, angle of

normalreflectedray

incidentray

normalreflectedray

incidentray

Reflection

reflection, laws of Two laws that applywhenever any form of radiation is re-flected, whatever the circumstances. Inorder to state the laws, the normal is de-fined – the perpendicular to the surface atthe point of incidence. All angles namedare measured from the normal.(1) The reflected ray is in the same plane asthe incident ray and the normal.(2) The angle of reflection equals the angleof incidence and lies on the other side ofthe normal.

reflection, total internal See total inter-nal reflection.

reflection factor See reflectance.

reflectivity /ree-flek-tiv-ă-tee/ See re-flectance.

reflector /ri-flek-ter/ (reflecting telescope)An optical telescope in which the objective(the light collector) is a converging reflec-tor. The largest ones in use have mirrorsseveral meters in diameter. The problemwith reflecting telescopes is that the firstimage is formed in the incident beam.There are a number of types distinguishedby different optical systems for avoidingthis and taking the light to the eyepiece. SeeCassegrainian telescope; coudé telescope;Gregorian telescope; Newtonian telescope.

refracting telescope See refractor.

refraction /ri-frak-shŏn/ The process inwhich radiation incident on the boundary

between two media passes on into the sec-ond medium. Any kind of radiation – waveor stream of particles – can be refracted.Unless the radiation meets the surface at aright angle (down the normal) it willchange direction on refraction. The behav-ior of refraction in any case depends on therefractive constant (index) of the pair ofmedia. Whenever a ray is refracted, thelaws of refraction can be used to find thedirection into which the ray is turned (de-viated).

Diffuse refraction occurs when the radi-ation is scattered on transmission throughthe medium, as on passage throughtranslucent media such as wax or frostedglass. The opposite effect is regular refrac-tion, in which the beam is not scattered andundistorted images can be formed.

Refraction also occurs within a mediumin which there is a gradient of properties.The apparent position of a star, especiallynear the horizon, is affected by refractionin the atmosphere the density of whichchanges with altitude. Sound waves are re-fracted in the atmosphere as a result oftemperature variation with height.

See also refraction, laws of; refractiveindex.

refraction, angle of See angle of refrac-tion.

refraction, laws of Two laws that applywhenever any radiation is refracted, what-ever the circumstances. In order to state thelaws, the normal is defined – the perpen-dicular to the surface at the point of refrac-tion. All angles named are measured fromthe normal.(1) The refracted ray is in the same plane asthe incident ray and the normal.(2) The sine of the angle of incidence di-vided by the sine of the angle of refractionis constant for a given wavelength and agiven pair of media; the angles lie on oppo-site sides of the normal.

The second law is sometimes calledSnell’s law (named for the Dutch mathe-matician and physicist Willebrord van Roi-jen Snell (1591–1626)). It leads to adefinition for the refractive constant (n)

reflection, laws of

210

secondmedium

refracted ray

first medium

normal

incidentray

i

r

Refraction

concerned with a given wavelength and agiven pair of media:

n = (sini)/(sinr)Special care needs to be taken with the lawsof refraction in situations related to polar-ization of the radiation.

See also birefringent crystal; refractiveconstant.

refractive constant /ri-frak-tiv/ (refrac-tive index) Symbol: n When monochro-matic radiation passes through theinterface between two media it is refractedso that

1n2 = sini/sinr (Snell’s law)where 1n2 is defined as the refractive con-stant for radiation passing from medium 1to medium 2. For radiation in the reversedirection, 2n1 = 1/1n2. For successive re-fractions at the boundaries between media1, 2, and 3:

1n3 = 1n2 × 2n3Partial reflection also occurs at the inter-face. For two media such that the angle ofrefraction is greater than the angle of inci-dence, transmission only occurs for anglesof incidence up to a critical angle p, atwhich the angle of refraction is 90°. At an-gles above p there is total internal reflec-tion:

1n2 = sinpThe absolute refractive constant of amedium is that for radiation passing froma vacuum into the medium. For many pur-poses it is sufficiently accurate to regard airas equivalent to a vacuum.

If λ1 and λ2 are the wavelengths in twomedia and v1 and v2 are the phase speeds,then

1n2 = λ1/λ2 = v1/v2The apparent depth of a medium is relatedto its real depth by 1n2 = real depth/appar-ent depth. Refractive constants often varywith the frequency of the radiation (see dis-persion; anomalous dispersion). For opti-cal materials it is common to give valuesfor a standard radiation, usually the yellowlight from sodium vapor (D-lines).

For electromagnetic radiation at ordi-nary frequencies the absolute refractiveconstants of all materials are greater thanunity. For x-radiation generally the valuesare slightly less than one, such that total in-

ternal reflection can be obtained at grazingincidence going from vacuum to the mat-erial. Thus the phase speeds of x-rays inmaterials are greater than the speed of lightin a vacuum. The group speed (at whichquantities such as momentum, energy, andmass are propagated) cannot in any cir-cumstances be greater than the speed oflight in a vacuum.

refractive index See refractive constant.

refractivity /ree-frak-tiv-ă-tee/ A measureof the ability of a medium to bend (deviate)radiation entering its surface.

refractometer /ree-frak-tom-ĕ-ter/ A de-vice for measuring the refractive constantof a medium. There are many types, eachusing one or other of the relations givingthe refractive constant, directly or as ap-plied in special circumstances. In the ele-mentary laboratory, methods based on theapparent-depth and critical-angle expres-sions are most effective.

refractor /ri-frak-ter/ (refracting tele-scope) An optical TELESCOPE in which theobjective (the light collector) is a converg-ing lens. Practical problems preclude thedesign of such telescopes with lenses morethan about one meter in diameter. Tele-scopes used in astronomy produce an in-verted image; KEPLERIAN TELESCOPES areinvariably used. For non-astronomical usea terrrestrial telescope is employed – eithera GALILEAN TELESCOPE or a Keplerian tele-scope with an added inverting lens.

refrigerant /ri-frij-ĕ-rănt/ The workingfluid in a refrigerator.

refrigerator /ri-frij-ĕ-ray-ter/ (icebox) Arefrigerator is equivalent to a heat enginerun in reverse. A working substance istaken through a cycle of operations inwhich work is done upon it (usually by anelectric motor) so that it can take heat froma cold box and discharge heat to the at-mosphere. By the first law of thermody-namics the heat discharged equals thework done on the working substance plusthe heat taken from the cold box. Certain

211

refrigerator

refrigerators are operated by a heat sourcesuch as a gas flame. In such devices a heatengine and a refrigerator are effectivelycombined in one device. See also heatpump.

regelation /ree-jĕ-lay-shŏn/ The refreez-ing of ice melted by pressure that takesplace when the pressure is removed.

Regnault’s apparatus /ren-yohz/ An ap-paratus for measuring the absolute thermalexpansivity (γ) of a liquid. It consists of ashaped U-tube (see illustration) with onelimb at ice temperature and the other at aconstant temperature θ (usually the steamtemperature). The value of γ can be calcu-lated from the difference between the liq-uid heights in the two limbs of the tubes.The apparatus is named for the French sci-entist Henri Victor Regnault (1800–78).

regular reflection See reflection.

regular refraction See refraction.

rejector circuit See resonance.

relative atomic mass Symbol: Ar Theratio of the average mass per atom of thenaturally occurring element to 1/12 of themass of an atom of nuclide 12C. It was for-merly called atomic weight.

relative density Symbol: d The density ofa substance divided by the density of a ref-erence substance. For liquids the density ofwater at 4°C (the temperature at which itsdensity is a maximum) is usually used. Thetemperature of the substance is eitherstated or is understood to be 20°C. Rela-tive densities are also stated for gases, usu-ally relative to air at STP. Relative densitywas formerly called specific gravity.

relative humidity A measure of theamount of water vapor in the air, ex-pressed as a proportion of the maximumamount the air could hold at the tempera-ture concerned. (The higher the tempera-ture the more water vapor air can hold.)For a fixed amount of water and air, therelative humidity therefore decreases astemperature rises and increases as it falls. Ifthe temperature falls to the point where therelative humidity equals one, the watervapor starts to condense out as droplets onsurfaces or in the air (dew or mist). Thistemperature is the saturation temperatureor the dew temperature (dew point). Com-pare absolute humidity.

relative molecular mass Symbol: MrThe ratio of the average mass per moleculeof the naturally occurring form of an ele-ment or compound to 1/12 of the mass ofan atom of nuclide 12C. This was formerlycalled molecular weight. It does not have tobe used only for compounds that have dis-crete molecules; for ionic compounds (e.g.NaCl) and giant-molecular structures (e.g.BN) the formula unit is used.

relative permeability See permeability.

relative permittivity Symbol: εr For aparallel-plate capacitor (say) with a givenmaterial between the plates, the relativepermittivity is the ratio of the capacitanceobserved (Cm) to the capacitance (C0) if thematerial were removed (free space betweenthe plates); i.e. εr = Cm/C0. Relative permit-tivity measures the effect of a material onan electric field relative to free space. It isequal to ε/ε0, where ε is the (absolute) PER-MITTIVITY of the material and ε0 the per-mittivity of free space (the electric

regelation

212

A H h3–h1

h3

C B G F

h1

h0

ice 0oC steam oC h

ED

h2

room 1oC

Regnault’s apparatus: modified apparatus for absolute expansivity

constant). An early term for relative per-mittivity was dielectric constant.

relative velocity If two objects are mov-ing at velocities vA and vB in a given direc-tion, the velocity of A relative to B is vA –vB in that direction. In general, if two ob-jects are moving in the same frame at non-relativistic speeds their relative velocity isthe vector difference of the two velocities.

relativistic mass /rel-ă-ti-vis-tik/ Themass of an object as measured by an ob-server at rest in a frame of reference inwhich the object is moving with a velocityv. It is given by m0 = m√(1 – v2/c2), wherem0 is the rest mass, c is the speed of light,and m is the relativistic mass. The equationis a consequence of the special theory ofRELATIVITY, and is in excellent agreementwith experiment. No object with a non-zero REST MASS can travel at the speed oflight because its mass would then be infi-nite.

relativistic particle A particle that istraveling at a RELATIVISTIC VELOCITY.

relativistic velocity Any velocity that issufficiently high to make the mass of an ob-ject significantly greater than its rest mass.It is usually expressed as a fraction of c, thespeed of light. At a velocity of c/2 the REL-ATIVISTIC MASS of an object increases by15% over the REST MASS.

relativity, theory of /rel-ă-tiv-ă-tee/ Atheory put forward in two parts by AlbertEinstein. The special theory (1905) re-ferred only to non-accelerated (inertial)frames of reference. The general theory(1915) is also applicable to accelerated sys-tems.

The special theory was based on twopostulates:(1) That physical laws are the same in allinertial frames of reference.(2) That the speed of light in a vacuum isconstant for all observers, regardless of themotion of the source or observer.

The second postulate seems contrary to‘common sense’ ideas of motion. Einsteinwas led to the theory by considering the

problem of the ‘ether’ and the relation be-tween electric and magnetic fields in rela-tive motion. The theory accounts for thenegative result of the Michelson–Morleyexperiment and shows that theLorentz–Fitzgerald contraction is only anapparent effect of motion of an object rel-ative to an observer, not a ‘real’ contrac-tion. It leads to the result that the mass ofan object moving at a velocity v relative toan observer is given by:

m = m0/√(1 – v2/c2)where c is the speed of light and m0 themass of the object when at rest relative tothe observer. The increase in mass is signif-icant at high velocities. Another conse-quence of the theory is that an object hasan energy content by virtue of its mass, andsimilarly that energy has inertia. Mass andenergy are related by the famous equationE = mc2.

The general theory of relativity seeks toexplain the difference between acceleratedand non-accelerated systems and the na-ture of the forces acting in both of them.For example, a passenger in a car roundinga bend at constant speed is in an acceler-ated frame of reference because his or hervelocity is changing. He experiences a ficti-tious force known as a centrifugal force.This force is fictitious because to an outsideobserver the force is simply a result of thepassenger’s tendency to continue in astraight line. This analysis of forces led Ein-stein to the view that gravitation is a con-sequence of the geometry of the universe.He visualized a four-dimensional space-time continuum in which the presence of amass affects the geometry – the space is‘curved’ by the mass.

relay /ree-lay/ An electromagnetic switch-ing device consisting of a coil of insulatedwire with a central soft iron core acting asarmature. When the coil is energized, thearmature moves and operates a switch inanother circuit. THYRISTORS can be used assolid-state relays. See also solenoid.

reluctance (‘magnetic resistance’) Sym-bol: R The ratio of magnetomotive force tototal magnetic flux in a MAGNETIC CIRCUIT.

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reluctance

The SI unit of reluctance is the henrymeter–1 (H m–1).

reluctivity /rel-ŭk-tiv-ă-tee/ The recipro-cal of magnetic permeability.

rem /rem/ (radiation equivalent man) Am.k.s. unit formerly used for measuringequivalent ionizing radiation doses ab-sorbed by living tissue. One rem is equiva-lent to a dosage of one roentgen of x-raysor gamma rays absorbed by an averageadult male. In SI derived units it is equal to10–2 sievert.

remanence /rem-ă-nĕns/ See hysteresiscycle.

resistance, electrical Symbol: R Theratio of the potential difference across anelectrical element to the current in it. Re-sistance measures the opposition of thecomponent to the flow of charge. The SIunit is the ohm. In an alternating-currentcircuit resistance is only one factor in theresponse of the component. See imped-ance. See also effective resistance; Ohm’slaw.

resistance box A device for providingvariable known resistances. One type has athick brass bar with gaps at intervals acrosswhich are connected fixed resistances.Combinations of these resistances can bechosen by inserting brass plugs in the gaps,thus shorting out selected resistors. Othertypes of resistance box have multi-switchesto give the selection.

resistance thermometer A thermometerthat measures temperature by the changein electrical resistance of a conductor. Usu-ally a small coil of pure fine platinum wireis used, wound on a mica former. It is in-corporated into one arm of a Wheatstonebridge; the other arm has a variable resis-tor and a pair of ‘dummy’ leads, to com-pensate for temperature effects in the leadsof the measuring coil.

The resistance varies with temperatureaccording to an approximate equation ofthe form:

R = R0(1 + aθ)where R is the resistance at θ°C, R0 the re-sistance at 0°C, and a is a constant.

More strictly:R = R0(1 + aθ + bθ2)

where b is a second constant.

resistance wire Wire used to introduce aresistance into an electrical circuit. Resis-tance wire is made from alloys. Where thewire is likely to attain high temperatures,Nichrome is suitable. Constantan is usedfor resistors for accurate work with alter-nating current as it has a very low temper-ature coefficient of resistance, but it is lesssuitable for d.c. as it gives disturbing ther-moelectric e.m.f.s in conjunction with cop-per connectors. Manganin is suitable forprecise d.c. resistors.

resistivity /ree-zis-tiv-ă-tee/ Symbol: ρThe tendency of a material to oppose theflow of an electric current. The resistivity isa property of the material at a given tem-perature and does not depend on the sam-ple. The resistance R of a sample is givenby ρl/A, where A is the cross section areaand l the length. The unit is the ohm meter(Ωm). Resistivity was formerly called spe-cific resistance. At normal temperaturesthe resistivities of pure metals are typicallyof the order 10–8 to 10–7 ohm. Alloys gen-erally have higher values than pure metals,typically 10–7 to 10–6 ohm. The values forinsulators can be very much higher – in therange 106 to 1018 ohm. Semiconductor re-sistivities can vary between these extremes,their values depending greatly on the pu-rity of the specimen.

resistor A component included in an elec-tric circuit because of its resistance. Resis-tors may be variable or have a fixed value;they are made of resistance wire or carbon.Some types have a ceramic coating incor-porating a color coding in the form of cir-cular bands or stripes, which identify thevalue of the resistance.

resolution The ability to distinguish twoclose objects separately, rather than as onesingle object. The resolution obtained with

reluctivity

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an optical system depends on the magnifi-cation and on the RESOLVING POWER.

resolution of vectors The determinationof the components of a vector in two givendirections at 90°. The term is sometimesused in relation to finding any pair of com-ponents (not necessarily at 90° to eachother).

resolving power A measure of the abilityof an optical system to form detectably sep-arate images of close objects or to separateclose wavelengths of radiation.

The resolving power depends on theaperture (a) and the wavelength (λ) of theradiation. For separation of images it is thesmallest angular separation of the images.It can be defined ideally as λ/a (the unitbeing the radian). In practice, diffractioneffects limit the resolution. In a telescopeforming images of two stars, each imagewill be a bright central portion surroundedby light and dark rings. The Rayleigh crite-rion for resolution (named for the Englishphysicist John William Strutt, LordRayleigh (1842–1919)) is that the centralportion of one image falls on the first min-imum of the other. The resolving power isthen 1.22λ/a. The resolving power of a mi-croscope is often given as the actual mini-mum distance between two points that canbe separated (a small distance is a high re-solving power). Again it depends on wave-length and aperture. Larger apertures giveincreased resolving power. The immersionobjective is a method of increasing the ef-fective aperture. Electron microscopeshave higher resolving powers because thewavelengths of electrons are much smallerthan those of visible radiation. The resolv-ing power of the human eye is about 10–3

rad. At the standard near-point distance(250 mm) points about 100 micrometerapart can just be resolved.

resonance 1. The large-amplitude vibra-tion of an object or system when given im-pulses at its natural frequency. Forinstance, a pendulum swings with a naturalfrequency that depends on its length. If it isgiven a periodic ‘push’ at this frequency –for example, at each maximum of a com-

plete oscillation – the amplitude is in-creased with little effort. Much more effortwould be required to produce a swing ofthe same amplitude at a different fre-quency.2. An electric circuit containing both ca-pacitance and inductance can be arrangedso that a very large (resonant) response oc-curs at a particular (resonant) frequency ofalternating supply. An inductance (L) andcapacitance (C) in series are known as a se-ries resonant or acceptor circuit, and in itthere is a large alternating current at theresonant frequency (f). Resonance occurswhen f.L = 1/f.C. In a parallel resonant orrejector circuit, L and C are in parallel;then a minimum current flows at the reso-nant frequency. In a tuning circuit, the res-onant frequency may be varied by alteringthe capacitance or the inductance. This ishow radio receivers are tuned to the broad-cast frequency. See also impedance; reac-tance.3. One of a large number of excited statesof elementary particles. Many resonancesare known; all have very short lifetimes.

restitution, coefficient of /res-tă-tew-shŏn/ Symbol: e For the impact of twobodies, the elasticity of the collision is mea-sured by the coefficient of restitution. It isthe relative velocity after collision dividedby the relative velocity before collision (ve-locities measured along the line of centers).For spheres A and B:

vA1 – vB

1 = –e(vA – vB)v indicates velocity before collision; v1 ve-locity after collision. Kinetic energy is con-served only in a perfectly elastic collision.Different possibilities are shown in thetable.

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restitution, coefficient of

RESTITUTION COEFFICIENTS

Type of collision restitutioncoefficient (e)

perfectly inelastic 0inelastic >0, <1perfectly elastic 1superelastic >1

rest mass Symbol: m0 The mass of an ob-ject at rest as measured by an observer atrest in the same frame of reference. See alsorelativistic mass.

resultant /ri-zul-tănt/ A vector with thesame effect as a number of vectors. Thus,the resultant of a set of forces is a force thathas the same effect; it is equal in magnitudeand opposite in direction to the equili-brant. Depending on the circumstances,the resultant of a set of vectors can befound by different methods. See parallelforces; parallelogram of vectors; principleof moments.

retardation plate /ree-tar-day-shŏn/ Athin transparent plate cut from a piece ofbirefringent material (e.g. quartz or mica)parallel to the optic axis. For light trans-mitted by the plate normal to the opticaxis, the ordinary and extraordinary raystravel at different speeds. The thickness isdesigned to induce a desired phase differ-ence between the transmitted rays. Thehalf-wave plate introduces a phase differ-ence of π, and the ordinary and extraordi-nary rays are out of step by one-halfwavelength. The quarter-wave plate pro-duces a phase difference of π/2 and the raysare out of step by one-quarter wavelength.

retina (pl. retinas or retinae) /ret-ă-nă/The light-sensitive inner surface of the EYE:its function is to convert incident light intonerve signals.

reverberation /ri-ver-bĕ-ray-shŏn/ Persis-tence of sound after the source has stoppedas a result of repeated reflections fromwalls, ceilings, and other surfaces. Rever-beration characteristics are important inthe design of concert halls, theaters, etc.

reversal A change in the direction of themagnetic field of the Earth. Reversalsoccur because of changes in the motion ofliquid iron inside the Earth’s core. Experi-mental evidence for reversals is providedby the ‘zebra stripe’ pattern of the magnet-ism of rocks on the floor of the AtlanticOcean. They seem to occur over relatively

short time periods but at long intervals oftens of thousands of years.

reversible change A change in the pres-sure, volume, or other properties of a sys-tem, in which the system remains atequilibrium throughout the change. Suchprocesses could be reversed; i.e. returned tothe original starting position through thesame series of stages. They are never real-ized in practice. An isothermal reversiblecompression of a gas, for example, wouldhave to be carried out infinitely slowly andinvolve no friction, etc. Ideal energy trans-fer would have to take place between thegas and the surroundings to maintain aconstant temperature.

In practice, all real processes are irre-versible changes in which there is not anequilibrium throughout the change. In anirreversible change, the system can still bereturned to its original state, but notthrough the same series of stages. For aclosed system, there is an entropy increaseinvolved in an irreversible change.

Reynolds number /ren-ŏldz/ Symbol: ReA dimensionless quantity used to describefluid flow. It is equal to ρcl/η, where ρ isthe fluid’s density, c its velocity, η its vis-cosity, and l is a length characteristic of thegeometry. For a long pipe, for example, lwould be the internal diameter. TheReynolds number is used in making scalemodels of fluid flow. The size (l) may bescaled down by a factor of four, for in-stance, if the model fluid has a value of ρ/ηequal to a quarter that of the fluid beingmodeled. Because Re is unchanged theflow pattern will be similar and the CRITI-CAL SPEED will be the same. The number isnamed for the British physicist OsborneReynolds (1842–1912).

RF See radio frequency.

rhenium /ree-nee-ŭm/ A rare silvery tran-sition metal that usually occurs naturallywith molybdenum. The metal is chemicallysimilar to manganese and is used in alloysand catalysts.

Symbol: Re; m.p. 3180°C; b.p. 5630°C;r.d. 21.02 (20°C); p.n. 75; r.a.m. 186.207.

rest mass

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rheology /ree-ol-ŏ-jee/ The study of fluidflow.

rheostat /ree-ŏ-stat/ A variable resistor,usually operated by a sliding contact on acoil. See also potentiometer.

rhodium /roh-dee-ŭm/ A rare silvery hardtransition metal. It is difficult to work andhighly resistant to corrosion. Rhodium oc-curs native but most is obtained from cop-per and nickel ores. It is used in protectivefinishes, alloys, and as a catalyst.Symbol: Rh; m.p. 1966°C; b.p. 3730°C;r.d. 12.41 (20°C); p.n. 45; r.a.m.102.90550.

ribbon microphone See microphone.

Richardson–Dushman equation /rich-erd-sŏn dŭŭsh-măn/ An equation that de-scribes the emission of electrons from a hotconductor. It states that J = AT2

exp(–W/kT), where J is the current density,A is a constant, T is the absolute tempera-ture, W the work function of the conduc-tor, and k the Boltzmann constant. Thisequation was derived from the electrontheory of metals by Sir Owen Richardsonsoon after the discovery of electrons andsubsequently modified by Saul Dushman inthe 1920s by taking quantum mechanicsinto account.

right-hand rule See Fleming’s rules.

rigid-body dynamics The dynamics ofrigid bodies, i.e. bodies in which the dis-tance between any two particles making upthe body is always constant. Rigid-bodydynamics can be applied to the motion offlywheels, gyroscopes, etc. and, to a certainextent, the rotation of the Earth.

rigidity modulus See elastic modulus.

ring main A way of wiring electric sock-ets (outlets) in parallel round a building sothat they form a ring or chain from andback to the supply point.

ripple tank A device for producing waves(ripples) on the surface of water and view-

ing these under stroboscopic light. It isused to demonstrate interference effectsand other wave properties.

RMS value See root-mean-square value.

Rochon prism /roh-shon/ A type of po-larizing prism. The ordinary ray passesthrough undeviated; the extraordinary rayleaves from the side. This result is the re-verse of that given by the Nicol prism.

rods The more sensitive cells of the retinaof the EYE. They are of most importance invision in poor light, but cannot providecolor information. Their action is notknown in detail. It appears to be based onthe photochemical breakdown of a reddishdye called rhodopsin (formerly visual pur-ple).

roentgen /rent-gĕn/ Symbol: R A c.g.s.unit of radiation exposure, formerly usedfor x-rays and γ-rays, defined in terms ofthe ionizing effect of one electrostatic unitof electricity on one cubic centimeter of air.In SI units one roentgen is equal to 2.58 ×10–4 coulomb. The unit is named for theGerman physicist Wilhelm Conrad Rönt-gen (1845–1923).

roentgenium /rent-gĕn-ee-ŭm/ A radioac-tive element produced synthetically. It isnamed for Wilhelm Roentgen

Symbol: Rg; p.n. 111.

Roentgen rays A former name for x-rays.

rolling friction See friction.

root-mean-square value (RMS value) 1.The square root of the average of thesquares of a group of numbers or values.For example, the RMS value of 2, 4, 3,2.5 is

√[22 + 42 + 32 + 2.52)/4] = 5.9372. For continuous quantities, such as alter-nating electric current, the root-mean-square value is used to measure the averageeffect. The root-mean-square value of analternating current (also called the effectivevalue) is the value of the direct current thatwould produce the same energy transfer

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root-mean-square value

per second in a given resistor. For a sinewave, this is Im/√2, where Im is the peakvalue.

rotary converter A combination of ana.c. electric motor and a d.c. dynamo, usedto convert alternating current into directcurrent.

rotational motion Motion of a bodyturning about an axis. The physical quan-tities and laws used to describe linear mo-tion all have rotational analogs; theequations of rotational motion are theanalogs of the equations of motion (linear).

They normally include T = Iα, the ana-log of F = ma, as well as the ‘kinematic’equations themselves. Here T is the turningmoment, or torque, I is the moment of in-ertia, and α is the angular acceleration.

The other equations relate the angularvelocity, ω1, of the object at the start oftiming to its angular velocity, ω2, at somelater time, t, and thus to the angular dis-placement θ. The examples in the table areequations that apply to motion about afixed axis with uniform angular accelera-tion. See equations of motion.

rotor The rotating part, or armature, ofan electric motor or dynamo, or similar de-vice. See also stator.

RSI value See r-value.

rubidium /roo-bid-ee-ŭm/ A soft silveryhighly reactive element. Naturally occur-ring rubidium comprises two isotopes, oneof which, 87Rb, is radioactive (half-life 5 ×1010 years). The element is used in vacuumtubes, photocells, and in making specialglass.

Symbol: Rb; m.p. 39.05°C; b.p. 688°C;r.d. 1.532 (20°C); p.n. 37; r.a.m. 85.4678.

rubidium–strontium dating A methodof radioactive dating used for estimatingthe age of certain rocks. It is based of thedecay or 87Rb to 87Sr (half-life 5 × 1010

years). The technique is useful for verylarge ages, of the order 1 × 109 years to 4 ×109 years.

ruthenium /roo-th’ee-nee-ŭm/ A transi-tion metal that occurs naturally with plat-inum. It forms alloys with platinum thatare used in electrical contacts. Rutheniumis also used in jewelry alloyed with palla-dium.

Symbol: Ru; m.p. 2310°C; b.p.3900°C; r.d. 12.37; p.n. 44; r.a.m. 101.07.

rutherford Symbol: rd A unit of radioac-tivity equal to that of a radioactive nuclideundergoing 106 disintegrations per second,equal to 106 becquerels in SI derived units.It is named for the New Zealand physicistErnest Rutherford, First Baron Rutherfordof Nelson (1871–1937).

rutherfordium /ruth-er-for-dee-ŭm/ A ra-dioactive metal not found naturally onearth. It is the first transactinide metal.Atoms of rutherfordium are produced bybombarding 249Cf with 12C or by bom-barding 248Cm with 18O.

Symbol: Rf; m.p. 2100°C (est.); b.p.5200°C (est.); r.d. 23 (est.); most stableisotope 261Rf (half-life 65s).

Rutherford–Royds experiment /roidz/An experiment performed by ErnestRutherford and T. Royds in 1909 thatdemonstrated that alpha particles were he-lium nuclei. The alpha particles given offby radon were collected and the resultinghelium gas was characterized by its spec-trum.

Rutherford scattering /ruth-er-ferd/ Thescattering of charged particles, such asalpha particles, by atomic nuclei. This typeof scattering was analyzed by ErnestRutherford in 1911 to explain the resultsof experiments, which he correctly inter-

rotary converter

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ROTATIONAL EQUATIONS OF MOTION

Variables Equationα, ϖ1, ϖ2, t, (θ) ϖ2 = ϖ1 + αtϖ1, ϖ2, t, θ, (α) θ = (ϖ1 + ϖ2)t/2α, ϖ1, t, θ, (ϖ1) θ = ϖ1t + αt2/2α, ϖ2, t, θ, (ϖ1) θ = ϖ2t – αt2/2α, ϖ1, ϖ2, θ, (t) ϖ2

2 = ϖ12 + 2αθ

preted as indicating the existence of atomicnuclei.

r-value A measure of the thermal insu-lance (resistance to heat flow) of a giventhickness of a material such as insulation,with higher values indicating greater ther-mal insulance. The SI deried unit of ther-mal insulance is the square meter degreeCelsius per watt (m2°CW–1). The SI valueof thermal insulance is known as RSI value

Rydberg constant /rid-berg/ See Bohrtheory.

Rydberg formula An equation that givesthe wave number of a line in a spectrum:

1/γ = R(1/n2 –1/m2),where n and m are positive whole numbersand R is the Rydberg constant (equal to1.096 77 x 107 m–1 for hydrogen). The for-mula is named for the Swedish physicistJohannes Robert Rydberg (1854–1919).

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Rydberg formula

220

saccharimeter /sak-ă-rim-ĕ-ter/ See po-larimeter.

salt bridge An inverted U-tube containinga concentrated solution of a salt (such aspotassium chloride), used to connect twoHALF CELLS.

samarium /să-mair-ee-ŭm/ A silvery ele-ment of the lanthanoid series of metals. Itoccurs in association with other lan-thanoids. Samarium is used in the metal-lurgical, glass, and nuclear industries.

Symbol: Sm; m.p. 1077°C; b.p.1791°C; r.d. 7.52 (20°C); p.n. 62; r.a.m.150.36.

satellite A body that orbits a planet, withthe orbiting body being much smaller thanthe planet. The satellite can be a naturalsatellite, such as the Moon, or an artificialsatellite, such as the satellites used for com-munications and astronomy.

saturated vapor pressure See vaporpressure.

saturation The freedom from white of acolor. A pure spectral color (single wave-length) is a hue, and is said to be saturated.Unsaturated colors are tints; i.e. huesmixed with white.

saturation, magnetic A magnetic mater-ial is saturated if it can be magnetized nomore strongly. This can easily be explainedusing the domain theory; i.e. it is the statein which all the magnetic domains arealigned. See also hysteresis cycle.

sawtooth wave A waveform generatedelectronically (such as the variation of volt-age with time), having a uniform increase

that regularly and rapidly drops to the ini-tial value. A sawtooth wave is used as thetime base for scanning circuits in a cath-ode-ray tube.

scalar /skay-ler/ A measure in which di-rection is unimportant or meaningless. Forinstance, distance is a scalar quantity,whereas displacement is a VECTOR. Mass,temperature, and time are examples ofscalars – they are each quoted as a purenumber with a unit.

scalar product A multiplication of twovectors to give a scalar. The scalar productof A and B is defined by A.B = ABcosθ,where A and B are the magnitudes of A andB and θ is the angle between the vectors.An example is a force F displaced s. Herethe scalar product is energy transferred (orwork done):

W = F.sW = Fscosθ

where θ is the angle between the line of ac-tion of the force and the displacement. Ascalar product is sometimes called a dotproduct. See also vector product.

scaler An electronic counting device thatmeasures the amount of energy transfer orcharge that results from radiation, record-ing one ‘count’ after a certain number ofinput pulses. See counter.

scandium /skan-dee-ŭm/ A lightweightsilvery element. It is found in minuteamounts in over 800 minerals, often asso-ciated with lanthanoids. Scandium is usedin high-intensity lights and in electronic de-vices.

Symbol: Sc; m.p. 1541°C; b.p. 2831°C;r.d. 2.989 (0°C); p.n. 21; r.a.m.44.955910.

S

scanning electron microscope See elec-tron microscope.

scattering The ‘spreading out’ of a beamof radiation as it passes through matter, re-ducing the energy moving in the originaldirection. Depending on the circumstances,scattering can follow any combination ofthree processes as the radiation interactswith matter particles – reflection (elasticscattering), absorption followed by re-radi-ation (inelastic or Compton scattering),and diffraction. Thus sunlight is scattered(or diffused) as it passes through cloud anddust in the atmosphere. However, evenperfectly clear air scatters sunlight, makingthe sky color blue – high frequencies arescattered more than low frequencies.

schlieren technique /shleer-ĕn/ A methodof studying turbulent flow by high-speedphotography. If turbulent flow occurs in afluid, there are localized short-lived regionsof low density. These can be recorded byphotography because they have a differentrefractive constant, and appear as streakson the photograph.

schorl /shorl/ See tourmaline.

Schottky defect /shot-kee/ See defect.

Schrödinger equation /shroh-ding-er/ Anequation for the wave function of a parti-cle, such as an electron in an atom (i.e., ittreats the electron’s behavior as a three-di-mensional stationary wave). The solutionof the equation gives the probability thatthe electron will be located at a particularplace. The equation is named for the Aus-trian physicist Erwin Schrödinger (1887–1961).

Schrödinger’s cat A thought experimentfirst put forward by Erwin Schrödinger in1935. In quantum mechanics, a particle isdescribed by a wave function, which ex-presses the probability of finding it in aparticular region of space and time. Theconventional view of physicists is that theparticle exists in some type of indetermi-nate or indefinite state until a measurement(or observation) is made, at which point it

becomes a definite particle. It is said thatthe observation ‘collapses’ the wave func-tion. Schrödinger put forward his thoughtexperiment to show that this idea mighthave logical consequences that seem ridicu-lous.

He suggested a closed box containing asample of radioactive material, a tube ofcyanide, and a cat. The apparatus was tobe constructed so that decay of a nucleusejected a particle, which activated a mech-anism to break the tube of cyanide. After acertain time, if a nucleus had decayed thecat would have died; if not the cat wouldstill be alive.

Schrödinger pointed out that, accord-ing to our way of interpreting quantummechanics, the nucleus had neither de-cayed nor not decayed until an observationwas made, and it followed that the cat wasneither dead nor alive until someoneopened the box and observed it. The ideahas caused considerable argument amongpeople interested in the nature of QUANTUM

MECHANICS. Most physicists would behappy with the idea that a particle could bein an indeterminate form until observed.Few would accept that a cat could be nei-ther alive nor dead. The problem, which isstill not fully resolved, concerns the differ-ence in nature between events on the mi-croscopic scale (e.g. nuclei) and events onthe macroscopic scale (e.g. cats). See alsoBell’s paradox.

scintillation counter /sin-tă-lay-shŏn/ Adetector of radiation in which radiationproduces scintillations (flashes of light) in aphosphor. These are used to produce anelectric pulse by means of a photomulti-plier. As well as crystalline scintillatorsvarious liquids can be used.

sclerotic /skli-rot-ik/ The hard outer coat-ing of the eyeball. See eye.

scotopic vision /skoh-top-ik/ Vision atlow levels of light intensity (night-time vi-sion). Under such conditions the rods in theretina are the main receptors and no colorscan be distinguished. Compare photopicvision.

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scotopic vision

screen grid See tetrode.

screw A type of simple machine, related tothe inclined plane, and, in practice, to theclass two lever. The efficiency of screw sys-tems is very low because of friction. Evenso, the force ratio (F2/F1) can be very high.

The distance ratio is given by 2πr/p,where r is the radius and p the pitch of thescrew (the angle between the thread and aplane at right angles to the barrel of thescrew).

seaborgium /see-bor-gee-ŭm/ A radioac-tive metallic element not occurring natu-rally on Earth. It can be made bybombarding 249Cf with 18O nuclei using acyclotron. Six isotopes are known. The el-ement is named for the American physicistGlenn Theodore Seaborg (1912–99).

Symbol: Sg; most stable isotope 266Sg(half-life 27.3s).

search coil A small coil, in which inducedcurrents are used to measure magnetic fieldstrengths. See fluxmeter.

Searle’s bar /serlz/ An apparatus for mea-suring the thermal conductivity of a goodconductor. The specimen is a long narrowlagged bar heated at one end by a temper-ature bath or electric coil. It is cooled at theother end by a coil of copper tubingthrough which a steady stream of water ispassed. The temperatures of the input andoutput water are measured (θ3 and θ4 re-spectively). In this way a temperature gra-dient is produced along the bar, which isfound by measuring the temperatures (θ2and θ3) at two intermediate points adistance l apart. These temperatures aremeasured by thermocouples or by ther-mometers placed in holes in the bar. Understeady-state conditions, thermal conductiv-ity is calculated from the equation:

kA(θ2 – θ1)/l = mc(θ4 – θ3)m being the mass of water passed in unittime, c the specific thermal capacity of thewater, and A the bar’s cross-sectional area.

second 1. Symbol: s The SI base unit oftime. Since 1967 it has been defined as theduration of 9 192 631 770 periods of a

particular wavelength of radiation corre-sponding to a transition between two hy-perfine levels in the ground state of thecesium-133 atom. Prior to 1967 the secondwas defined as 1/86 400 of a mean solarday or as a fraction of a tropical year. Dueto irregularities in the Earth’s rotation,however, these definitions proved too inac-curate for modern scientific and technicalwork. For less exacting purposes the sec-ond is considered to be a duration of 1/60of a minute or 1/3600 of an hour.2. Symbol: ″ A unit of angle: 1/3600 of adegree.

secondary cell See accumulator.

secondary colors The colors formed bymixing pairs of primary colors (hues). Theeffects can be shown by overlapping thebeams from three projectors, each project-ing a primary color (see diagram).

secondary emission The emission ofelectrons from a surface as a result of theimpact of high-energy electrons or ions.The incident particles must have sufficientenergy to eject the ‘free’ electrons in thesolid; i.e. to overcome the work function ofthe material.

screen grid

222

primaryRED

primaryGREEN

primaryBLUE

secondaryYELLOW

yellow = red + green = white – bluecyan = green + blue = white – redmagenta = blue + red = white – green

secondaryCYAN

secondaryMAGENTA

Secondary colors

secondary wavelets See Huygens’ con-struction.

secondary winding See transformer(voltage).

Seebeck effect /see-bek/ The productionof an e.m.f. in a circuit having two conduc-tors, when the junctions between the twoconductors are at different temperatures.The Seebeck effect is the phenomenon pro-ducing the e.m.f. in thermocouples. The ef-fect is named for the Estonian-bornGerman physicist Thomas Johann Seebeck(1770–1831). Compare Peltier effect.

seismic waves Waves that move throughthe Earth or on the surface of the Earth be-cause of an earthquake. The different typesof seismic wave have been used to obtaininformation about the interior structure ofthe Earth.

selenium /si-lee-nee-ŭm/ A metalloid ele-ment existing in several allotropic forms.The common gray metallic allotrope isvery light-sensitive and is used in photo-cells, solar cells, some glasses, and in xe-rography. The red allotrope is unstable andreverts to the gray form under normal con-ditions.

Symbol: Se; m.p. 217°C (gray); b.p.684.9°C (gray); r.d. 4.79 (gray); p.n. 34;r.a.m. 78.96.

selenium cell A photoconducting cellconsisting of a piece of light-sensitive sele-nium semiconductor, which decreases itselectrical resistance when light falls on it. Itis powered by a battery. See also photocell.

self-absorption (self-shielding) The ab-sorption by a large radioactive source ofsome of the radiation it produces, resultingin an overall decrease in external radiation.

self-inductance See self-induction.

self-induction The production of ane.m.f. in a conductor (e.g. a coil) caused bychanges in the current in the conductor it-self. The electromotive force is sometimesknown as the back e.m.f. as its direction

opposes the current change in accordancewith Lenz’s law. The relationship betweenthe e.m.f. (E) and the rate of change of cur-rent (dI/dt) is given by the equation:

E = L(dI/dt)where L is a constant for the coil known asits self-inductance. The SI unit of induc-tance is the henry (H). Compare mutual in-duction.

semiconductor /sem-ee-kŏn-duk-ter/ Amaterial, such as silicon or germanium,that has a resistivity midway (on a loga-rithmic scale) between that of conductorsand that of insulators. In a pure semicon-ductor material, called an intrinsic semi-conductor, the concentrations of negativecharge carriers (electrons) and positivecharge carriers (holes) are the same. Inpractice, absolutely pure semiconductormaterial does not exist, but the intrinsicconductivity is used as a reference level foran impure semiconductor. The conductiv-ity increases considerably when certain im-purities are added, depending strongly onthe type and concentration of the impurity.Such a material is called an extrinsic semi-conductor. The process of adding impurityto control the conductivity is called dop-ing.

Addition of, for example, phosphorusincreases the number of electrons availablefor conduction, and the material is de-scribed as n-type, i.e. the charge carriersare negative. The impurity, or dopant, iscalled a donor impurity in this case.

Addition of, for example, boron has theeffect of removing electrons; the dopant inthis case being called an acceptor impuritybecause its atoms accept electrons for thecompletion of atomic bonds, leaving be-hind positive holes. The material is de-scribed as p-type, i.e. the charge carriersare positive; the holes are regarded as mo-bile.

Holes in p-type and electrons in n-typesemiconductors are described as majoritycarriers; there are also electrons in p-typeand holes in n-type semiconductors, butthey are in the minority and are called mi-nority carriers.

The electrical properties of semiconduc-tors are related to the fact that in such ma-

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semiconductor

terials there is only a small energy gap be-tween the valence and conduction bands.

Semiconductors have very many uses.They distinguish solid-state devices fromthermionic tubes, now mostly supersededby transistors. See also diode; integratedcircuit; transistor.

semiconductor counter A device for de-tecting ionizing radiation, consisting of asemiconductor crystal with a potential dif-ference across it. Particles striking the crys-tal produce electron-ion pairs, whichincrease the conductivity of the crystal fora brief period. Pulses of current are thusproduced, and can be counted.

semiconductor diode See diode.

series Elements in a circuit are in series ifconnected so that each carries the samecurrent in turn.

For resistors in series, the resulting re-sistance is given by:

R = R1 + R2 + R3 + …For cells in series, the resulting e.m.f. isgiven by:

E = E1 + E2 + E3 + …For capacitors in series, the resulting ca-pacitance is given by:

1/C = 1/C1 + 1/C2 + 1/C3 + …Compare parallel.

series-wound motor An electric motorin which the field winding is connected inseries with the armature winding. Series-wound motors are used for applications inwhich a high starting torque is required(e.g. in cranes). Initially the current is veryhigh through both armature and field coil,and the torque is large. Series-wound mo-tors, however, are less suitable than shunt-wound motors for maintaining steadyspeeds. Compare shunt-wound motor.

sextant /sex-tănt/ A navigational instru-ment used for the accurate measurement ofthe angle of a heavenly body above thehorizon. Two mirrors are used: one sightsthe object; the other, part silvered, reflectsan image of that object as well as showingthe horizon.

shadow The result of the interception of

semiconductor counter

224

Shadow formationwith a point source

Shadow formationwith an extendedsource: A is the edgeof the umbra; B isthe dark edge of thepenumbra; C is alighter region ofthe penumbra

point source

umbra

screen

penumbraumbra

the shadow on the screen

point source

obstacle

AB

C

obstacle

Shadow

light by an opaque obstacle. As light raystravel in straight lines, light from thesource cannot be detected behind the ob-stacle. A point source of light will producea very sharp dark shadow behind an obsta-cle. This is called an umbra (total shadow).A larger extended source will also producean umbra behind an obstacle. Howeverthis will be surrounded by a penumbra(partial shadow). Each point in the penum-bra will receive some light, so will not be intotal shadow. Exactly the same ideas applyto shadows formed in other radiations.

shear modulus See elastic modulus.

shear strain See strain.

shell See electron shell.

SHF See superhigh frequency.

shielding The existence of a barrier thatprevents bodies on one side of the barrierfrom the full effects of a field on the otherside of the barrier. For example, barrierscan be put round a body to protect it fromelectric or magnetic fields or, in the case ofa nuclear reactor, to prevent dangerous ra-diation from escaping from the reactor. Inatoms, the inner electrons can be regardedas a barrier that prevents the outer elec-trons from feeling the full electrostatic at-traction of the positive nuclear charge.

s.h.m. See simple harmonic motion.

shock wave A high-intensity sound wavein air resulting from lightning or an explo-sion, or produced by an object travelingfaster than the speed of sound in air.

short circuit The connection of twopoints in an electric circuit across a verylow resistance, so that most of the currentbypasses part of the circuit. Short circuitsmay occur accidentally because of wiringfaults.

short sight See myopia.

shunt An element connected in parallelwith another component and used to take

part of the current in an electrical circuit.Thus, a low resistance in parallel with anammeter, whose value can be selected inorder to change the range of the meter, iscalled a shunt.

shunt-wound motor An electric motorin which the field winding is connected inparallel with the armature winding. Shunt-wound motors are used for maintaining afairly steady speed (e.g. in machine tools).If the load increases the back e.m.f. fallsand the current increases, tending to main-tain the speed. Compare series-woundmotor.

SI See SI units.

sideband A range of frequencies con-tained in a modulated carrier wave, eitherabove or below the unmodulated fre-quency (hence upper and lower sidebands).The existence of sidebands is a conse-quence of the modulation process. For in-stance, in an amplitude modulated wave, ifthe carrier frequency is fc and the modulat-ing signal frequency is fs, then the modu-lated wave has three components offrequency fc – fs, fc, and fc + fs. See also car-rier wave; modulation.

sidereal /sÿ-deer-ee-ăl/ Based on the stars,used especially of measurements.

sidereal time See day; time; year.

siemens /see-mĕnz/ (mho) Symbol: S TheSI unit of electrical conductance, equal to aconductance of one ohm–1. The unit isnamed for the German electrical engineerErnst Werner von Siemens (1816–92).

sievert /see-vert/ Symbol: Sv. The derivedSI unit of dose equivalent of ionizing radi-ation on living tissue, equal to one joule perkilogram. It is the absorbed dose multi-plied by a factor that takes account of therelative effectiveness of different types ofradiation of a given energy in causing bio-logical damage. The statutory limits for ex-posure of the whole body, or specifiedparts of the body, of various categories ofperson are expressed in terms of this unit.

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sievert

The unit is named for the Swedish physicistRolf Sievert (1898–1966). See gray; rem;ionizing radiation.

sigma particle See elementary particles.

signal-to-noise ratio The ratio of theamplitude of an electrical signal to the av-erage amplitude of the unwanted electricaldisturbances (the noise).

sign convention A set of rules for deter-mining the signs of distances related byvarious formulae in optics. In the real ispositive, virtual is negative system, dis-tances to real objects, images, and focalpoints are positive; distances to virtualpoints are negative. The other main signconvention is the New Cartesian conven-tion. Intended to relate directly to the signconvention in the mathematical treatmentof Cartesian coordinates, it treats distancesto the right of the pole as positive; dis-tances to the left of it are negative.

silicon /sil-ă-kŏn/ A hard brittle gray met-alloid element. It has the electronic config-uration of neon with four additional outerelectrons; i.e., [Ne]3s23p2. Silicon accountsfor 27.7% of the mass of the Earth’s crustand occurs in a wide variety of silicateswith other metals, clays, micas, and sand,which is largely SiO2. It is used widely insemiconductor applications.

Symbol: Si; m.p. 1410°C; b.p. 2355°C;r.d. 2.329 (20°C); p.n. 14; r.a.m. 28.0855

silicon chip An INTEGRATED CIRCUIT man-ufactured from a thin wafer of silicon. Itconsists of alternate semiconductor and in-sulator layers into which the circuit isetched.

silver A transition metal that occurs na-tive and as the sulfide and chloride. It is ex-tracted as a by-product in refining copperand lead ores. Silver darkens in air due tothe formation of silver sulfide. It is used incoinage alloys, tableware, and jewelry. Sil-ver compounds are used in photography.

Symbol: Ag; m.p. 961.93°C; b.p.2212°C; r.d. 10.5 (20°C); p.n. 47; r.a.m.107.8682.

simple harmonic motion (s.h.m.) Anymotion that can be drawn as a sine wave.Examples are the simple oscillation (vibra-tion) of a pendulum or a sound source andthe variation involved in a simple wavemotion. Simple harmonic motion is ob-served when the system, moved away fromthe central position, experiences a restor-ing force proportional to the displacementfrom this position.

The equation of motion for such a sys-tem can be written in the form:

md2x/dt2 = –λxλ being a constant. During the motionthere is an exchange of kinetic and poten-tial energy, the sum of the two being con-stant (in the absence of damping). Theperiod (T) is given by:

T = 1/for

T = 2π/ωwhere f is frequency and ω is the pulsa-tance. Other relationships are:

x = x0sinωtdx/dt = ±ω√(x0

2 – x2)d2x/dt2 = –ω2x

Here x0 is the maximum displacement;i.e. the amplitude of the vibration. In thecase of angular motion, as for a pendulum,θ is used rather than x.

sigma particle

226

TYPICAL FORMS OF SIMPLE HARMONIC MOTION

System Period Symbol Notes

mass on spring 2π√(m/k) k = spring constant Hooke’s law region

uniform bobbing float 2π√(h/g) h = immersion at rest

liquid in U-tube 2π√(l/2g) l = column length

simple pendulum 2π√(l/g) l = pendulum length approximate s.h.m.

simple pendulum See pendulum.

sine wave The waveform resulting fromplotting the sine of an angle against theangle. Any motion that can be plotted so asto give a sine wave is a simple harmonicmotion.

singularity A point in space–time, such asthe center of a BLACK HOLE or the source ofthe BIG BANG, for which general relativitytheory predicts that certain physical quan-tities have an infinite value. The existenceof singularities is usually interpreted as alimitation of general relativity theory. It ishoped that a quantum theory of gravitywill deal with the problem of singularitiesin physics.

sinusoidal /sÿ-ŭ-soid-ăl/ Describing aquantity that has a waveform that is a sinewave.

siphon A device consisting of an invertedU-tube full of liquid used for moving a liq-uid from one place to another at a lowerlevel.

siren /sÿ-rĕn/ A device for producing loudsounds consisting of a disk with radial lou-vers which is rotated at high speed. Airpasses at high pressure through the lou-vers, generating a wailing sound. The termsiren is also applied to various devices thatproduce loud noises electronically.

SI units (Système International d’Unités)The modern, coherent, rationalized inter-nationally adopted metric system of units.It has seven base units (the kilogram, sec-ond, kelvin, meter, ampere, mole, and can-dela) and two dimensionless units,formerly called supplementary units (theradian and steradian). Derived units areformed by multiplication and/or divisionof base units; a number have special names.Standard decimal prefixes are used formultiples and submultiples of SI units.

skin effect The phenomenon that causesvery high-frequency electric currents totravel in only the thin outermost layer of

metal in a conductor (or the innermostlayer of a waveguide).

sky wave A radio wave that is transmit-ted between points by reflection from theionosphere (a region of electrons andcharged particles high in the Earth’s at-mosphere). Compare ground wave.

slide projector See projectors.

sliding friction See friction.

slip A way in which plastic deformation ofa metal occurs. Slabs consisting of manylayers of atoms within the metal grains slipover each other in one or more slip planes.See also creep.

slow neutron (thermal neutron) A neu-tron with low energy which can be cap-tured by an atomic nucleus, particularly toinitiate NUCLEAR FISSION. See fast neutron;moderator.

Snell’s law See refraction; laws of.

sodium /soh-dee-ŭm/ A soft reactivemetal. It has the electronic configuration ofa neon structure plus an additional outer 3selectron. Electronic excitation in flames orthe familiar sodium lamps gives a distinc-tive yellow color arising from intense emis-sion at the so called ‘sodium-D’ line pair.The metal has a body-centred structure.

Symbol: Na; m.p. 97.81°C; b.p. 883°C;r.d. 0.971 (20°C); p.n. 11; r.a.m.22.989768.

soft iron A form of iron (containing littlecarbon) that can easily be magnetized, butdoes not retain its magnetization when theexternal field is removed. Many such sub-stances are now known. They are of greatvalue as the core material of electromag-netic machines, such as transformers, gen-erators, and electromagnets.

soft vacuum See vacuum.

solar cell A device for generating electric-ity using solar energy. See photocell.

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solar cell

solar constant

228

BASE AND SUPPLEMENTARY SI UNITS

Physical quantity Name of SI unit Symbol for SI unitlength meter mmass kilogram kgtime second selectric current ampere Athermodynamic temperature kelvin Kluminous intensity candela cdamount of substance mole mol*plane angle radian rad*solid angle steradian sr

*supplementary units

DERIVED SI UNITS WITH SPECIAL NAMES

Physical quantity Name of SI unit Symbol for SI unitfrequency hertz Hzenergy joule Jforce newton Npower watt Wpressure pascal Paelectric charge coulomb Celectric potential difference volt Velectric resistance ohm Ωelectric conductance siemens Selectric capacitance farad Fmagnetic flux weber Wbinductance henry Hmagnetic flux density tesla Tluminous flux lumen lmilluminance (illumination) lux lxabsorbed dose gray Gyactivity becquerel Bqdose equivalent sievert Sv

DECIMAL MULTIPLES AND SUBMULTIPLES USED WITH SI UNITS

Submultiple Prefix Symbol Multiple Prefix Symbol10–1 deci- d 101 deca- da10–2 centi- c 102 hecto- h10–3 milli- m 103 kilo- k10–6 micro- µ 106 mega- M10–9 nano- n 109 giga- G10–12 pico- p 1012 tera- T10–15 femto- f 1015 peta- P10–18 atto- a 1018 exa- E10–21 zepto- z 1021 zetta- Z10–24 yocto- y 1024 yotta- Y

solar constant See irradiance.

solar eclipse See eclipse.

solar energy Energy from the Sun, mainlyelectromagnetic radiation consisting oflight (including ultraviolet) and heat. TheSun’s rays are directly used to heat water ina heat exchanger (radiator) or, directed bymirrors, to produce high temperatures in asolar furnace. Solar energy can be con-verted into electricity using photocells. Seeheat exchanger; photocell.

solar neutrino problem The problemthat, in experiments, fewer neutrinos aredetected being emitted from the Sun thantheories of the nuclear processes in the Sunpredict. It is now thought that NEUTRINO

OSCILLATIONS between the different types ofneutrino can modify the theory to explainthe discrepancy.

solar system The system consisting of theSun, the planets that orbit round it, themoons of the planets, and the asteroids,comets, and other celestial objects thathave their motion dictated by their gravita-tional interactions with the Sun. The Suncontains well over 99% of the mass of thesolar system.

solar time See day; time; year.

solenoid /soh-lĕ-noid/ A tight coil of insu-lated wire with a diameter that is smallcompared with the length. When carryinga current, the solenoid’s external magneticfield is similar to that of a bar magnet. Itcan be used as an electromagnet if a core ofsoft iron is used.

The flux density is given by µ0NI/l,where N is the number of turns, I the cur-rent, and l the length.

solid See states of matter.

solid angle Symbol: Ω The three-dimen-sional analog of angle; it is subtended at apoint by a surface (rather than by a line).The unit is the STERADIAN (sr), which is de-fined analogously to the radian (rad) – thesolid angle subtending unit area at unit dis-

tance. As the area of a sphere is 4πr2, thesolid angle corresponding to the revolution(2π radians) is 4π steradians.

solidification /sŏ-lid-ă-fă-kay-sŏn/ Seefreezing.

solid solution A solid homogeneousphase consisting of two or more sub-stances. Many metal alloys are solid solu-tions.

solid state Describing electronic devicesthat use semiconductor circuit elementsrather than thermionic tubes.

solid-state physics The branch of physicsthat deals with matter in the solid phase,especially SEMICONDUCTORS and supercon-ductors. See superconductivity.

solubility /sol-yŭ-bil-ă-tee/ A measure ofhow much solute will dissolve in a givensolvent; usually the temperature is alsospecified because solubility can vary widelywith temperature. Solubility is generallyexpressed as mass per unit volume or as apercentage.

solute /sol-yoot, soh-loot/ A substancethat dissolves in a solvent to form a solu-tion.

solution A homogeneous mixture, usuallyliquid, of a solute and a solvent. See alsomolar; solid solution.

solvent /sol-vĕnt/ A substance, usually liq-uid, in which a solute dissolves to form asolution.

sonar /soh-nar/ (asdic) An acronym forsound navigational ranging. A techniquefor locating objects underwater by trans-mitting a pulse of ultrasonic ‘sound’ anddetecting the reflecting pulse. The timedelay between transmission of the pulseand reception of the reflected pulse indi-cates the depth of the object. An apparatusfor determining depths in this way is calledan echo sounder.

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sonar

sone /sol-vĕnt/ A unit of loudness, equal to40 PHON or 40 decibels above the averagethreshold of hearing.

sonic boom A shock wave that is createdwhen an object is moving faster than thespeed of sound in the atmosphere of theEarth. The loud boom occurs when thewave given off by the object hits the Earth’ssurface.

sonometer /sŏ-nom-ĕ-ter/ (monochord) Adevice for investigating the vibration of afixed string or wire. Essentially, it is a hol-low box with the wire stretched across thetop. One end of the wire is fixed; the otherpasses over a pulley and supports a load,which gives it tension. The vibrating lengthof wire is determined by two inverted V-shaped bridges under the wire. The wire isplucked and the note determined by com-parison with tuning forks. In this way theeffect of length and tension can be investi-gated. The frequency (f) produced is givenby

f = (1/2l)√(T/m).where l is the length, T the tension, and mthe mass per unit length of the string.

sorption /sorp-shŏn/ Absorption of gasesby solids.

sorption pump A type of vacuum pumpin which gas is removed from the system byabsorption onto a porous solid (e.g. zeoliteor charcoal) cooled in liquid nitrogen.

sound Vibrations transmitted by air, orsome other material medium, in the formof alternate compressions and rarefactionsof the medium. Sound is often called apressure wave. Sound is a longitudinalwaveform, and is characterized by its pitch(frequency), loudness (intensity), and qual-ity. The speed of sound depends on themedium transmitting it. In air at 0°C it is331.3 meter second–1, in water at 25°C it is1498 meter second–1, and in glass at 20°Cit is 5000 meter second–1. The speed ofsound in a medium is given by:

V = √(E/ρ)where ρ is the density of the medium and Ea modulus of elasticity. For a solid rod, E is

the Young modulus; for a broad solid spec-imen it is the axial modulus; for liquids andgases, it is the adiabatic bulk modulus. Ex-cept at high pressures, this gives for gases:

V = √(γp/ρ)where p is the pressure and γ the ratio ofthe principal specific heat capacities. Thisis equivalent to

V = √(γRT/M)where R is the molar gas constant, T thethermodynamic temperature, and M themass of one mole of the gas. V is indepen-dent of pressure and is proportional to thesquare root of the temperature.

Solids also transmit transverse and tor-sional vibrations at a speed given by

V = √(G/ρ)where G is the shear modulus.

source See field-effect transistor.

south pole See poles; magnetic.

space charge A region in a vacuum, gas,or semiconductor in which there is a netelectric charge resulting from an excess ordeficiency of electrons.

space-time In Newtonian (pre-relativity)physics space and time are separate and ab-solute quantities; that is they are the samefor all observers in any FRAME OF REFER-ENCE. An event seen in one frame is alsoseen in the same place and at the same timeby another observer in a different frame.

After Einstein had proposed his theoryof relativity, Minkowski suggested thatsince space and time could no longer be re-garded as separate continua, they shouldbe replaced by a single continuum of fourdimensions, called space-time. In space-time the history of an object’s motion inthe course of time is represented by a linecalled the ‘world curve’. See also relativity.

spark, electric See electric spark.

spark chamber An apparatus for detect-ing ionizing particles and making theirtracks visible. A stack of up to 100 platesare connected alternately to a source ofpositive and negative high-voltage electric-ity and the chamber is filled with helium

sone

230

and neon. An incoming particle creates ionpairs along its track, the gas becomes con-ducting, and sparks jump between theplates (and can be photographed).

spark counter A type of detector forcounting alpha particles. It consists of awire (or mesh) held a close distance abovean earthed plate. The wire has a high posi-tive potential, less than that required tocause a spark. When an alpha particlepasses close to the wire the electric field in-creases and a spark occurs between theelectrodes. The sparks can be counted by asuitable circuit.

special theory See relativity.

specific /spĕ-sif-ik/ Denoting a physicalquantity per unit mass. For example, vol-ume (Vm) per unit mass (m) is called spe-cific volume: Vm = V/m. In certain physicalquantities the term does not have thismeaning: for example, the old term specificgravity is properly called relative density;likewise specific resistance is resistivity.

specific activity For a radioisotope, thenumber of disintegrations per unit massper unit time.

specific gravity See relative density.

specific heat See specific thermal capac-ity.

specific humidity See humidity.

specific latent heat See latent heat.

specific latent thermal capacity See la-tent heat.

specific resistance See resistivity.

specific rotatory power Symbol: αm Therotation of plane-polarized light in degreesproduced by a 10 cm length of solutioncontaining 1 g of a given substance per mil-liliter of stated solvent. The specific rota-tory power is a measure of the opticalactivity of substances in solution. It is mea-sured at 20°C using the D-line of sodium.

specific thermal capacity (specific heatcapacity) Symbol: c The heat required toraise the temperature of unit mass of agiven substance by unit temperature. Gen-erally, it is given as the heat in joules thatraises the temperature of one kilogram byone kelvin; the units are then joules perkilogram per kelvin (J kg–1 K–1).

Note that specific THERMAL CAPACITY isthermal capacity per unit mass, and is aproperty of the material or substancerather than of a given sample. Water, forexample, has a specific thermal capacity ofaround 4.2 kJ kg–1 K–1.

Strictly speaking, specific thermal ca-pacities depend on the way in which pres-sure and volume change during heattransfer. Two principal specific heat capac-ities are defined: one at constant pressure(cp) and one at constant volume (cv). Forsolids and liquids these differ by only a fewpercent. The quantity measured directly isalways cp, but cv can then be calculated.For gases, the principal values differ muchmore and both can be measured directly.For an ideal gas,

cp – cv = R/Mwhere R is the molar gas constant and Mthe mass of a mole of gas.

The ratio cp/cv is given the symbol γ(gamma). According to classical theory, inthe case of an ideal gas this depends on thenumber of degrees of freedom (F) of themolecules according to the relationship γ =1 + 2/F.

See also molar thermal capacity.

spectral emissivity See emissivity.

spectral line A particular wavelength oflight emitted or absorbed by an atom, ion,or molecule. See line spectrum.

spectral series A group of related lines inthe absorption or emission spectrum of asubstance. The lines in a spectral seriesoccur when the transitions are all betweenthe same energy level and a set of differentlevels. See also Bohr theory.

spectrograph /spek-trŏ-graf, -grahf/ Aninstrument for producing a photographicrecord of a spectrum.

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spectrograph

spectrometer /spek-trom-ĕ-ter/ 1. Aninstrument for examining the differentwavelengths present in electromagnetic ra-diation. A simple type of spectrometer hasa flat rotatable table on which a prism ordiffraction grating is placed. Light is di-rected onto this through a collimator tube,and the transmitted light is observedthrough a telescope. The telescope can bemoved on an angular scale, so that differ-ent wavelengths of radiation can be seen.

There are many other types of spec-trometer for producing and investigatingspectra over the whole range of the electro-magnetic spectrum. Often spectrometersare called spectroscopes.2. Any of various other instruments for an-alyzing the energies, masses, etc., of parti-cles. See mass spectrometer.

spectrophotometer /spek-troh-foh-tom-ĕ-ter/ A form of spectrometer able to mea-sure the intensity of radiation at differentwavelengths in a spectrum. Spectropho-tometers can be made to work with in-frared and ultraviolet radiation as well aswith visible radiation.

spectroscope /spek-trŏ-skohp/ An instru-ment for examining the different wave-lengths present in electromagneticradiation. See also spectrometer.

spectroscopy /spek-tros-kŏ-pee/ 1. Theproduction and analysis of spectra. Thereare many spectroscopic techniques de-signed for investigating the electromag-netic radiation emitted or absorbed bysubstances. Spectroscopy, in variousforms, is used for analysis of mixtures, foridentifying and determining the structuresof chemical compounds, and for investigat-ing energy levels in atoms, ions, and mole-cules. In astronomy it is used fordetermining the composition of celestialobjects and for measuring red shifts.2. Any of various techniques for analyzingthe energy spectra of beams of particles orfor determining mass spectra.

spectrum (pl. spectra) /spek-trŭm/ 1. Arange of electromagnetic radiation emittedor absorbed by a substance under particu-

lar circumstances. In an emission spec-trum, light or other radiation emitted bythe body is analyzed to determine the par-ticular wavelengths produced. The emis-sion of radiation may be induced by avariety of methods; for example, by hightemperature, bombardment by electrons,absorption of higher-frequency radiation,etc. In an absorption spectrum radiationwith a continuous spectrum is passedthrough the sample. The radiation is thenanalyzed to determine which wavelengthsare absorbed. See also band spectrum; con-tinuous spectrum; line spectrum.2. In general, any distribution of a prop-erty. For instance, a beam of particles mayhave a spectrum of energies. A beam ofions may have a mass spectrum (the distri-bution of masses of ions). See mass spec-trometer.

spectrum, electromagnetic See electro-magnetic spectrum.

specular reflection /spek-yŭ-ler/ See re-flection.

speed Symbol: c Distance moved in unittime: c = d/t. Speed is a scalar quantity; theequivalent vector is velocity, or displace-ment in unit time.

Usage can be confusing. It is commonto meet the word velocity where speed ismore correct. For instance c0 is the speed oflight in free space, not its velocity; tempera-ture relates to the root-mean-square speedof particles.

speed of light A fundamental constantequal to 2.997 924 58 × 108 m s–1. Seelight.

speed of sound See sound.

spherical aberration See aberration.

spherical polar coordinates A methodof defining the position of a point in spaceby its radial distance, r, from a fixed point,the origin O, and its angular position onthe surface of a sphere centred at O. Theangular position is given by two angles θand φ. θ is the angle that the radius vector

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makes with a vertical axis through O (fromthe south pole to the north pole). It is calledthe co-latitude. For points on the verticalaxis above O, θ = 0. For points lying in the‘equatorial’ horizontal plane, θ = 90°. Forpoints on the vertical axis below O, θ =180°. φ is the angle that the radius vectormakes with an axis in the equatorial plane.It is called the azimuth. For all points lyingin the axial plane, that is, on, verticallyabove, or vertically below this axis, φ = 0on the positive side of O and φ = 180° onthe negative side. This plane correspondsto the plane y = 0 in rectangular Cartesiancoordinates. For points in the verticalplane at 90° to this, (x = 0 in rectangularCartesian coordinates) φ = 90° in the posi-tive half-plane and 270° in the negativehalf-plane. For a point P(r,θ,φ), the corre-sponding rectangular Cartesian coordi-nates (x,y,z) are:

x =rcosφsinθy = rsinφsinθ

z =rcosθCompare cylindrical polar coordinates.

spherometer /sfi-rom-ĕ-ter/ An instru-ment for measuring the curvature of aspherical surface.

spin A property of certain elementary par-ticles whereby the particle acts as if it werespinning on an axis; i.e. it has an angularmomentum. Such particles also have amagnetic moment. In a magnetic field thespins line up at an angle to the field direc-tion and precess around this direction. Cer-tain definite orientations to the fielddirection occur such that msh/2π is thecomponent of angular momentum alongthis direction. ms is the spin quantum num-ber and h is the Planck constant. For anelectron it has values +½ and –½.

spinthariscope /spin-tha-ră-skohp/ Aninstrument for observing the scintillationsproduced by ionizing radiation when itstrikes a zinc sulfide screen.

S-pole See poles; magnetic.

square wave A stream of regular on-offpulses, usually in an electrical signal. Thepulses are of equal height and the durationof each pulse is the same as the interval be-tween them.

stability A measure of how hard it is todisplace an object or system from EQUILIB-RIUM.

Three cases are met in statics (see equi-librium). They differ in the effect on thecenter of mass of a small displacement. Anobject’s stability is improved by: (a) lower-ing the center of mass; or (b) increasing thearea of support; or by both. See also virtualwork.

stable equilibrium Equilibrium such thatif the system is disturbed a little, there is atendency for it to return to its originalstate. See equilibrium; stability.

standard cell A voltaic cell whose e.m.f.is used as a standard. See Clark cell; We-ston cadmium cell.

standard electrode A half cell used formeasuring electrode potentials. The hydro-gen electrode is the basic standard but, inpractice, calomel electrodes are usuallyused.

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centimeter/millimeterscale micrometer

scale

Spherometer

standard model The combination ofQUANTUM CHROMODYNAMICS and the WEIN-BERG–SALAM MODEL. In spite of its greatsuccess in describing all the non-gravita-tional interactions it is not a complete the-ory of elementary particles, firstly becauseit does not include gravity and secondly be-cause many quantities of interest such asthe mass of electrons, are empirical para-meters rather than calculated from firstprinciples. There are theories of elementaryparticles that attempt to go beyond thestandard model including GRAND UNIFIED

THEORIES and SUPERSTRING THEORY. Seequark.

standard near-point distance See near-point.

standard pressure An internationallyagreed value; a barometric height of 760mmHg at 0°C; 101 325 Pa (approximately100 kPa).

This is sometimes called the atmosphere(used as a unit of pressure). The millibar,used mainly in meteorology, is 100 Pa ex-actly.

standard temperature An internation-ally agreed value for which many measure-ments are quoted. It is the meltingtemperature of water, 0°C (273.15 K). Seealso STP.

standard temperature and pressure SeeSTP.

standing wave See stationary wave.

star A heavenly body that generates itsown light. The Sun is the most familiar ex-ample of a star. The heat and light given offby stars is due to nuclear fusion reactionsinside the star. Stars gather together ingalaxies.

Stark effect The splitting and displace-ment of atomic spectral lines in a strongtransverse electric field. The effect is namedfor the German physicist Johannes Stark(1874–1957). See also Zeeman effect.

stat- A prefix used with a practical c.g.s.electrical unit to name the correspondingelectrostatic unit. For example, the electro-static unit of charge is called the stat-coulomb. Compare ab-.

states of matter The three states – solid,liquid, and gas – in which matter normallyexists.

Solids have fixed shapes and volumes –i.e. they do not flow, like liquids and gases,and they are difficult to compress. In solidsthe atoms or molecules occupy fixed posi-tions in space. In most cases there is a reg-ular pattern of atoms – the solid iscrystalline.

Liquids have fixed volumes (i.e. lowcompressibility) but flow to take up theshape of the container. The atoms or mol-ecules move about at random, but they arequite close to one another and the motionis hindered.

Gases have no fixed shape or volume.They expand spontaneously to fill the con-tainer and are easily compressed. The mol-ecules have almost free random motion.

A PLASMA is sometimes considered to bea fourth state of matter.

static electricity 1. See electrostatics.2. Electricity characteristic of charges thatare at rest, as opposed to current electric-ity.

static friction See friction.

static pressure The pressure exerted by afluid at rest, or flowing in such a way thatthe pressure at the point of interest is unaf-fected by the flow.

statics A branch of mechanics dealingwith the forces on an object or in a systemin equilibrium. In such cases there is no re-sultant force or torque and therefore no re-sultant acceleration.

stationary wave (standing wave) The in-terference effect resulting from two wavesof the same type and equal frequency andintensity moving in opposite directions inthe same region. The effect is most oftencaused when a WAVE is reflected back along

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its original path. At certain places the am-plitude of one type of disturbance is a max-imum. These places, which are calledantinodes for this disturbance, occur at aseparation of half a wavelength. Betweenthese are places where this disturbance isalways zero; these are called NODES. Thenodes for one kind of disturbance are an-tinodes for the other. For example, inacoustics the closed end of a resonatingpipe is a pressure antinode, which is a par-ticle-velocity node. Just outside the openend there is a pressure node, which is anantinode for particle velocity. See also in-terference.

statistical mechanics The derivation ofthermodynamics arising from the consider-ation of the distribution of energy (or cer-tain other quantities) among theconstituent particles of a system in equilib-rium.

See Bose–Einstein statistics; entropy;Fermi–Dirac statistics; Maxwell–Boltz-mann statistics

stator /stay-ter/ The fixed part of an elec-tric motor or dynamo; or some similar de-vice. See also rotor.

steam Water in the gaseous state. Notethat the white ‘steam’ seen when boilingwater contains tiny droplets of liquidwater.

steam engine A type of HEAT ENGINE inwhich mechanical energy is generated fromthe pressure of steam. Steam engines wereused extensively in the second half of the19th century and the scientific analysis oftheir performance was one of the factorscontributing to the development of ther-modynamics as a subject. The steam engineis an example of an external combustionengine. See also internal combustion en-gine.

steam point See International PracticalTemperature Scale.

steelyard An ancient weighing device, stillwidely used, as shown or in more complexarrangements. In use, the movable rider is

placed so that the device rests horizontally.The weight of the load is then read fromthe scale directly.

Stefan–Boltzmann constant /stef-ănz/See Stefan’s law.

Stefan’s law The principle that the totalenergy, W, radiated by the surface of aBLACK BODY is proportional to the fourthpower of the thermodynamic temperature(T). For a surface, M = σT4, where M is theenergy radiated per unit area per second.The constant σ is known as the Stefan con-stant and is equal to 5.7 × 10–8 wattmetre–1 kelvin–4 (W m–1 K–4). The law wasproposed by the Austrian physicist JosefStefan (1835–93) in 1879 on experimentalevidence and derived by Boltzmann in1884 by thermodynamic theory. It waslater shown to be a consequence ofPlanck’s radiation law.

stellar dynamics The dynamics of starsinsofar as they interact together in clustersor galaxies. Stellar dynamics is describedby Newtonian gravity. For systems with alarge number of stars Newtonian gravity issometimes combined with the methods ofstatistical mechanics.

step-down transformer A transformerfor reducing an alternating voltage.

step-up transformer A transformer forincreasing an alternating voltage.

steradian /sti-ray-dee-ăn/ Symbol: sr TheSI unit of solid angle, equal to that sub-tended at the center of a sphere by the areaof a square on the sphere’s surface, each of

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l1l2

load F2F1

rider

scale

at balance: F2 /l2 = F1 /l1

Steelyard

whose sides are equal in length to that ofthe sphere’s radius.

stereophony /ste-ree-off-ŏ-nee, steer-ee-/A type of sound reproduction that uses twoor more channels and loudspeakers to pro-duce sounds more like the original than canbe reproduced by monaural techniques.

stereoscope /ste-ree-ŏ-skohp, steer-ee-/ Adevice that shows different views of thesame scene to each eye in such a way as togive the impression of depth. Stereoscopeswere very popular in the last century. Al-though they can be extremely effective,they are now rare.

stereoscopic vision /ste-ree-ŏ-skop-ik,steer-ee-/ See binocular vision.

stilb An m.k.s.a. unit of luminance, equalto the luminance produced by one candela(cd) per square centimeter (cm–2). 1st = 1cdcm–2.

stimulated emission If an atom or mole-cule is in an excited state it may make atransition to a lower-energy state sponta-neously, with emission of a photon. Alter-natively, radiation may be incident on theexcited particle having the same frequencyas would be emitted spontaneously. In thiscase the particle may undergo stimulatedemission. The emitted radiation has thesame direction and phase as the incidentradiation, so the intensity is doubled. Seelaser.

stokes /stohks/ Symbol: St A former unitof kinematic viscosity used in the c.g.s. sys-tem. It is equal to 10–4 m2 s–1. The unit isnamed for the British mathematician andphysicist Sir George Gabriel Stokes(1819–1903).

Stokes’ law 1. The law giving the viscousforce F opposing the motion of a sphere ra-dius r at a low speed c in a fluid of viscos-ity η

F = 6πrηcWhen a sphere falls under gravity the speedincreases until the downward force on itequals F when c has its maximum value,

the terminal speed. Observation of the ter-minal speed can be used to determine vis-cosity.

For speeds such that REYNOLDS’ NUMBER

(ρrc/η) is greater than about unity (ρ is thefluid density) the flow becomes turbulentand the resulting force is greater than thatgiven by Stokes’ law. The fall of a smallraindrop is resisted by viscosity while thatof a large raindrop is opposed by turbulentresistance. Stokes’ law does not apply tolarge rapidly moving bodies such as tennisballs and pendulum bobs. See also turbu-lent flow.2. In fluorescence, the rule that the emittedradiation has longer wavelength than theincident radiation.

stop An aperture, such as an iris or di-aphragm, in an optical system.

storage battery See accumulator.

storage ring A torroidal evacuated ringthat forms a part of some particle accelera-tors. Resembling a synchrotron in design,the ring has a stationary magnetic field tocontain subatomic particles, which may becollided at high energies using two inter-laced rings or by having particles circling ineach direction in a single ring. See acceler-ator.

STP (NTP) Standard temperature andpressure. Conditions used internationallywhen measuring quantities that vary withboth pressure and temperature (such as thedensity of a gas). The values are 101 325Pa (approximately 100 kPa) and 0°C(273.15 K). See also standard pressure;standard temperature.

straight conductor An electrical conduc-tor in the form of a long straight line. Themagnetic flux density for the magnetic fieldassociated with the electric current in along straight conductor can easily be calcu-lated and shown to be inversely propor-tional to the perpendicular distance fromthe conductor.

strain The fractional change in dimensionproduced by a STRESS applied to a body.

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Tensile strain applies to the stretching of abody. It is the change in length divided bythe original length (∆l/l). Bulk strain occurswhen a body is subjected to a change ofpressure. It is the change in volume dividedby the original volume. Shear strain occurswhen an angular deformation occurs, andis equal to the angular displacement pro-duced. See also elasticity; elastic modulus.

strain gauge A device for measuring thestrain or distortion on a surface. Somestrain gauges work by changes in the elec-trical resistance of a wire attached to thesurface. Others use magnetic induction intwo coils, one fixed to the surface. Capaci-tance changes can be used in a similar way.

strange attractor A path in PHASE SPACE

that is not closed. Strange ATTRACTORS arecharacteristic of chaotic behavior.

strangeness See quark.

streamline A line following the directionof the fluid in LAMINAR FLOW or streamlineflow. Where the speed increases, as it doesin a narrower section of a pipe, the stream-lines are closer together.

stress When a system of opposing forcesacts on a body the material is subject tosome form of stress. This is expressed interms of one of the forces divided by thearea on which it acts. Bulk stress is achange of pressure applied to a fluid, or ap-plied by a fluid to a solid. Tensile stress is astress that stretches a body. Shear stresscauses a deformation without any changeof volume. See also elasticity; elastic mod-ulus; strain.

string A one-dimensional object that ap-pears in elementary-particle theory. Stringssometimes appear as solutions of the equa-tions of quantum field theories. For exam-ple, cosmic strings are solutions for certaingrand unified theories. Strings are the fun-damental entities in string theories, i.e. the-ories in which pointlike elementaryparticles are replaced by strings of a finitelength (open strings) or loops (closedstrings). SUPERSTRING THEORY is the combi-

nation of string theory and SUPERSYMME-TRY.

strobe /strohb/ See stroboscope.

stroboscope /stroh-bŏ-skohp/ (strobe) Adevice that allows something to be viewedas a series of short separate scenes, ratherthan continuously. It may be a light givingregular short intense flashes, or a rotatingdisk with slots through which the system isviewed. Stroboscopes are used in physics toinvestigate periodic motions (rotation orvibration). If the frequency of the illumina-tion is equal to the frequency of vibration,the system is seen at the same point in itscycle at each view, and appears stationary.

strong interaction See interaction.

strontium /stron-shee-ŭm, -tee-/ A softlow-melting reactive metal. The electronicconfiguration is that of krypton with twoadditional outer 5s electrons.

Symbol: Sr; m.p. 769°C; b.p. 1384°C;r.d. 2.54 (20°C); p.n. 38; r.a.m. 87.62.

strontium unit Symbol S.U. A measure ofthe concentration of the radioisotopestrontium-90 in bones, milk, or soil in rela-tion to their calcium content.

subatomic particles /sub-ă-tom-ik/ Seeelementary particles.

subcritical /sub-krit-ă-kăl/ Describing anarrangement of fissile material that doesnot permit a sustained chain reaction be-cause too many neutrons are absorbedwithout causing fission or otherwise lost.Compare supercritical. See also multiplica-tion factor.

sublimation /sub-lă-may-shŏn/ A directchange of state from solid to vapor withoutmelting.

subsonic /sub-sonn-ik/ Describing a speedthat is less than the speed of sound in themedium concerned. See sound; supersonic.

substance /sub-stăns/ The substance of abody is expressed in terms of the number of

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constituent particles. Compare matter. Seealso mole.

subtractive process /sŭb-trak-tiv/ Aprocess of color mixing by subtraction. Seecolor.

sulfur /sul-fer/ A low melting non-metallicsolid, yellow colored in its common forms.It has the electronic configuration[Ne]3s23p4. The element exhibits allotropyand its structure in all phases is quite com-plex. The common crystalline modifica-tion, rhombic sulfur, is in equilibrium witha triclinic modification above 96°C. Bothhave structures based on S8-rings but thecrystals are quite different. If molten sulfuris poured into water a dark red ‘plastic’form is obtained in a semielastic form. Thestructure appears to be a helical chain of Satoms.

Symbol: S; m.p. 112.8°C; b.p. 444.6°C;r.d. 2.07; p.n. 16; r.a.m. 32.066.

Sun The star that is nearest to the Earth.It is nearly 150 million kilometers from theEarth and has a mass of about 1.9 × 1030

kilograms and a radius of nearly 700 000kilometers. The Sun is about five billionyears old and is about half-way through itslife. The heat and light from the Sun, whichsustains life on Earth, come from nuclearfusion reactions inside the Sun, which con-vert hydrogen into helium.

superatom /soo-per-at-ŏm/ See Bose-Ein-stein condensation.

superconductivity /soo-per-kon-duk-tiv-ă-tee/ Certain substances when cooledbelow a characteristic transition tempera-ture become superconducting; that is, theylose all electrical resistance. At the sametime they exhibit the Meissner effect – theexclusion of magnetic flux. Currents in-duced in circuits of materials in the super-conducting state persist indefinitelywithout measurable change.

Most known superconductors havetransition temperatures of only a fewkelvins, so experiments have to be donewith specimens cooled in liquid helium.Some superconductors with transition tem-

peratures up to about 18 K have beenknown for many years. In the 1980s anumber of ceramic materials were discov-ered that show superconductivity at muchhigher temperatures. Substances areknown that are superconducting at liquid-nitrogen temperatures, and it is possiblethat materials may be produced that aresuperconducting at normal laboratorytemperatures. Superconductors have im-portant practical applications. For exam-ple, very strong magnetic fields can beproduced by using electromagnets with su-perconducting coils (ordinary electromag-nets are limited by the saturation of ironcores at about 2 tesla). Other possible usesmay be in high-speed computers and incheap long-distance power transmission.The theory of ordinary superconductivityis well established in terms of pairs of elec-trons, with the pairing being due to inter-action between the electrons and the latticevibrations. The theory of high-temperaturesuperconductivity is not yet well estab-lished.

supercooling /soo-per-koo-ling/ Thecooling of a liquid at a given pressure to atemperature below its melting temperatureat that pressure without solidifying it. Theliquid particles lose energy but do notspontaneously fall into the regular geomet-rical pattern of the solid. A supercooled liq-uid is in a metastable state and will usuallysolidify if a small crystal of the solid is in-troduced to act as a ‘seed’ for the forma-tion of crystals. As soon as this happens,the temperature returns to the melting tem-perature until the substance has completelysolidified.

supercritical /soo-per-krit-i-kăl/ Describ-ing an arrangement of fissile material thatsustains a branching chain reaction; i.e.more neutrons are being produced than arewasted and escape. Compare subcritical.See also multiplication factor.

superelastic collision /soo-per-i-las-tik/A collision for which the restitution coeffi-cient is greater than one. In effect the rela-tive velocity of the colliding objects afterthe interaction is greater than that before.

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The apparent energy gain is the result oftransfer from potential energy. For exam-ple, if a collision between two trolleyscauses a compressed spring in one to be re-leased against the other, the collision maybe superelastic. See also restitution; coeffi-cient of.

superficial expansivity See expansivity.

superfluidity /soo-per-floo-id-ă-tee/ Aproperty of liquid helium at very low tem-peratures. At 2.186 K liquid helium makesa transition to a superfluid state, which hasa high thermal conductivity and flowswithout friction. The isotope helium-3 alsobecomes a superfluid but at much lowertemperatures than helium-40.

superheating /soo-per-hee-ting/ 1. Theraising of the temperature of a liquid abovethe normal boiling temperature at the ap-plied pressure. See also bumping.2. The raising of the temperature of avapor (usually steam) so that it is above theliquid–vapour equilibrium temperature atthe applied pressure. The vapor is then saidto be superheated or dry. In modern steamturbines the steam is normally passed fromthe boiler into a superheater before enter-ing the turbine. This increases the effi-ciency and reduces damage to the turbineblades. See also efficiency; heat engine.

superheterodyne /soo-per-het-ĕ-roh-dÿn/See heterodyne.

superhigh frequency /soo-per-hÿ/ (SHF)A radio frequency in the range between 30GHz and 3 GHz (wavelength 1–10 cm).

supermembrane theory A theory thatcombines SUPERSYMMETRY with the basicentities being two-dimensional extendedobjects (called membranes). There are seri-ous difficulties with supermembrane the-ory as a starting point for a unified theoryof forces and particles but it may emergefrom M THEORY.

supermodel A model that describes ele-mentary particles that incorporates SUPER-SYMMETRY. Supersymmetric GUTs and the

supersymmetric standard model are exam-ples of supermodels.

supernova The sudden explosive bright-ening of a star that occurs when a large starcollapses to a NEUTRON STAR. A supernovais brighter than the whole of the rest of thegalaxy it occupies. Supernova explosionsare important in NUCLEOSYNTHESIS becausemany of the elements heavier than iron arecreated only in supernova explosions. Inaddition, supernova explosions scatterother elements made inside stars intospace.

superposition, principle of /soo-per-pŏ-zish-ŏn/ See principle of superposition.

supersaturated solution /soo-per-sach-ŭ-ray-tit/ A solution that contains moresolute than a saturated solution at the sametemperature. It is unstable and readily crys-tallizes to form a saturated solution.

supersonic /soo-per-sonn-ik/ Describing aspeed that is greater than the speed ofSOUND in the medium concerned. Seesound; subsonic.

superstring theory /soo-per-string/ Aunified theory of the fundamental interac-tions that combines STRING THEORY withSUPERSYMMETRY. In superstring theory thebasic entities are one-dimensional objectscalled superstrings which are about 10–35m long. This very short distance is equiva-lent to energies of about 1019 GeV.

A purely bosonic string, i.e. a string thatis associated with bosons and does not con-tain fermions is only consistent as a quan-tum theory in 26-dimensional space–time.A superstring contains both bosons andfermions and is only consistent as a quan-tum theory in 10-dimensional space–time.There is some evidence that superstringtheory is free of the infinities that plagueattempts to construct a quantum field the-ory of gravity. However, a complete proofof this has not yet been established.

Superstrings can either be open stringsor closed strings. By the mid 1980s it wasfound that there were five superstring the-ories which are consistent. In the mid-

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1990s it was found that the five types of su-perstring theory and also 11-dimensionalsupergravity theory are related to eachother by a set of dualities. This has led tothe postulate that there may be a theory in11-dimensional space–time called M-the-ory which contains all the five superstringtheories and supergravity theory as limit-ing cases.

supersymmetry /soo-per-sim-ĕ-tree/ Atype of symmetry that can unify fermionsand bosons into one mathematical struc-ture. Supersymmetry is thought to be a fun-damental principle of elementary particletheory, with supersymmetry being a bro-ken symmetry. It is hoped that supersym-metric ‘partners’ of all the knownelementary particles will be discovered bythe end of the first decade of the twenty-first century.

supertransuranics (superheavy ele-ments) The very heavy elements withatomic numbers of about 114, which arepredicted to be relatively stable by nuclearshell theory, with 114 being a magic num-ber. There is some evidence that some ofthese elements have been observed.

supplementary units The dimensionlessunits – the radian and the steradian – usedalong with base units to form derived units.See SI units.

suppressor grid See pentode.

surface charge density See charge den-sity.

surface tension Symbol: γ or σ The at-traction between molecules (cohesion) inthe plane of the surface of a liquid, whichthus acts a bit like an elastic skin contain-ing the liquid. Surface tension explainswhy water can drip slowly from a tap andwhy mercury gathers into globules on a flatsurface. Molecules that are surrounded byothers are, on average, attracted equally inall directions, since the liquid is under pres-sure. At the surface, however, the inter-molecular spacings are larger in the planeof the surface, and the molecules attract

each other. Consequently, the surface layeris in tension.

γ is defined as the force per unit lengthacting normally in the plane of the surfaceon either side of a line in the surface. It ismeasured in units of newton metre–1.Sometimes called free surface energy, itmay also be defined as the work done in in-creasing the surface area by a square meter.Both are defined at given temperature, assurface tension falls with temperature rise.

surfactant /ser-fak-tănt/ (surface activeagent) A substance that reduces the SUR-FACE TENSION of a liquid and thereby im-proves its wetting properties. Surfactantsare used in detergents, foaming agents andwetting agents.

susceptibility /sŭ-sep-tă-bil-ă-tee/ Symbol:χ The ratio, for a given substance, of themagnetization of a sample to the magneticfield strength applied. In SI it equals (µr –1), where µr is the relative permeability.The value of χ determines whether a sub-stance shows paramagnetism, diamagnet-ism, or ferromagnetism. A diamagneticmaterial has a negative susceptibility whileparamagnetic and ferromagnetic materialshave small and large positive susceptibili-ties respectively.

suspension A mixture that consists of afluid in which small solid particles are sus-pended, i.e. the particles neither float norsink but are distributed uniformly through-out the fluid.

switch A mechanical or solid-state devicefor opening and closing an electric circuit.

symmetry The set of invariances of a sys-tem, i.e. the set of operations, known assymmetry operations, on a system thatleave the system unchanged. Examples ofsymmetry operations include rotations andreflections for molecules and translationsfor crystals. Symmetry is studied systemat-ically by a branch of mathematics calledGROUP THEORY. Symmetry and BROKEN

SYMMETRY are two of the most importantconcepts throughout physics and chem-istry.

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synchrocyclotron /sink-rŏ-sÿ-klŏ-tron/ Adevice for accelerating particles to high en-ergies; a development of the cyclotron inwhich the frequency applied to the ‘dees’ isdecreased to compensate for the progres-sively increased period of revolutioncaused by the relativistic increase in massat high energies, typically hundreds ofMeV. For example, the 4.7-m machine atBerkeley in the United States can produceparticles of energy up to 730 MeV. Thesynchrocyclotron is also sometimes calleda frequency modulated (FM) cyclotron.

synchronous motor An electric motorthan runs at a speed proportional to thefrequency of the voltage supply. A rotatingmagnetic field is produced by separatefixed coils energized by an alternating cur-rent supply. This field pulls the rotating

part round with it. The rotating part of thedevice consists of a permanent magnet oran electromagnet. When starting, themotor behaves like an induction motoruntil the synchronous speed is reached. Seealso electric motor; induction motor.

synchronous orbit See parking orbit.

synchrotron radiation /sink-rŏ-tron/Electromagnetic radiation produced byelectric charges that are moving veryrapidly in a magnetic field. Synchrotron ra-diation is used extensively in the study ofmatter and occurs naturally in various as-trophysical contexts, notably in pulsars.

Système International d’Unités /see-stem an-tair-nas-yo-nal doo-nee-tay/ See SIunits.

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242

tachyon /tak-ee-on/ A hypothetical sub-atomic particle that can travel faster thanthe speed of light.

tandem generator An arrangement oftwo linear accelerators end to end. Theends are grounded and there is a commonanode at the center at a potential differenceof up to 20 million volts. Negative ions areaccelerated from ground potential at oneend to the center, where the surplus elec-trons are stripped off to convert them intopositive ions, which then continue to accel-erate to the far end. They thus get the ac-celeration due to the high potential twiceover. Protons can be given energies up to40 MeV.

tangent galvanometer A galvanometerin which a magnetized needle is pivoted torotate in a horizontal plane at the center ofa large fixed vertical coil. Current flowingthrough the coil turns the needle. Tangentgalvanometers are now rarely used.

tantalum /tan-tă-lŭm/ A silvery transitionelement. It is strong, highly resistant to cor-rosion, and is easily worked. Tantalum isused in turbine blades and cutting toolsand in surgical and dental work.

Symbol: Ta; m.p. 2996°C; b.p. 5425 ±100°C; r.d. 16.654 (20°C); p.n. 73; r.a.m.180.9479.

tau-particle /taw, tow/ A type of leptonthat has exceptionally high mass and thesame negative charge as the electron andmuon. See lepton.

technetium /tek-nee-shee-ŭm/ A transi-tion metal that does not occur naturally onEarth. It is produced artificially by bom-barding molybdenum with neutrons and

also during the fission of uranium. It isradioactive.

Symbol: Tc; m.p. 2172°C; b.p. 4877°C;r.d. 11.5 (est.); p.n. 43; r.a.m. 98.9063(99Tc); most stable isotope 98Tc (half-life4.2 × 106 years).

telecommunications Any method ofcommunicating at a distance, usually takento mean those methods that use electricityor radio waves. They include telegraphy,telephony, radio, television, and radar.

telegraphy A form of telecommunica-tions that employs pulses of electricity ascoded signals carried along wires. The sig-nals are send along radio beams in radiotelegraphy.

telemetry A method of sending informa-tion over long distances, usually as a mod-ulated radio signal.

telephony A form of telecommunicationsthat employs a varying electric current tocarry voice signals along wires. The signalsare send along radio beams in radio tele-phony.

telephoto lens A lens that is used in cam-eras to obtain an image of a distant objectwithout using a lens with a very long focallength. A telephoto lens has the combina-tion of a converging lens and a weak di-verging lens, which is nearer the film in thecamera.

telescope An optical system for collectingradiation from a distant object and pro-ducing an enlarged image. Optical tele-scopes use visible radiation. There are twotypes: REFRACTORS (or refracting tele-scopes) in which the light is collected by a

T

converging lens; and REFLECTORS (or re-flecting telescopes) in which a convergingmirror is used. The light collected by theobjective forms an image, which is magni-fied by an eyepiece. A large objective is de-sirable in that it collects more light fromfaint distant objects. A large objective alsominimizes diffraction effects.

Reflector systems have a number of ad-vantages over refractors in theory andpractice, and the largest astronomical tele-scopes are all reflectors. They do not havethe same problems of chromatic aberra-tion; large, comparatively cheap, robustinstruments can give good images. Tele-scopes for non-astronomical use are refrac-tors that produce an upright image (knownas terrestrial telescopes).

The performance of telescopes is de-scribed in terms of:(1) magnifying power – the angular magni-fication obtained (usually the ratio of focaldistance of objective to that of eyepiece).(2) aperture – determining the amount oflight admitted, and thus the minimummagnitude of sources that can be seen.(3) resolving power – the ability to separateimages of close objects.

Telescopes for use in astronomy havebeen developed for other forms of electro-magnetic radiation.

television A form of telecommunicationsthat employs radio to transmit picture(video) and sound (audio) signals over adistance. Closed-circuit television (CCTV)generally operates over only small dis-tances and the signals are carried alongwires.

tellurium /te-loor-ee-ŭm/ A brittle silverymetalloid element belonging to group 16 ofthe periodic table. It is found native and incombination with metals. Tellurium isused mainly as an additive to improve thequalities of stainless steel and various met-als.

Symbol: Te; m.p. 449.5°C; b.p.989.8°C; r.d. 6.24 (20°C); p.n. 52; r.a.m.127.6.

temperature A measure of the ‘hotness’of a body. Heat flows from bodies of

higher temperature to ones at lower tem-perature. It can be shown that the energiesof the particles in a body are related in acomplicated way to temperature, in allcases increasing as the temperature israised. Formerly temperature was definedarbitrarily in terms of the variations in cer-tain physical properties. It is now definedin absolute terms in relation to the laws ofthermodynamics. See also temperaturescale; thermometer; thermodynamic tem-perature.

temperature coefficient A coefficientdetermining how some physical propertychanges with temperature. For example,the temperature coefficient of resistance isthe coefficient in the equation showinghow resistance or resistivity varies withtemperature. See resistance thermometer.

temperature scale A practical scale foruse in measuring temperature. Formerlytemperature scales were defined arbitrarilyin terms of the changes of certain physicalquantities, calibrated at two fixed points.For example, a mercury-in-glass scale wasdefined such that temperature intervalswere proportional to the length of thethread of mercury in the capillary tube of amercury thermometer. The fixed pointswere originally the ice point and the nor-mal human body temperature. The latterwas later replaced by the steam point. Thedifference between the fixed points wascalled the fundamental interval. This inter-val was divided into temperature units. Inthe case of the Celsius (centigrade) scale theinterval between the ice and steam pointswas 100 degrees. Such arbitrary scales nec-essarily agree at the fixed points, but gen-erally differ at other temperatures. Thus acertain temperature might be 200°C on amercury-in-glass scale, 210°C on a certainresistance thermometer scale, 198°C on acertain constant-volume gas scale, and soon.

Modern thermometry is based uponKelvin’s thermodynamic (ideal gas) scale,which is independent of the properties ofany real substance. It has one fixed point,the triple point of water. The unit (thekelvin, K) is defined so that the triple point

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temperature scale

is at 273.16 K measured from absolutezero. In practice, temperatures are meas-ured on the International Practical Tem-perature Scale (1968), which is defined byeleven fixed points together with standardmethods of measurement between thesepoints, so as to reproduce the theoreticalscale as nearly as possible.

On the absolute thermodynamic scalethe ice point is 273.15 K and the steampoint is 373.15 K. Hence it is possible touse a Celsius thermodynamic scale wherethe ice point is 0°C and the steam point is100°C. The degrees have the same size onthe Celsius and absolute scales.

temporary magnetism Substances showtemporary magnetism if any magnetismdisappears as soon as the inducing field isremoved. They are easy to magnetize, andare often called ‘soft’, as in ‘soft iron’.

tensile strain See strain.

tensile strength The tensile stress atwhich a material breaks apart or deformspermanently.

tensimeter /ten-sim-ĕ-ter/ A device thatmeasures the difference in vapor pressuresbetween two liquids.

tension A stretching force. See strain;stress; surface tension.

tensometer /ten-som-ĕ-ter/ A machine formeasuring the tensile strength and othermechanical properties of materials.

tera- Symbol: T A prefix denoting 1012.For example, 1 terawatt (TW) = 1012 watts(W).

terbium /ter-bee-ŭm/ A soft ductile mal-leable silvery rare element of the lan-thanoid series of metals. It occurs inassociation with other lanthanoids. One ofits few uses is as a dopant in solid-state de-vices.

Symbol: Tb; m.p. 1356°C; b.p. 3123°C;r.d. 8.229 (20°C); p.n. 65; r.a.m.158.92534.

terminal A point in an electric circuit towhich a connecting lead can be attached.

terminal speed The steady final speedreached by a body in a fluid when the re-sultant force on it is zero.

terrestrial magnetism See Earth’s mag-netism.

terrestrial telescope A refracting tele-scope for non-astronomical use: oneproducing an erect image. Terrestrial tele-scopes are either GALILEAN TELESCOPES orKEPLERIAN TELESCOPES with added invertinglenses. See also refractor.

tesla /tess-lă/ Symbol: T The SI unit ofmagnetic flux density, equal to a fluxdensity of one weber per square meter. 1 T= 1 Wb m–2. The unit is named for theCroatian–American physicist Nikola Tesla(1856–1943).

Tesla coil A device for producing highvoltage oscillations from a low voltage di-rect current source. It consists of a trans-former with a high ratio of secondary toprimary turns and a make-and-breakmechanism to interrupt the current in thesecondary circuit.

tetrode /tet-rohd/ A THERMIONIC TUBE

with one grid more than the TRIODE, calledthe screen grid. It is placed between thecontrol grid and the anode, and is normallykept at a fixed positive potential. The pur-pose of the screen grid is to minimize thecapacitance between the control grid andthe anode and thus improve the high-fre-quency performance of the triode as an am-plifier or oscillator.

A disadvantage of the tetrode is that, athigh anode voltages, secondary electronsemitted from the anode are captured by thescreen grid, causing a drop in the anodecurrent. This is overcome in the PENTODE.

thallium /thal-ee-ŭm/ A soft malleablegrayish metallic element belonging togroup 13 of the periodic table. Thallium ishighly toxic and was used previously as arodent and insect poison. Various com-

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pounds are now used in photocells, in-frared detectors, and low-melting glasses.

Symbol: Tl; m.p. 303.5°C; b.p. 1457°C;r.d. 11.85 (20°C); p.n. 81; r.a.m.204.3833.

theodolite /th’ee-od-ŏ-lÿt/ An optical in-strument (using prisms and lenses) formeasuring horizontal and vertical angleswith great accuracy. It is an essential toolin surveying.

theorem of parallel axes If I0 is the mo-ment of inertia of an object about an axis,the moment of inertia I about a parallelaxis is given by:

I = I0 + md2

m is the mass of the object and d is the sep-aration of the axes.

theory of everything (TOE) A unifiedtheory of all the fundamental interactions,elementary particles, and cosmology. Atheory of everything will involve a modelthat accounts for both quantum mechanicsand gravity. It is hoped that SUPERSTRING

THEORY will be developed into such atheory.

therm A unit of heat energy equal to 105

British thermal units (1.055 056 joules).

thermal capacity (heat capacity) Symbol:C The heat required to raise the tempera-ture of a body by one unit. It is usually injoules per kelvin (J K–1). The thermal ca-pacity may be affected by volume changes.Two principal thermal capacities are de-fined – one at constant pressure (Cp) andone at constant volume (Cv). For liquidsand solids, these may differ by only a fewpercent, but for gases the differences aremuch larger. See also molar thermal capac-ity; specific thermal capacity.

thermal conductivity See conductivity(thermal).

thermal diffusion A method of separat-ing gas molecules of different masses bymaintaining one part of the gas at a lowertemperature than the other (i.e. producinga temperature gradient along a column of

gas) – the more massive molecules tend tostay at the low-temperature end. It can beused for the separation of isotopes.

thermal equilibrium A state in whichthere is no net flow of heat. If two bodiesare in thermal equilibrium, then they havethe same temperature. See also equilib-rium.

thermal expansion See expansion; ther-mal.

thermalization /ther-mă-li-zay-shŏn/ Theslowing down of FAST NEUTRONS to thermalenergies (converting them to SLOW NEU-TRONS) so that they can initiate nuclear fis-sion. In a nuclear reactor, it is carried outby a MODERATOR.

thermal neutron See moderator; slowneutron.

thermal radiation See radiant heat; radi-ation.

thermal reactor See nuclear reactor.

thermionic diode /ther-mee-on-ik/ Seediode

thermionic emission The emission ofelectrons from the surface of a heatedmetal or metal oxide. The energy of theemitted electrons is relatively low, andtheir rate of emission increases with thetemperature of the surface. The thermal en-ergy of the electrons is sufficient to ejectthem against the counter-attraction of thesurface atoms. Heated cathodes are used assources of electrons in thermionic tubesand electron guns.

thermionics /ther-mee-on-iks/ The branchof physics that deals with the emission ofelectrons or ions from a heated substance.It is a part of electronics. See thermionicemission.

thermionic tube A device that uses thethermionic effect and exhibits the action ofa valve, i.e. current flow in one directiononly. In the simplest type, a diode valve,

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thermionic tube

the electron-emitting cathode surface iscontained in an evacuated glass envelopetogether with the second electrode, theanode. Electrons emitted from the cathodeby THERMIONIC EMISSION, flow toward theanode if it is made positive with respect tothe cathode. This constitutes a current. Re-versal of the potential causes the current tofall to zero. There is no current, or very lit-tle, in the reverse direction because theanode does not emit electrons.

There are many other types of vacuumtube incorporating additional electrodes,called GRIDS. Some of these types may befilled with gas at low pressure, in whichcase the valve is called a thyratron. Formany of its original uses the thermionictube has been replaced by solid-state tran-sistors, but it is still used in special casessuch as high-power amplification (forradio transmission), cathode-ray tubes,and the klystron and magnetron oscilla-tors. See also pentode; tetrode; triode.

thermistor /ther-mist-er/ An electricalcomponent with a high temperature coeffi-cient of resistance (i.e. the electrical resis-tance changes rapidly with temperature).Thermistors are usually semiconductor de-vices; in one type the resistance decreaseswith temperature rise. They can be used assensitive resistance thermometers, whichoperate at various temperatures. Theirthermal capacity is small, so they rapidlyattain the temperature to be measured. An-other use is in electronic circuits in which itis desirable that the current should increaseto a maximum value slowly.

thermocouple /ther-moh-kup-ăl/ A pairof wires of different conductors or semi-conductors, welded or soldered at one end,used to measure temperature. A smalle.m.f. is produced at the junction betweenthe metals, and this changes with tempera-ture. The thermocouple (or thermojunc-tion) can thus be used as a thermoelectricthermometer.

Thermocouples are convenient andhave low thermal capacity. In inaccuratework a single junction can be used with agalvanometer in the circuit to measure thecurrent produced by the thermoelectric

e.m.f. In more accurate work two identicaljunctions are connected in series. One junc-tion is maintained at a constant lowtemperature and the other used fortemperature measurement. A potentiome-ter is used to measure the e.m.f.

See also International PracticalTemperature Scale; Seebeck effect; ther-mometer; thermopile.

thermodynamic equilibrium /ther-moh-dÿ-nam-ik/ See equilibrium.

thermodynamics /ther-moh-dÿ-nam-iks/The study of the internal energy of bodiesand the effects on this of the processes heatand work. It has applications in engin-eering, physical chemistry, and manybranches of physics.

The first law of thermodynamics statesthat the total energy in a closed system isconserved (constant). This means that en-ergy cannot be created or destroyed, but inall processes is simply converted from oneform to another, or transferred from onesystem to another, or both.

A mathematical statement of the firstlaw is:

δQ = δU + δWHere, δQ is the heat transferred to the

system, δU the change in internal energy(resulting in a rise or fall of temperature),and δW is the external work done by thesystem. A gas for example may expand atconstant pressure, in which case δW = pδV.

The second law of thermodynamics canbe stated in a number of ways, all of whichare equivalent. One is that heat cannot passfrom a cooler to a hotter body withoutsome other process occurring. Another isthe statement that heat cannot be totallyconverted into mechanical work – i.e. heatengine cannot be 100% efficient.

The third law of thermodynamics statesthat the entropy of a pure substance tendsto zero as its thermodynamic temperatureapproaches zero. This implies that absolutezero is an unattainable limit.

Often a zeroth law of thermodynamicsis given: that if two bodies are each in ther-mal equilibrium with a third body, thenthey are in thermal equilibrium with eachother. This is considered to be more funda-

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mental than the other laws because they as-sume it. See also Carnot cycle; entropy; sta-tistical mechanics.

thermodynamic temperature Tempera-ture measured on a scale that is indepen-dent of any real substance. The usual scaleis that proposed by Thomson (later LordKelvin) in 1848, slightly amended in laterwork. It is based on the concept of an idealreversible heat engine. Since the EFFICIEN-CIES of all such engines working betweentwo given temperatures are equal, Thom-son proposed defining the scale in terms ofthese efficiencies. The thermodynamic tem-peratures T1 and T2 of the isothermalprocesses of a Carnot cycle are defined tobe in the ratio of the heat intake to the heatoutput:

T1/T2 = Q1/Q2To complete the definition the value of onestandard temperature must be specified.This is now that of the triple point of water(273.16 K). The unit on this scale is calledthe kelvin (symbol: K). Kelvin showed thatthis scale was identical to one defined interms of an ideal gas. In statistical mechan-ics it can be shown that the thermodynamictemperature determines the distribution ofenergies among the particles of a body.

See also Carnot’s principle; gas laws;International Practical Temperature Scale;temperature scale.

thermoelectric effects /ther-moh-i-lek-trik/ Effects relating thermal energy andelectricity. See Peltier effect; Seebeck effect;Thomson effect.

thermoelectric thermometer See ther-mocouple.

thermojunction /ther-moh-junk-shŏn/See thermocouple.

thermoluminescent dating /ther-moh-loo-mă-ness-ĕnt/ A method for dating thefiring of samples of pottery. As a result ofabsorbed alpha radiation, electrons be-come trapped at energy levels higher thannormal. If the temperature is raised, theyrevert to the ground state with emission ofphotons (light). The amount of light emit-

ted can be measured. This depends on thenumber of trapped electrons, which in turndepends on the lapse of time since the pot-tery was fired. It also depends on theamount of irradiation by alpha particlesduring that period and the type of material.

thermometer /ther-mom-ĕ-ter/ Any in-strument or apparatus used for measuringtemperature. Thermometers depend fortheir action on a thermometric property –i.e. a physical property that changes in aknown way with temperature. For in-stance, a mercury thermometer depends onthe expansion of a thin column of mercuryfrom a bulb into a capillary tube. The ma-terial or substance used for its thermomet-ric property is the working substance of thethermometer. See also pyrometer.

thermometer, clinical See clinical ther-mometer.

thermometer, maximum and mini-mum See maximum-and-minimum ther-mometer.

thermometric property /ther-moh-met-rik/ See thermometer.

thermometry /ther-mom-ĕ-tree/ Thebranch of physics concerned with methodsof temperature measurement.

thermonuclear reaction /ther-moh-new-klee-er/ See fusion.

thermopile /ther-moh-pÿl/ A radiant en-ergy detector or meter. It consists of a se-ries of thermocouples, usually made ofantimony and bismuth. Radiation strikesthe blackened hot junctions, while the coldjunctions are kept shielded. Measurementof the thermoelectric e.m.f. produced, en-ables the temperature of the hot junction tobe calculated and hence the total radiationreceived from the source.

thermostat An instrument used for main-taining temperature within certain limits. Ituses a device that cuts off the power whenthe required temperature is exceeded, thenreconnects the supply when the tempera-

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thermostat

ture falls. A common method is to exploitthe expansion and contraction of a sub-stance with temperature. See also bimetal-lic strip.

thin-film interference The interferenceof light that occurs when light interactswith a thin film of material. It occurs be-cause there is reflection and refraction ofthe light in each layer in the material, withinterference occurring between reflectedlight from different layers. The colors ob-served in a thin film of oil is an example ofthin-film interference.

thixotropy /thiks-ot-rŏ-pee/ The propertyof certain types of fluid whose viscosity de-creases when the fluid is stressed.Thixotropic fluids are used to make non-drip paints.

Thomson effect The production of anelectric potential gradient along a conduc-tor as a result of a temperature gradientalong it. Points at different temperatures inthe conductor have different electrical po-tentials. The effect is named for the Britishphysicist William Thomson (subsequentlyLord Kelvin) (1824–1907).

thorium /thor-ee-ŭm, thoh-ree-/ A toxicradioactive element of the actinoid seriesthat is a soft ductile silvery metal. It hasseveral long-lived radioisotopes found in avariety of minerals including monazite.Thorium is used in magnesium alloys, in-candescent gas mantles, and nuclear fuelelements.

Symbol: Th; m.p. 1780°C; b.p. 4790°C(approx.); r.d. 11.72 (20°C); p.n. 90;r.a.m. 232.0381.

thorium series See radioactive series.

thoron /thor-on, thoh-ron/ See emanation.

three-body problem The problem of un-derstanding the motion of three bodies thatinteract in some specified way. The three-body problem cannot be solved exactly ei-ther in Newtonian mechanics or inquantum mechanics. Related to this,

chaotic motion can occur in the three-bodyproblem.

thulium /thoo-lee-ŭm/ A soft malleableductile silvery element of the lanthanoid se-ries of metals. It occurs in association withother lanthanoids.

Symbol: Tm; m.p. 1545°C; b.p.1947°C; r.d. 9.321 (20°C); p.n. 69; r.a.m.168.93421.

thyratron /th’ÿ-ră-tron/ A gas-filledthermionic tube, a type of triode, that canbe used as a RELAY.

thyristor /th’ÿ-ris-ter/ (silicon-controlledrectifier) A semiconductor device, a type ofdiode, that can be used to control currentsupply, for example to an a.c. motor.

tidal power Power obtained by harness-ing the tidal movement of water in theoceans. One method employs water tur-bines turned by the flow of tidal water.Other experimental methods use largefloats that rise and fall with the tide.

tides The variation in water levels on thesurface of the Earth due to the gravita-tional interactions between the Earth andthe Moon and the Sun. When the Sun,Moon and Earth are all in a straight linespring tides, i.e. the tides with the biggestrange, result. When the gravitational forcesbetween the Earth and the Moon and be-tween the Earth and the Sun are at right an-gles to each other neap tides, i.e. the tideswith the least range, result. The tide-pro-ducing effect of the Moon is about twicethat of the Sun.

timbre /tim-ber, tam-ber/ See quality ofsound.

time Measurement of duration betweenevents. The SI unit, the second, is based onvibration of radiation absorbed by cesiumatoms. Time is based on astronomicalmeasurements. Solar time is measured withrespect to the Sun. Sidereal time is based onmeasurement with respect to the stars.Lunar time is based on the lunar month(the time between successive New Moons).

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Fluctuations in the motion of astronomicalbodies have made it necessary to adopt theatomic clock using cesium radiation as anabsolute standard.

time constant Symbol T or τ. A time thatcharacterizes the rate of discharge of a ca-pacitor in a circuit consisting of the capac-itor and a resistor. The time constant isgiven by CR seconds where C is in faradsand R is in ohms.

tin A white lustrous metal of low meltingpoint. Its electronic structure has outer s2p2

electrons ([Kr]4d105s25p2). The element isof low abundance in the Earth’s crust(0.004%) but is widely distributed. Tin hasthree crystalline modifications or al-lotropes, α-tin or ‘gray tin’ (diamond struc-ture), β-tin or ‘white tin’, and γ-tin; thelatter two are metallic with close packedstructures. Tin also has several isotopes. Itis used in a large number of alloys includ-ing Babbit metal, bell metal, Britanniametal, bronze, gun metal, and pewter aswell as several special solders.

Symbol: Sn; m.p. 232°C; b.p. 2270°C;r.d. 7.31 (20°C); p.n. 50; r.a.m. 118.710.

tint The color sensation of mixing a hue (aspectral color) with white. This reduces thesaturation of the hue.

titanium /tÿ-tay-nee-ŭm, ti-/ A silverytransition metal. It is used in the aerospaceindustry as it is strong, resistant to corro-sion, and has a low density. It forms com-pounds with oxidation states +4, +3, and+2, the +4 state being the most stable.

Symbol: Ti; m.p. 1660°C; b.p. 3287°C;r.d. 4.54 (20°C); p.n. 22; r.a.m. 47.867.

TOE See theory of everything.

tog A unit of thermal insulance used fortextiles, equal to ten times the difference, indegrees Celsius, between two surfaceswhen the heat transfer between them is onewatt per square meter.

Tokamak /toh-kă-mak/ A type of reactorwith a toroidal (donut) shape, used in ex-periments to produce nuclear fusion. The

plasma is guided round the toroid bystrong magnetic fields in such a way that itdoes not touch the walls of the container.

ton /tun/ 1. Either of two f.p.s. units ofmass. The short ton, chiefly used in NorthAmerica, is equal to 2000 pounds avoirdu-pois, or to 907.184 74 kilograms (kg) in SIunits. The long ton, chiefly used in the UK,is equal to 2240 pounds, or to1016.046 91 kg in SI units.2. See tonne.3. An f.p.s. unit of refrigeration power, de-fined as the heat needed to melt one shortton of ice in 24 hours, or 12 000 Britishthermal units per hour. In SI derived unitsa ton of refrigeration is equal to 3514watts.4. See megaton.5. (displacement ton) An f.p.s. unit usedchiefly in the U.S. to measure the displace-ment of a long ton of seawater by ships,considered to be 35 cubic feet. In SI derivedunits it is equal to 991.09 cubic decimeters.6. (register ton) An f.p.s. unit used chieflyin the U.S. to measure the internal capacityof ships, equal to 100 cubic feet. In SI de-rived units it is equal to 2.8317 cubic me-ters.7. (measurement ton) An f.p.s unit usedchiefly in the U.S. to determine the cargocapacity of a ship, considered to be 40cubic feet. In SI derived units it is equal to1.1327 cubic meters.

tone See note.

tonne /tun/ (metric ton) Symbol: t A unitof mass equal to 103 kilograms.

torque /tork/ Symbol: T A turning mo-ment or couple. The torque of a force Fabout an axis (or point) is Fs, where s is theperpendicular distance from the axis to theline of action of the force. The unit is thenewton meter. Note that the unit of work,also the newton meter, is called the joule.Torque is not however measured in joules.The two physical quantities are not in factthe same. Work (a scalar) is the scalarproduct of force and displacement. Torqueis the vector product and is a vector at 90°to the plane of the force and displacement.

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See also couple; moment.

torr A unit of pressure equal to a pressureof 1/760 atmospheres (133.322 Pa). It isequal to the mmHg. The unit is named forthe Italian physicist Evangelista Torricelli(1608–47)

torsion /tor-shŏn/ Angular strain (twist)caused by applying opposing torques (cou-ples) to opposite ends of a body such as arod or wire. If Hooke’s law applies theangle of twist is proportional to either cou-ple. For a cylinder of radius a and length l,the angle φ is given by

T = (πa2Gφ)/2lwhere T is the torque and G is the shearmodulus.

torsional wave /tor-shŏ-năl/ A wave mo-tion in which the vibrations in the mediumare rotatory simple harmonic motionsaround the direction of energy transfer.

torsion balance A device for measuringvery small forces by the torsion they causein a wire or fiber. The angle of twist is usu-ally measured by the displacement of abeam of light reflected from an attachedmirror (i.e. by an optical lever).

total eclipse See eclipse.

total internal reflection The total reflec-tion of radiation that can occur in amedium at the boundary with anothermedium of lower refractive constant. Insuch cases, rays incident at small angleswill be refracted ‘away from the normal’;in other words, the angle of refraction (r) isgreater than the angle of incidence (i). Be-cause r is greater than i, it is possible to in-crease i to a value at which r is 90° (or justunder). That value of i is called the criticalangle c. The relation for the refractive con-stant for radiation entering this medium is:

1n2 = 1/sincIf i is increased still further, refraction

cannot occur. The radiation must then allbe reflected. Normally, when radiationmeets the boundary between two mediasome will be reflected and some will be re-fracted. Total internal reflection is the only

exception – here all the energy is reflected.Because of this, optical instruments ofteninclude totally internally reflecting prismsrather than mirrors. The critical angles ofoptical glasses at visible wavelengths aretypically 40° or less.

total radiation pyrometer An instru-ment used for measuring high tempera-tures. Radiation from the source is focusedby a concave mirror onto a blackened foilto which is attached a thermocouple. Thethermoelectric e.m.f. produced can bemeasured and hence the temperature of thefoil. The temperature of the radiatingsource may then be calculated. See also op-tical pyrometer.

tourmaline /toor-mă-leen, -lin/ (schorl) Acomplex bluish or brownish mineral im-portant for its polarizing effect on light. Itis a dichroic material.

trajectory /tră-jek-tŏ-ree/ The path of amoving object – a projectile – acted uponby air resistance, gravity, and other forces.

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(a)surface

normal

r

iii iii

(b)(b)(b)

medium 2medium 2medium 2

medium 1medium 1medium 1ccc

(c)(c)(c)

c = critical angle

Total internal reflection

transducer /trans-dew-ser, tranz-/ 1. A de-vice that converts one form of energy intoanother. For example, a microphone con-verts sound into an electric current, and aloudspeaker does the reverse.2. A device for converting a physical effectinto a voltage (so giving a measure of thephysical effect).

transformer, voltage /trans-for-mer/ Adevice for changing the voltage of an alter-nating supply. Transformers have no mov-ing parts and operate by the current in onecoil, the primary winding, electromagneti-cally inducing a current in another, the sec-ondary winding, which forms part of aseparate electrical circuit. The ratio of thevoltages in the primary and secondary cir-cuits, V1/V2, is approximately equal to theratio of the number of turns in the primaryand secondary coils. In an ideal trans-former there is no power loss and the pri-mary to secondary current ratio, I1/I2, isthe inverse of the voltage ratio; i.e. V1I1 =V2I2. In practice, some power is lost be-cause of eddy currents, hysteresis, resis-tance of the coils, and incomplete linkingof the magnetic flux between the coils.Usually the primary and secondary wind-ings are wound around a laminated ironcore designed to give maximum flux link-age. With careful design, transformers canbe more than 98% efficient.

Step-up transformers are used to in-crease voltage and reduce the current of theoutput from power stations so that lossesin transmission lines are minimized. Thevoltage is reduced in stages by step-downtransformers nearer the user.

transient /tran-see-ĕnt, -zee-/ A suddenbrief disturbance of a system.

transistor /tran-zis-ter/ A device incorpo-rating two junctions between n-type and p-type SEMICONDUCTORS, and having theproperty that a current flowing across onejunction modulates the current flowingacross the other junction. Electrical contactis made by three electrodes attached one toeach piece of semiconductor, called theemitter, base, and collector. There are twotypes of transistor, called p-n-p and n-p-n.

Both types may be regarded as twodiodes connected back to back, so thatwhen a voltage is applied across the deviceone diode is forward biased and the otherreverse biased. Current flows across theforward biased junction, i.e. majority car-riers (electrons in n-type and holes in p-type semiconductors) move from theemitter toward the collector. The base re-gion is thin enough not to prevent this.

In the n-p-n transistor, electrons fromthe emitter cross into the base, and someholes from the base (p-type) cross into theemitter. Those electrons entering the basemove slowly toward the collector-basejunction, which is reverse biased. The baseregion is relatively thin, and once electronsenter the collector region they are sweptthrough it by the applied voltage. In the op-posite direction holes cross the base to theemitter junction, causing the hole concen-tration in the base to fall. This effect wouldreduce the forward voltage sufficiently tostop the forward current unless the base re-gion was made to increase its hole concen-tration by losing electrons through theexternal connection to the base. Hence thebase-emitter junction must always be for-ward biased. In such a case current ampli-fication is possible; a small base currentcontrols a larger collector current. The cur-rent gain is defined by the ratio of collectorcurrent to base current, given by the sym-bol β (beta). This use of the transistor iscalled the common emitter connection, inwhich an input signal is applied to the base.This is the most common way in which atransistor is used as an amplifier.

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transistor

collector

emitter

base

n

p

nelec

tro

ns

con

ven

tio

nal

curr

ent

n-p-n transistor

transition temperature A temperature atwhich some definite physical change oc-curs in a substance. Examples of such tran-sitions are change of state, change ofcrystal structure, and change of magneticbehavior.

translation /trans-lay-shŏn, tranz-/ Seetranslatory motion.

translatory motion /trans-lă-tor-ee, -toh-ree, tranz-/ (translation) Motion involvingchange of position; it compares with rota-tory motion (rotation) and vibratory mo-tion (vibration). Each is associated withkinetic energy. Translatory motion is usu-ally described in terms of (linear) speed orvelocity and acceleration.

translucent /trans-loo-sĕnt, tranz-/ Ableto pass radiation, but with much deviationand/or absorption. Compare transparent.

transmission electron microscope/trans-mish-ŏn, tranz-/ See electron micro-scope.

transmittance /trans-mit-ăns, tranz-/(transmission coefficient) The ratio of thetransmitted energy that a substance allowsthrough to the energy incident upon it.

transmitter A device used in a telecom-munication system to generate and propa-gate an electrical signal.

transparent Able to pass radiation with-out significant deviation or absorption.Note that a substance transparent to oneradiation may be opaque to another. Thedivide between transparency and translu-cency is not well defined. Thus some peo-ple call a filter transparent (as it does notdistort radiation): others would call itTRANSLUCENT (as it absorbs some of the ra-diation). See also opaque.

transport The transfer of matter or radi-ation. Transport phenomena can be ana-lyzed from first principles usingnon-equilibrium statistical mechanics. Inpractice, it is convenient to use equationsfrom kinetic theory. Electrical and thermal

conductivity are examples of transportphenomena.

transport coefficients Quantities, suchas electrical and thermal conductivity, thatquantify the transport of matter or radia-tion. Transport coefficients may be calcu-lated using non-equilibrium statisticalmechanics or kinetic theory. An inversetransport coefficient, such as resistivity,quantifies the opposition to transport in asystem.

transport number /trans-port (n.); trans-port (vb.)/ Symbol t The fraction of thetotal current passing through an electrolytecarried by a particular ion.

transuranic elements /trans-yû-ran-ik,tranz-/ Elements that have a proton num-ber greater than 92 (i.e. greater than that ofuranium). The transuranic elements are allunstable (radioactive) and are produced bynuclear reactions induced either by bom-barding heavy elements with high-energynuclei of light elements or by the capture ofslow neutrons, followed by beta decay. Innuclear explosions, transuranic elementsmay be produced by numerous successivecaptures of neutrons by uranium nuclei.

transverse wave A wave motion in whichthe motion or change is perpendicular tothe direction of energy transfer. Electro-magnetic waves are examples of transversewaves. See polarization. Compare longitu-dinal waves.

traveling wave See wave

triangle of forces See triangle of vectors.

triangle of vectors A triangle describingthree coplanar vectors acting at a pointwith zero resultant. When drawn to scale –shown correctly in size, direction, andsense, but not in position – they form aclosed triangle. Thus three forces acting onan object at equilibrium form a triangle offorces. Similarly a triangle of velocities canbe constructed.

transition temperature

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triangle of velocities See triangle of vec-tors.

triatomic /trÿ-ă-tom-ik/ Describing a mol-ecule consisting of three atoms. Water(H2O) and carbon dioxide (CO2) are ex-amples.

triboelectricity /trÿ-boh-ĕ-lek-tris-ă-tee/(frictional electricity) Static electricity pro-duced by friction.

tribology /trÿ-bol-ŏ-jee/ The study of fric-tion, lubricants, and lubrication.

triboluminescence /trÿ-boh-loo-mă-ness-ĕns/ See luminescence.

triode /trÿ-ohd/ A THERMIONIC TUBE withthree electrodes; i.e. one GRID, called thecontrol grid, in addition to the anode andcathode. The grid is placed nearer to thecathode than the anode, and so is able tocontrol the current by the application ofrelatively small voltages to this grid. Innormal operation the grid is biased nega-tively, so that no current flows on to it; but

a small voltage fluctuation, or input, su-perimposed on the GRID BIAS causes largeanode current changes, or output. Theratio of output voltage change to inputvoltage change is called the voltage gain, oramplification factor.

triple point The only point at which thegas, solid, and liquid phases of a substancecan coexist in equilibrium. The triple pointof water (273.16 K) is used to define thekelvin. Some substances (e.g. carbon diox-ide) have pressures at the triple pointgreater than atmospheric. Such materialscan appear as liquids only when underpressure.

tritiated /trit-ee-ay-tid, trish-/ See tritium.

tritium /trit-ee-ŭm, trish-/ Symbol: T, 3HA radioactive isotope of hydrogen of massnumber 3. The nucleus contains 1 protonand 2 neutrons. Tritium decays with emis-sion of low-energy beta radiation to give3He. The half-life is 12.3 years. Tritium isfound in the atmosphere, possibly as a re-sult of the bombardment of nitrogen byneutrons from cosmic rays:

14N + 1n → 12C + 3HIt is useful as a tracer in studies of chem-

ical reactions. Compounds in which 3Hatoms replace the usual 1H atoms are saidto be tritiated.

triton /trÿ-tŏn/ A nucleus of a tritiumatom, consisting of two neutrons and oneproton.

true north Geographical north, the direc-tion toward the North Pole (as opposed toMAGNETIC NORTH).

truth See quark.

tungsten /tung-stĕn/ A transition metal,formerly called wolfram. It is used as thefilaments in electric lamps and in variousalloys.

Symbol: W; m.p. 3410 ± 20°C; b.p.5650°C; r.d. 19.3 (20°C); p.n. 74; r.a.m.183.84.

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tungsten

(a) force diagram for an object at rest on a rough slope

M = centerof mass

R

F

W

MMM

(b) corresponding triangle(b) corresponding triangle(b) corresponding triangle

WWW

FFF

RRR

Triangle of vectors

tuning fork A metal fork designed to vi-brate when struck gently to produce a puresound tone.

tunnel diode A highly doped p-n junctionDIODE that has a large reverse current, and,in the forward direction, a negative sloperesistance over part of the voltage-currentcharacteristic.

The ‘tunnel effect’ explains the shape ofthe characteristic. Electrons are able totunnel through the conduction band,which is normally forbidden to them be-cause they do not possess sufficient energyto cross the potential barrier of the junc-tion. See also diode.

tunnel effect The passage of a particlethrough a potential barrier, even though ithas not enough energy to pass the barrieron classical grounds. The tunnel effect canbe explained by quantum mechanics. The

process of alpha decay is an example of thetunnel effect. See tunnel diode.

turbulent flow Fluid flow in which thespeed at any point varies rapidly in magni-tude and direction. Fluid flow becomes tur-bulent when its speed increases beyond acritical speed. This corresponds to a criticalvalue of the REYNOLDS NUMBER that de-pends on the geometry of the system. Forhighly turbulent flow, the resistance to mo-tion is proportional to the product of thedensity of the fluid, the speed squared, andthe square of the linear dimensions. It hasproved very difficult to construct a mathe-matical theory of turbulence. Comparelaminar flow.

turns ratio The ratio of the number ofturns in the primary coil of a voltage trans-former to the number in the secondary coil.

two-body problem The problem of un-derstanding the motion of two bodies gov-erned by some interaction. The two-bodyproblem can be solved exactly in the caseof two massive bodies interacting by New-tonian gravity and two electrically chargedbodies in quantum mechanics. The prob-lem of two interacting massive bodies de-scribed by general relativity theory cannotbe solved exactly.

Tyndall effect /tin-dăl/ The scattering oflight by suspended particles or a colloidalsolution. The effect is named for the Britishphysicist John Tyndall (1820–93).

tuning fork

254

currentnegative

slope

voltagenormal p n

junctioncharacteristic

Tunnel diode

UHF See ultrahigh frequency.

ultracentrifuge /ul-tră-sen-tră-fyooj/ Ahigh-speed CENTRIFUGE used for separatingout very small particles. The sedimentationrate depends on the particle size, and theultracentrifuge can be used to measure themass of colloidal particles and large mol-ecules (e.g. proteins).

ultrahigh frequency /ul-tră-hÿ/ (UHF) Aradio frequency in the range between 3GHz and 0.3 GHz (wavelength 10 cm–1m).

ultrahigh vacuum See vacuum.

ultramicroscope /ul-tră-mÿ-krŏ-skohp/A modified compound microscope able toview the sub-microscopic particles in a col-loidal suspension when this is suitably illu-minated.

ultrasonic frequency /ul-tră-sonn-ik/ Asound frequency above the range normallyaudible by humans, i.e. greater than about20 kHz.

ultrasonics /ul-tră-sonn-iks/ The study ofsounds that are too high-pitched to be de-tected by the human ear; i.e. have a fre-quency greater than about 20 kHz.Ultrasound is used in a similar way to x-rays, for medical diagnosis and testing forflaws in metal. It is also used to clean sur-faces and to break up particles in suspen-sion. Ultrasound is often generated by thepiezoelectric effect. See also sonar.

ultraviolet /ul-tră-vÿ-ŏ-lĕt/ (UV) A formof electromagnetic radiation, shorter inwavelength than visible light. Ultravioletwavelengths range between about 1 nm

and 400 nm. Ordinary glasses are nottransparent to these waves; quartz is amuch more effective material for makinglenses and prisms for use with ultraviolet.

Like light, ultraviolet radiation is pro-duced by electronic transitions between theouter energy levels of atoms. The distinc-tion between the two types of radiation isin fact physiological rather than physical.However, having a higher frequency, ultra-violet photons carry more energy thanthose of light.

See also electromagnetic spectrum.

ultraviolet catastrophe In the late nine-teenth century it was realized that theshort-wavelength region of black-body ra-diation could not be explained by the theo-ries of physics of the time (classicalphysics). The problem – sometimes calledthe ultraviolet catastrophe – was resolvedby the concept of quantization of energy.See Planck’s radiation law; Rayleigh–Jeanslaw.

umbra (pl. umbrae or umbras) /um-bră/Total shadow. See shadow.

uncertainty principle See Heisenberg’suncertainty principle.

underdamping /un-der-damp-ing/ Seedamping.

uniaxial crystal /yoo-nee-aks-ee-ăl/ Atype of birefringent crystal having only oneaxis along which the ordinary and extraor-dinary rays travel at the same speed. Seeoptic axis.

unified field theory A single theory toaccount for the electromagnetic, gravita-tional, strong, and weak interactions by

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U-V

uniform acceleration

256

one set of equations. So far, attempts tofind such a theory have been unsuccessful,although there has been some progress inunifying the weak and electromagnetic in-teractions.

uniform acceleration Acceleration thatis constant in magnitude and direction.

uniform electric field An electric field inwhich the field strength is the same at allpoints in the region of the field. For exam-ple, a uniform electric field may be pro-duced by two long parallel electricallycharged plates, with the field strength hav-ing the same value between the plates.

uniform motion A vague phrase, usuallytaken to mean motion at constant velocity(constant speed in a straight line).

uniform speed Constant speed.

uniform velocity Constant velocity, de-scribing motion in a straight line with zeroacceleration.

unipolar transistor /yoo-nă-poh-ler/ Seefield-effect transistor.

unit A reference value of a quantity usedto express other values of the same quan-tity. See also SI units.

unit cell The smallest unit of entities suchas atoms, molecules or ions which are re-peated in a periodic way in a crystal.

universal constants See fundamentalconstants.

unsaturated /un-sach-ŭ-ray-tid/ Describ-ing a color that is a tint; i.e. a hue mixedwith white. See saturation.

unstable equilibrium EQUILIBRIUM suchthat if the system is disturbed a little, thereis a tendency for it to move farther from itsoriginal position rather than to return. Seestability.

upthrust An upward force on an object ina fluid. In a fluid in a gravitational field the

pressure increases with depth. The pres-sures at different points on the object willtherefore differ; the resultant is verticallyupward. See Archimedes’ principle; buoy-ancy; flotation (law of).

uranium /yû-ray-nee-ŭm/ A toxic ra-dioactive silvery element of the actinoid se-ries of metals. Its three naturally occurringradioisotopes, 238U (99.283% in abun-dance), 235U (0.711%), and 234U(0.005%), are found in numerous mineralsincluding the uranium oxides pitchblende,uraninite, and carnotite. The readily fis-sionable 235U is a major nuclear fuel andnuclear explosive, while 238U is a source offissionable 239Pu.

Symbol: U; m.p. 1132.5°C; b.p.3745°C; r.d. 18.95 (20°C); p.n. 92; r.a.m.238.0289.

uranium–lead dating A method of ra-dioactive DATING used for estimating theage of certain rocks. It is based on thedecay of 238U to 206Pb (half-life 4.5 × 109

years) or 235U to 207Pb (half-life 0.7 × 109

years). The technique is useful for time pe-riods from 107 years ago back to the age ofthe Earth (about 4.6 × 109 years).

uranium–radium series See radioactiveseries.

US Customary units The f.p.s. system ofweights and measures established in theformer American colonies prior to theAmerican Revolutionary War. Today theyremain in use only in the US, Liberia, andMyanmar (Burma).

US Customary units for length and,with the exception of the ton and stone,weight or mass, are essentially the same asthose used in other f.p.s. systems, includingthe IMPERIAL UNITS system. Significant dif-ferences occur in units for volume and ca-pacity, however. Thus the US gallon of 128US fluid ounces, which is equal to3.785 412 cubic decimeters (dm3) in SIunits, is considerably smaller than the Im-perial gallon of 160 Imperial fluid ounces,which is equal to 4.546 09 dm3 in SI units.Similarly, the Imperial bushel, equal in SIunits to 36.367 72 dm3, is about 3% larger

than the US bushel, which is equal in SIunits to 35.239 07 dm3. Conversely the USfluid ounce, equal in SI units to 29.573 53cubic centimeters (cm3), is slightly largerthan the Imperial fluid ounce, which in SIunits is equal to 28.423 062 cm3.

The US system further differs from theImperial system in having separate dry andliquid units for certain volumetric mea-sures. Whereas the Imperial quart, for ex-ample, equal in SI units to 1.136 522 dm3,is used for both liquid and dry measure,there are separate US Customary quarts fordry goods, equal in SI units to 1.101 221dm3, and liquids, equal in SI units to0.946 352 9 dm3. The different US unitsarise from the fact that they are based ondivisions of the US bushel (for dry goods)and the US gallon (for liquids).

UV See ultraviolet.

vacancy See defect.

vacuum (pl. vacuums or vacua) A spacecontaining gas below atmospheric pres-sure. A perfect vacuum contains no matterat all, but for practical purposes soft (low)vacuum is usually defined as down toabout 10–2 pascal, and hard (high) vacuumas below this. Ultrahigh vacuum is lowerthan 10–7 pascal.

vacuum distillation Distillation carriedout at reduced pressure, which lowers theboiling point of the liquid.

vacuum flask See Dewar flask.

vacuum pump See diffusion pump.

vacuum state The lowest energy state ina system described by relativistic quantumfield theory. The vacuum state is analogousto the ground state in a system described byquantum mechanics.

vacuum tube See thermionic tube.

valence band See energy bands.

valence electron In an atom, an electronin an incompletely filled (usually outer)

shell, available for chemical bonding toform a molecule. See electron shell.

valley of stability A concept that is use-ful in discussing the stability of nuclei. Ifthe number of protons in a nucleus is plot-ted on one horizontal axis, the number ofneutrons in the nucleus is plotted on a hor-izontal axis perpendicular to the first axis,and the energy of the nucleus is plotted ona vertical axis for all nuclei the resultingsurface is a valley. Stable nuclei are nearthe bottom of this valley of stability, withiron and nickel occupying positions closeto the lowest points.

valve See thermionic tube.

valve voltmeter See electrometer.

vanadium /vă-nay-dee-ŭm/ A silvery tran-sition element used in alloy steels.

Symbol: V; m.p. 1890°C; b.p. 3380°C;r.d. 6.1 (20°C); p.n. 23; r.a.m. 50.94.

Van de Graaff accelerator /van-dĕ-graf,-grahf/ A particle accelerator in which thehigh voltage from a Van de Graaff genera-tor is used to accelerate charged particles.The accelerator is named for the Americanphysicist Robert Jemison Van de Graaff(1901–67).

Van de Graaff generator An electrosta-tic generator capable of producing highp.d.s (up to millions of volts). It consists ofa large smooth metal sphere on top of ahollow insulating cylinder. An endless in-sulating belt runs between pulleys at eachend of the cylinder. Charge is sprayed frommetal points connected to a high-voltagesource on to the bottom of the belt. It isthen carried up to the top of the belt whereit is collected by other metal points and ac-cumulated on the outside of the sphere,which becomes highly charged.

van der Waals’ equation An equation ofstate for real gases. For one mole of gas theequation is

(p + a/Vm2)(Vm – b) = RT,

where p is the pressure, Vm the molar vol-ume, and T the thermodynamic tempera-

257

van der Waals’ equation

ture. a and b are constants for a given sub-stance and R is the gas constant. The equa-tion gives a better description of thebehavior of real gases than the perfect gasequation (pVm = RT).

The equation contains two corrections:b is a correction for the non-negligible sizeof the molecules; a/Vm

2 corrects for the factthat there are attractive forces between themolecules, thus slightly reducing the pres-sure from ideal. The equation is named forthe Dutch physicist Johannes Diderik Vander Waals (1837–1923).

van der Waals’ forces Attractive forcesexisting between molecules. These forcesare the ones giving the pressure correctionin the van der Waals’ equation. They aremuch weaker than chemical bonds and actover short range (inversely proportional tothe seventh power of distance). They arecaused by attraction between dipoles ofmolecules. For atoms or molecules withoutpermanent molecular dipole moments, theattractive forces result from attractions be-tween nucleus-electron dipoles (called dis-persion forces).

Van’t Hoff’s law At a given temperature,the osmotic pressure of a solution is thesame as the pressure that the solute wouldexert if it were in the gaseous phase and oc-cupying the same volume. The law isnamed for the Dutch chemist Jacobus Hen-ricus Van’t Hoff (1852–1911).

vapor A gas at any temperature at whichit may be liquefied by pressure alone; i.e. agas below its critical temperature. The crit-ical temperatures for water, carbon diox-ide, and nitrogen are 374°C, 31.1°C, and–147°C respectively. See also Andrews’ ex-periments; critical state.

vapor density The mass of a volume ofgas divided by the mass of an equal volumeof hydrogen at the same temperature andpressure, equal to half its relative molecu-lar mass.

vaporization A change of state from liq-uid or solid to vapor.

vapor pressure The pressure exerted at aparticular temperature by a vapor. When aliquid or solid evaporates, molecules arecontinuously escaping from the surface at arate that increases rapidly with tempera-ture; they exert a vapor pressure. Thosestriking the surface tend to re-enter the liq-uid or solid, so that eventually a state ofdynamic equilibrium is reached in whichthe number of molecules returning to thesurface per second is the same as the num-ber leaving it. The vapor now exerts itsequilibrium pressure for that temperature,the saturated vapor pressure (SVP). Thevalue of this depends only on the tempera-ture, and is independent of the volume (un-less all the vapor condenses or all the liquidevaporates).

variable capacitor A capacitor for whichthe capacitance can be changed. A com-mon form has two sets of parallel semi-cir-cular plates in which one set can swing intoor out of the other set, thereby changingthe area of overlap of the plates. Variablecapacitors are used in radio receivers.

variable star A star in which the bright-ness changes with time. This variability canbe regular or chaotic. There are manycauses for the variability. For example, aSUPERNOVA, which is an extreme manifesta-tion of the variability of a star, occurswhen the core of a large star collapses to aNEUTRON STAR.

variation, magnetic See magnetic varia-tion.

variometer /vair-ee-om-ĕ-ter/ A variableinductor, usually consisting of two coilsconnected in series and able to be movedwith respect to each other, so that the totalself-inductance can be changed.

vector /vek-ter/ A measure in which direc-tion is important and must usually be spec-ified. For instance, displacement is a vectorquantity, whereas distance is a scalar.Weight, velocity, and magnetic fieldstrength are other examples of vectors –they are each quoted as a number with aunit and a direction. The addition of vec-

van der Waals’ forces

258

tors must take account of direction. The re-sultant may be found by the parallelogramof vectors.

There are various ways of multiplyingvectors. A vector multiplied by a scalargives another vector; for example mass (ascalar) multiplied by velocity (a vector)gives momentum (a vector). Two vectorscan be multiplied together in two differentways. See scalar product; vector product.

For some purposes, it is useful to definetwo classes of vector. Those quantitiesdefining something that happens or may becaused to happen in a particular direction(e.g. displacement, acceleration, momen-tum, force) are called polar vectors. Quan-tities using the orientation of an axis (e.g.angular velocity, moment of a force) areknown as axial vectors or pseudovectors.The vector product of two polar vectors isa pseudovector.

vector calculus The branch of mathe-matics concerned with rates of change ofvectors. There are three main operators invector calculus: curl, div, and grad.If V is a vector, curl V is a vector that re-sults from the vector product of the opera-tor ∇, where ∇ = i∂/∂x + j∂/∂y + k∂/∂z, andV, i.e. curl V = ∇ × V.The quantity div V is a scalar that resultsfrom the scalar product of ∇ and V, i.e. divV = ∇.V.The quantity grad φ, where φ is a scalarfunction, is a vector that results from theoperation of ∇ on φ, i.e. grad φ = ∇φ.Vector calculus is used extensively in manybranches of physics, particularly electro-magnetism and fluid mechanics.

vector product A multiplication of twovectors to give a vector. The vector productof A and B is written A ×× B. It is a vector ofmagnitude ABsinθ, where A and B are themagnitudes of A and B and θ is the anglebetween A and B. The direction of the vec-tor product is at right angles to A and B. Itpoints in the direction in which a right-handed screw would move turning from Atoward B.

Note, A ×× B = –B ×× A. An example of avector product is the force F on a moving

charge Q in a field B with velocity v (as inthe motor effect). Here

F = QB × vThe vector product is sometimes called

the cross product.See also scalar product.

vectors, parallelogram (law) of Seeparallelogram of vectors.

vectors, triangle (law) of See triangle ofvectors.

velocity Symbol: v Displacement per unittime. The unit is the meter per second (ms–1). Velocity is a vector, speed being thescalar form. If velocity is constant, it isgiven by the slope of a position/time graph,and by the displacement divided by thetime taken. If it is not constant, the meanvalue is obtained. If x is the displacement,the instantaneous velocity is given by v =dx/dt. See also equations of motion.

velocity modulation A type of modula-tion in which the velocity of a beam of elec-trons is made to fluctuate at the frequencyof a superimposed electric field, usually aradiofrequency. As faster electrons over-take slower electrons, bunching occurs inthe beam. High-frequency oscillators, suchas those used in radar, make use of veloc-ity-modulated beams of electrons. See alsomodulation; radar.

velocity of light See speed of light.

velocity of sound See sound.

259

velocity of sound

A

A x B

B

Vector product

velocity ratio See distance ratio.

Venturi tube /ven-toor-ee/ A cylindricalpipe that has a constriction at its center.The rate of flow of a fluid through the tubeincreases at the constriction and its pres-sure decreases. The difference in pressurebetween the ends of the tube and at theconstriction can be used to calculate therate of flow. The tube is named for the Ital-ian physicist Giovanni Battista Venturi(1746–1822).

vernier scale /ver-nee-er, ver-neer/ A smallauxiliary scale in a measuring instrumentwhich is put next to the main scale so thatdivisions in the main scale can be measuredaccurately. The scale is named for theFrench mathematician Pierre Vernier, whoinvented it in 1631.

very high frequency (VHF) A radio fre-quency in the range between 300 MHz and30 MHz (wavelength 1 m–10 m).

very large scale integration (VLSI) Theconstruction of electrical circuits in whicha large number of transistors are connectedtogether in a small region such as a siliconchip. The development of VLSI has been anessential ingredient in the success of theelectronics industry, particularly comput-ers.

very low frequency (VLF) A radio fre-quency in the range between 30 kHz and 3kHz (wavelength 10 km–100 km).

VHF See very high frequency.

vibrating-reed electrometer See elec-trometer.

vibration (oscillation) Any regularly re-peated to-and-fro motion or change. Ex-amples are the swing of a pendulum, thevibration of a sound source, and thechange with time of the electric and mag-netic fields in an electromagnetic wave.

vibration magnetometer See magne-tometer.

virial coefficient /vi-ree-ăl/ Quantities A,B, C, D, ... which occur in the virial equa-tion:PV = A + B/V + C/V2 + D/V4 + ...,where P is the pressure and V is the vol-ume. The virial coefficients B, C, D, etc.having nonzero values is an attempt to de-scribe real gases rather than ideal gases.

virtual image See image.

virtual object See object.

virtual particle An elementary particlepostulated to exist in interactions. For ex-ample, it is possible to explain the electro-magnetic interaction between two chargedparticles by assuming that they are ex-changing virtual photons.

virtual work The work done if a systemis displaced infinitesimally from its posi-tion. The virtual work is zero if the systemis in equilibrium.

viscometer /vis-kom-ĕ-ter/ An instrumentfor measuring fluid viscosity. Some typesmeasure the rate of fluid flow through anarrow tube. Others measure the time aball takes to fall through a known depth offluid. Effects such as the damping of me-chanical vibrations by the fluid and thefriction forces it transmits between twomoving parts (both of which are direct re-sults of viscosity) can also be used in vis-cometers.

viscosity /vis-koss-ă-tee/ (internal friction)Symbol: η The resistance of a fluid to flowat low speeds. Molasses, for example, hasa higher viscosity than water. It exerts agreater frictional force when it is stirred,the same object will fall through it moreslowly than through water, and it flowsmore slowly.

In steady flow of a fluid over a planesurface of area A the surface will be sub-jected to a force F in its plane and in the di-rection of flow, given by

F = ηA(dv/dx)where (dv/dx) is the gradient in the direc-tion normal to A of the velocity parallel tothe surface. The quantity η is called viscos-

velocity ratio

260

ity, dynamic viscosity, or coefficient of vis-cosity. For most fluids viscosity is a con-stant at constant temperature and theequation expresses Newton’s law of viscos-ity. For some fluids, such as pastes andpaints, η depends upon the velocity gradi-ent. These are called non-Newtonian flu-ids. The unit of viscosity is kg m–1 s–1, or Nm–2 s. See also Reynolds number; turbulentflow.

visible radiation See light.

visual acuity See acuity; visual.

vitreous humor The gelatinous sub-stance behind the lens in the eye. See eye.

VLF See very low frequency.

VLSI See very large scale integration.

volt Symbol: V The SI unit of electricalpotential, potential difference, and e.m.f.,defined as the potential difference betweentwo points in a circuit between which aconstant current of one ampere flows whenthe power dissipated is one watt. 1 V = 1 JC–1. The unit is named for the Italian physi-cist Count Alessandro Volta (1745–1827).

voltage Symbol: V E.m.f. or electrical po-tential difference measured in volts.

voltage divider (potential divider) Anumber of resistors, inductors, or capaci-tors connected in series with several termi-nals at intermediate points. The totalvoltage across the chain can be split intoknown fractions by making connections atthe various points.

voltaic cell /vol-tay-ik/ See cell.

voltameter /vol-tam-ĕ-ter/ (coulo(mb)-meter) A device for determining electriccharge or electric current using electrolysis.The mass m of material released is mea-sured and this can be used to calculate thecharge (Q) and the current (I) from theelectrochemical equivalent (z) of the ele-ment, using Q = m/z or I = m/zt. The termnow often refers to any case in which twoelectrodes are immersed in an electrolyte.

voltmeter /vohlt-mee-ter/ A meter used tomeasure electrical voltage. The commonesttypes are moving-coil instruments withhigh series resistances to keep the currentdrawn to a low value. For alternating volt-ages a rectifier must be used. Moving-ironinstruments with high series resistances canbe used for both direct and alternatingvoltages. Electrostatic instruments aresometimes used, especially for measuringhigh potential differences. Electronic in-struments can also be constructed, oftenwith digital display (digital voltmeters).The cathode-ray oscilloscope can also beused as a voltmeter. See also electrometer;potentiometer.

volume Symbol: V A measure of the spaceoccupied by an object or system.

volume charge density See charge den-sity.

vortex /vor-teks/ (pl. vortices) A circulat-ing eddy in a fluid. Vortices can be createdin the rapid flow of fluid around a bluntbody, with the streamlines forming vor-tices behind the body. The production ofvortices in this way is associated with largedrag forces on the body.

261

vortex

262

watt /wot/ Symbol: W The SI unit ofpower, defined as a power of one joule persecond. 1 W = 1 J s–1 The unit is named forthe Scottish instrument maker and inven-tor James Watt (1736–1819).

watt-hour A unit of electric power equalto one watt per hour consumed. See electricmeter.

wattmeter /wot-mee-ter/ An instrumentfor measuring power in an electric circuit.The most common type, used in alternat-ing-current circuits, consists of two coils,one fixed and one able to rotate. The fixedcoil is connected in series with the circuit(like an ammeter). The rotating coil has ahigh resistance (or has an additional resis-tance in series) and is connected across theload like a voltmeter. The deflection of thiscoil is opposed by hair springs, and itsvalue is proportional to the product of thecurrent and the potential difference –hence, the instrument can be calibrated togive the power.

wave Waves may be progressive or sta-tionary. A progressive (or traveling wave)is an oscillatory disturbance propagatedthrough a medium or, in the case of elec-tromagnetic waves, through space. In eachtype of wave there are two kinds of distur-bance. Electromagnetic waves involve elec-tric and magnetic fields oscillating indirections at right angles to each other andto the direction of propagation, equalamounts of energy being transferred by theelectric and magnetic fields. Waves on thesurface of a liquid involve motion of parti-cles in a vertical plane, there being hori-zontal (longitudinal) and vertical(transverse) oscillations. In the case of reg-ular waves such as ripples and ocean rollers

the water particles move very nearly in cir-cles so the longitudinal and transverse am-plitudes are equal. Sound waves involvefluctuations of pressure and particle veloc-ity. Waves in a stretched string involve os-cillations of particles at right angles to thestring and fluctuations of the tension.

A simple harmonic plane progressivewave can be expressed by the equation

y = asin2π(ft – x/λ)where y is the displacement at time t at adistance from the origin x. The maximumvalue of the displacement, a, is called theamplitude. f is the frequency and λ is thewavelength. The relationship can also beexpressed in the forms

y = asin2π(vt – x/λ)or

y = asin2π(t/T – x/λ)where v is the wave speed and T is the pe-riod. Such waves can equally be expressedin terms of cosines. If the minus sign is re-placed by a plus sign, these equations rep-resent waves traveling in the oppositedirection.

For electromagnetic waves two similarequations are required, the displacementbeing the electric field in one, and the mag-netic field in the other. The two distur-bances are in step. For waves on liquidstwo equations are needed, one representingthe vertical displacement and the other thehorizontal displacement. These are a quar-ter of a wavelength out of step. The waveprofile has narrow peaks and broadtroughs. In practice, waves never conformexactly to the ideal simple harmonic formsince this imply that there was infinite du-ration and infinite space, without any at-tenuation.

A stationary (or standing) wave is anoscillation equivalent to the resultant oftwo equal progressive waves traveling in

W

opposite directions. Combining the equa-tions

y = asin2π(ft – x/λ)and

y = asin2π(ft + x/λ)we obtain a resultant displacement

Y = 2asin2πftcos2πx/λThis represents a simple harmonic distur-bance whose amplitude varies with x ac-cording to a cosine law. Any given type ofwave requires two similar equations, onefor each kind of disturbance such thatwhere one has its maximum amplitude theother has its minimum.

See also antinode; interference; longitu-dinal wave; node; phase; transverse wave.

wave equation A partial differentialequation that describes wave propagation.In three spatial dimension, x, y, and z, ithas the form ∇2u = (1/c2) ∂2u/∂t2, where ∇2

is the Laplace operator, i.e. ∇2 = ∂2/∂x2 +∂2/∂y2 + ∂2/∂z2, u is the displacement of thewave, c is the speed of propagation of thewave, and t is the time.

waveform See wave.

wavefront A continuous surface associ-ated with a wave radiation, in which all thevibrations concerned are in phase. A paral-lel beam has plane wavefronts; the outputof a point source has spherical wavefronts.

wave function A mathematical quantity,used in wave mechanics, analogous to theamplitude of ordinary waves. The squareof the wave function of a particle at a par-ticular point represents the probability oflocating the particle in unit volume at thatpoint.

waveguide See microwaves.

wavelength Symbol: λ The distance be-tween the ends of one complete cycle of awave. Wavelength relates to the wavespeed (c) and its frequency (v) thus:

c = vλ

wave mechanics See quantum theory.

wave motion Any form of energy trans-

fer that may be described as a wave ratherthan as a stream of particles. The term isalso sometimes used to mean any harmonicmotion.

wave number Symbol: σ The reciprocalof the wavelength of a wave. It is the num-ber of wave cycles in unit distance, and isoften used in spectroscopy. The unit is themetre–1 (m–1). The circular wave number(symbol: k) is given by:

k = 2πσ

wave theory of light The theory thatlight is propagated in the form of waves.Hooke and Huygens assumed this theoryin the seventeenth century but it did not re-ceive general acceptance until after thepublication of researches on interference,diffraction, and polarization in the earlynineteenth century, especially by Young,Fresnel, Arago and Fraunhofer. At first,light was believed to be a form of elasticwave in the ether, but after the publicationof the theory of electromagnetism byMaxwell (1865) it was recognized as aform of electromagnetic wave. See also cor-puscular theory; duality.

W-boson A spin-one, electrically charged(+1 or –1) particle that is the quantum ofthe field that mediates the weak interac-tions with a change of electric charge. TheW-bosons were discovered at CERN in1983, with their masses being about 80GeV. See also Weinberg–Salam model; Z-boson.

weak interaction See interaction.

weber /vay-ber/ Symbol: Wb The SI unitof magnetic flux, equal to the magneticflux that, linking a circuit of one turn, pro-duces an e.m.f. of one volt when reduced tozero at a uniform rate in one second. 1 Wb= 1 V s.

The unit is named for the Germanphysicist Wilhelm Eduard Weber(1804–91).

weight Symbol: W. Unit: joule. 1. Theforce by which a mass is attracted by theEarth. This is usually expressed as W = mg,

263

weight

where g is the ACCELERATION OF FREE FALL,although there is a small error due to therotation of the Earth.2. The force which a body exerts on its sup-port when at rest. This is equal to the forcedefined in (1) but acts in a different place,on a different body, by a different mecha-nism.

In problems in mechanics the twomeanings (1) and (2) are often confused.Also, in everyday language ‘weight’ is oftenused to mean mass, so it is important toavoid misunderstanding.

weightlessness A condition experiencedby persons and equipment in spacecraftwhen in free fall, that is in an orbit whenno rockets are operating and there is no airresistance. All objects in the spacecrafthave the same acceleration as the space-craft itself in the gravitational field of theEarth, so there are no support forces andthe objects are said to be weightless. It isoften wrongly supposed that weightless-ness means that there is no gravitationalfield present, and the misleading term ‘zerogravity’ is used for this condition.

Weinberg–Salam model /wÿn-berg să-lahm A quantum field theory involvingbroken symmetry which gives a unifiedtheory of the weak and electromagnetic in-teractions. It predicts that weak interac-tions are mediated by fields, the quanta ofwhich are electrically charged W-BOSONS

and neutral Z-BOSONS. The masses of the Wand Z-bosons and other experimental find-ings are in accord with the predictions ofthe model, which was put forward bySteven Weinberg in 1967 and indepen-dently by Abdus Salam in 1968.

Weiss constant /vÿss/ See Curie’s law.

Weston cadmium cell A standard cellthat produces a constant e.m.f. of 1.018 6volts at 20°C. It consists of an H-shapedglass vessel containing a negative cad-mium-mercury amalgam electrode in oneleg and a positive mercury electrode in theother. The electrolyte – saturated cadmiumsulfate solution – fills the horizontal bar ofthe vessel to connect the two electrodes.

The e.m.f. of the cell varies very little withtemperature, being given by the equation:

E = 1.018 6 – 0.000 037 (T – 293)where T is the absolute temperature.

wet and dry bulb hygrometer See hy-grometer.

wet cell A type of cell, such as a car bat-tery, in which the electrolyte is a liquid so-lution. See also Leclanché cell.

Wheatstone bridge /wheet-stohn/ A cir-cuit for measuring electrical resistance.Four resistors, P, Q, R, and S, are con-nected in a loop (as if along four sides, or‘arms’, of a square). A battery is connectedacross the junctions between P and S andbetween Q and R. A sensitive galvanome-ter is connected across the two oppositejunctions (P–Q and R–S). If no currentflows through the galvanometer, then P/Q= S/R. The bridge is then said to be bal-anced. If R is an unknown resistance and P,Q, and S are known, then R can be found.P and Q are called the ratio arms of thebridge (they determine the ratio of S to R).

There are various ways of using this cir-cuit. In a meter bridge P and Q are a singlelength of uniform resistance wire with asliding contact. S is a standard resistor. Theposition of the contact is moved until thegalvanometer gives a zero reading. Thenthe ratio l1/l2 is equal to S/R. The circuit is

weightlessness

264

unknownresistor R

standardresistor S

G

variableresistor P

variableresistor Q

R/S = Q/P

Wheatstone bridge

named for the British physicist Sir CharlesWheatstone (1802–75).

white dwarf A compact heavenly bodyformed when a star with a mass which issimilar to that of the Sun exhausts its nu-clear fuel. A white dwarf has a volumewhich is similar to that of the Earth. It issupported against further gravitational col-lapse to a NEUTRON STAR or BLACK HOLE bythe DEGENERACY PRESSURE of electrons.

white light Visible radiation that gives asensation of whiteness. The effect is verysubjective and depends very much uponconditions and contrast. It is produced bya continuum over the whole visible spec-trum. The sensation of whiteness can alsobe produced by suitable combinations ofparts of the spectrum; for example, twocomplementary colors or three primarycolors.

white noise See noise.

Wiedemann–Franz law /vee-dĕ-mănfrantz/ An experimental finding aboutpure metals stating that, at a giventemperature, the ratio of the thermal con-ductivity to the electrical conductivity, isapproximately the same for all metals. Thislaw is reasonably well obeyed except attemperatures close to absolute zero. It wasdiscovered by Gustav Heinrich Wiede-mann and Rudolph Franz in 1853.

Wien’s displacement law /veenz/ Forblack-body radiation the rate of energy ra-diation per unit area per unit wavelengthrange at constant kelvin temperature T1can be plotted against wavelength. It isfound that there is a peak at wavelength λ1.For temperature T2 the peak comes at λ2,such that

λ1T1 = λ2T2 = constantThis rule was deduced by the Germanphysicist Wilhelm Wien (1864–1928).

Wilson’s cloud chamber See cloudchamber.

Wimshurst machine /wimz-herst/ A type

of electrostatic generator. It consists of twocircular disks of insulating material withradial strips of metal foil on their sides. Thedisks rotate in opposite directions and thecharge is produced by friction and col-lected by metal points. The machine isnamed for the British physicist JamesWimshurst (1832–1903).

Wollaston prism /wûl-ă-stŏn/ A type ofpolarizing prism named for the Englishscientist William Hyde Wollaston (1766–1828).

work When a force F acts on a body whileit undergoes a displacement s the body ex-erting the force is said to do work, given bythe scalar product of F and s

W = F.sthat is

W = Fscosθwhere F and s are the magnitudes of F ands and θ is the angle between them. Thismay be expressed as: work is the productof the force times the component of the dis-placement in the direction of the force; orwork is the product of displacement timesthe component of the force in the directionof the displacement.

When a torque T acts on a body whileit undergoes angular displacement θ aboutthe same axis the work done W = Tθ (θmeasured in radians).

When a surface at pressure p displaces avolume ∆V the work done is p∆V.

The system of electric units is so definedthat electric work can be expressed; workdone electrically when a charge Q is dis-placed between two points with a potentialdifference V is given by:

W = QVIn all cases the SI unit of work is the joule(J).

See also conservation of energy; heat;thermodynamics.

work function A measure of the extent towhich photoelectric or THERMIONIC EMIS-SION will take place, usually expressed asthe energy needed to remove an electron.See photoelectric effect.

265

work function

266

xenon /zen-on/ A colorless odorlessmonatomic element of the rare-gas group.It occurs in trace amounts in air. Xenon isused in thermionic tubes and strobe light-ing.

Symbol: Xe; m.p. –111.9°C; b.p.–107.1°C; d. 5.8971 (0°C) kg m–3; p.n. 54;r.a.m. 131.29.

x-radiation A form of electromagneticradiation with short wavelength. Thewavelength is commonly in the range10–10 m to 10–11 m but much shorter orlonger waves can be produced.

x-radiation is generated whenever high-energy electrons strike matter. In an x-raytube electrons from a hot filament are ac-celerated through a large potential differ-ence (typically 105 V) and focused upon atarget or anticathode usually made of ahigh-melting-point metal. Radiation isemitted from the region where the electronbeam strikes the target. The radiation isalso caused by high-voltage cathode-raytubes (such as are used in some televisionreceivers and computer terminals) andsome other electrical equipment. X-rays

are also generated when beta radiation isabsorbed in matter.

X-radiation is absorbed in mattermostly by the photoelectric effect, theprobability of which is proportional to thefourth power of the proton number Z.Thus bone, which contains calcium (Z =20) and phosphorus (Z = 15), absorbs farmore x-radiation than does soft tissue,which contains few atoms with greaterproton number than oxygen (Z = 8). Hencea body exposed to x-radiation casts ashadow on a photographic emulsion or flu-orescent screen, which can be used in diag-nosis. The radiation can be detected usingionization chambers, proportional coun-ters, Geiger–Müller tubes, photography,fluorescence, and other methods.

The spectrum of x-radiation showslines superimposed upon a continuum. Thecontinuous spectrum is caused by theabrupt slowing-down of electrons as theypass through matter, and is calledbremsstrahlung (German for ‘braking radi-ation’). The short-wavelength limit λ0 isproduced by the whole kinetic energy of anelectron going to generate a single quan-tum of radiation:

λ0 = hc/qVwhere h is the Planck constant, c is thespeed of light, q is the electron charge, andV is the p.d. across the x-ray tube. The linespectrum is caused by atoms that have hadinner electrons ejected by electron impact.As electrons from higher energy quantumstates enter the empty inner states, radia-tion is emitted with wavelengths character-istic of the element. Hence these lines canbe used in x-ray spectroscopy.

x-ray crystallography The use of x-raysto study crystal structure. The way inwhich x-rays are diffracted gives informa-

X-Z

intensity l

λ0 x-ray wavelength λ

X-rays

tion about the spacing between crystalplanes. The structure of molecules of bio-logical interest such as DNA and proteinshave been determined in this way.

x-ray fluorescence Softer (i.e. less ener-getic) secondary x-rays emitted by a sub-stance bombarded by high-energyelectrons or primary x-rays. The secondaryx-ray wavelengths are characteristic of thesubstance and can be used to identify it. Seespectroscopy; x-radiation.

x-rays Streams of x-radiation.

x-ray tube A vacuum tube used for pro-ducing x-rays. A strong electrostatic fieldaccelerates electrons emitted by a white-hot filament and directs them at a metaltarget, where x-rays are emitted.

year The time taken for the Earth to com-plete one orbit of the Sun. It is measured invarious ways. The solar year is the timetaken for the Sun to make two successiveappearances at the first point of Aries. It is365.242 19 mean solar days. The calendaryear is regulated (using leap years) so thatits average length is equal to that of thesolar year. The sidereal year is measuredwith respect to the fixed stars. It is 365.25636 mean solar days. The lunar year, whichis 12 lunar months, is 365.3671 mean solardays.

yellow spot (macula lutea) An area a fewmillimeters across in the human retina. Ithas a high concentration of rods, givinghigh visual acuity and color vision but lowsensitivity to dim light. See eye; fovea.

yield point See elasticity.

yocto- Symbol: y A prefix denoting 10–24.For example, 1 yoctometer (ym) = 10–24

meter (m).

yoke A piece of ferromagnetic metal thatconnects two or more magnetic cores.

yotta- Symbol: Y A prefix denoting 1024.For example, 1 yottameter (Ym) = 1024

meter (m).

Young modulus See elastic modulus.

Young’s interference experiment Anexperiment first performed by the Englishphysicist Thoms Young (1773–1829) inabout 1801. Light passing through a smallhole fell on a distant screen with two pin-holes. The light spread out by diffractionon passing through the pinholes so thatthere was a region of overlap. Parallel col-ored fringes were observed in the overlapregion as a result of interference.

Light is propagated in trains of waveslasting typically a few nanoseconds. Wavesfrom the same original wavetrain are se-lected by the first hole and then passthrough both pinholes. Hence in the over-lap region there is a regular relationship be-tween the phases of the waves coming bythe two routes – the sources are said to becoherent. The appearance of the fringes isquite different from what is seen with justone pinhole.

From the results of such experiments,and comparison with such observations asNewton’s rings, Young concluded thatlight was a form of wave motion. Similarexperiments have been done since, replac-ing the pinholes by slits and using mono-chromatic light sources to give sharplydefined light and dark fringes. The separa-tion between two light fringes (or two darkfringes) is λD/2d where d is the separationof the pinholes (or slits) and D is their dis-tance from the plane in which the fringesare observed.

See also biprism; Lloyd’s mirror.

267

Young’s interference experiment

*

DDDscreen

superpositionregion

source

slits

ddd

Young’s slits

ytterbium /i-ter-bee-ŭm/ A soft malleablesilvery element having two allotropes andbelonging to the lanthanoid series of met-als. It occurs in association with other lan-thanoids. Ytterbium has been used toimprove the mechanical properties of steel.

Symbol: Yb; m.p. 824°C; b.p. 1193°C;r.d. 6.965 (20°C); p.n. 70; r.a.m. 173.04.

yttrium /it-ree-ŭm/ A silvery metallic ele-ment. It is found in almost every lan-thanoid mineral, particularly monazite.Yttrium is used in various alloys, in yt-trium-aluminum garnets used in the elec-tronics industry and as gemstones, as acatalyst, and in superconductors. A mix-ture of yttrium and europium oxides iswidely used as the red phosphor on televi-sion screens.

Symbol: Y; m.p. 1522°C; b.p. 3338°C;r.d. 4.469 (20°C); p.n. 39; r.a.m.88.90585.

Z-boson A spin-one, electrically neutralparticle that is the quantum of the field thatmediates the weak interactions that do notinvolve a change of electric charge. The Z-boson was discovered at CERN in 1983,with its mass being about 90 GeV. See alsoW-boson; Weinberg–Salam model.

Zeeman effect /zay-mahn/ The splittingof atomic spectral lines into two or morecomponents in a transverse magnetic field.The effect is named for the Dutch physicistPieter Zeeman (1865–1943) who discov-ered it in 1897. A full explanation of theZeeman effect requires quantum mechan-ics. See also Stark effect.

Zener breakdown /zee-ner, zen-er/ SeeZener diode.

Zener diode A semiconductor DIODE withhigh doping levels on each side of the junc-tion. If the junction is reverse-biased,

breakdown occurs at a well-defined poten-tial, giving a sharp increase in current. Theeffect is called Zener breakdown; it occursbecause electrons are excited directly fromthe valence band into the conduction band.Zener diodes are used as voltage regula-tors. The Zener diode and Zener break-down are named for the Americanphysicist Clarence Zener (1905–93). Seealso transistor.

zepto- Symbol: z A prefix denoting 10–21.For example, 1 zeptometer (zm) = 10–21

meter (m).

zero-point energy The energy possessedby the atoms and molecules of a substanceat absolute zero (0 K).

zetta- Symbol: Z A prefix denoting 1021.For example, 1 zettameter (Zm) = 1021

meter (m).

zinc A bluish-white transition metal, ap-plied as a coating (galvanizing) to protectsteel from corrosion.

Symbol: Zn; m.p. 419.58°C; b.p.907°C; r.d. 7.133 (20°C); p.n. 30; r.a.m.65.39.

zirconium /zer-koh-nee-ŭm/ A hard lus-trous silvery transition element that occursin a gemstone, zircon (ZrSiO4). It is used insome strong alloy steels.

Symbol: Zr; m.p. 1850°C; b.p. 4380°C;r.d. 6.506 (20°C); p.n. 40; r.a.m. 91.224.

zone refining A method used to purifysolids, especially semiconductors. The ma-terial in the form of a bar is passed slowlythrough a localized heating region. Amolten zone forms, which moves slowlyalong the bar. Impurities tend to concen-trate in the molten zone and they can be lo-calized at the end of the bar.

ytterbium

268

APPENDIXES

270

Appendix I1

1

H2

He

1 2 3 4 5 6

3

Li

4

Be

5

B6

C7

N8

O9

F1

0 Ne

11 N

a1

2 Mg

13 A

l1

4 Si1

5

P1

6

S1

7 Cl

18 A

r

19 K

20 C

a2

1 Sc2

2 Ti

23 V

24 C

r2

5 Mn

26 Fe

27 C

o2

8 Ni

29 C

u3

0 Zn

31 G

a3

2 Ge

33 A

s3

4 Se3

5 Br

36 K

r

37 R

b3

8 Sr3

9 Y4

0 Zr

41 N

b4

2 Mo

43 T

c4

4 Ru

45 R

h4

6 Pd4

7 Ag

48 C

d4

9 In5

0 Sn5

1 Sb5

2 Te

53

I5

4 Xe

55 C

s5

6 Ba

57-7

1

La-

Lu

72 H

f7

3 Ta

74 W

75 R

e7

6 Os

77 Ir

78 Pt

79 A

u8

0 Hg

81 T

l8

2 Pb8

3 Bi

84 Po

85 A

t8

6 Rn

87 Fr

88 R

a89

-103

Ac-

Lr

10

4 Rf

10

5 Db

10

6 Sg1

07 Bh

10

8 Hs

10

9 Mt

11

0 Ds

11

1

Rg

11

2

Uub

11

3

Uut

11

4

Uuq

11

5

Uup

11

6

Uuh

23

45

67

89

10

11

12

13

14

15

16

17

18

Peri

odic

Tab

le o

f th

e E

lem

ents

- gi

vin

g gr

ou

p,

ato

mic

nu

mb

er,

and

ch

emic

al s

ymb

ol

Lan

than

ides

Act

inid

es

Mo

der

n f

orm

Eu

rop

ean

con

ven

tio

nN

. A

mer

ican

con

ven

tio

n

Th

e ab

ove

is

the

mo

der

n r

eco

mm

end

ed f

orm

of

the

tab

le u

sin

g 1

8gr

ou

ps.

Old

er g

rou

p d

esig

nat

ion

s ar

e sh

ow

n b

elo

w.

Period

6 7

57 L

a

89 A

c

58 C

e

90 T

h

59 Pr

91 Pa

60 N

d

92 U

61 Pm

93 N

p

62 Sm

94 Pu

63 E

u

95 A

m

64 G

d

96 C

m

65 T

b

97 B

k

66 D

y

98 C

f

67 H

o

99 E

s

68 E

r

10

0 Fm

69 T

m

10

1 Md

70 Y

b

10

2 No

71 L

u

10

3 Lr

12

34

56

78

91

01

11

21

31

41

51

61

71

8

IAII

AII

IAIV

AV

AV

IAV

IIA

VII

I (o

r V

IIIA

)IB

IIB

IIIB

IVB

VB

VIB

VII

B0

(o

r V

IIIB

)

IAII

AII

IBIV

BV

BV

IBV

IIB

VII

I (o

r V

IIIB

)IB

IIB

IIIA

IVA

VA

VIA

VII

AV

IIIA

(or

0)

7

271

Appendix IIThe Chemical Elements

(* indicates the nucleon number of the most stable isotope)

Element Symbol p.n. r.a.m Element Symbol p.n. r.a.m

actinium Ac 89 227*

aluminum Al 13 26.982

americium Am 95 243*

antimony Sb 51 112.76

argon Ar 18 39.948

arsenic As 33 74.92

astatine At 85 210

barium Ba 56 137.327

berkelium Bk 97 247*

beryllium Be 4 9.012

bismuth Bi 83 208.98

bohrium Bh 107 262*

boron B 5 10.811

bromine Br 35 79.904

cadmium Cd 48 112.411

calcium Ca 20 40.078

californium Cf 98 251*

carbon C 6 12.011

cerium Ce 58 140.115

cesium Cs 55 132.905

chlorine Cl 17 35.453

chromium Cr 24 51.996

cobalt Co 27 58.933

copper Cu 29 63.546

curium Cm 96 247*

darmstadtium Ds 110 269*

dubnium Db 105 262*

dysprosium Dy 66 162.50

einsteinium Es 99 252*

erbium Er 68 167.26

europium Eu 63 151.965

fermium Fm 100 257*

fluorine F 9 18.9984

francium Fr 87 223*

gadolinium Gd 64 157.25

gallium Ga 31 69.723

germanium Ge 32 72.61

gold Au 79 196.967

hafnium Hf 72 178.49

hassium Hs 108 265*

helium He 2 4.0026

holmium Ho 67 164.93

hydrogen H 1 1.008

indium In 49 114.82

iodine I 53 126.904

iridium Ir 77 192.217

iron Fe 26 55.845

krypton Kr 36 83.80

lanthanum La 57 138.91

lawrencium Lr 103 262*

lead Pb 82 207.19

lithium Li 3 6.941

lutetium Lu 71 174.967

magnesium Mg 12 24.305

manganese Mn 25 54.938

meitnerium Mt 109 266*

mendelevium Md 101 258*

mercury Hg 80 200.59

molybdenum Mo 42 95.94

neodymium Nd 60 144.24

272

Appendix II

The Chemical ElementsElement Symbol p.n. r.a.m Element Symbol p.n. r.a.m

neon Ne 10 20.179

neptunium Np 93 237.048

nickel Ni 28 58.69

niobium Nb 41 92.91

nitrogen N 7 14.0067

nobelium No 102 259*

osmium Os 76 190.23

oxygen O 8 15.9994

palladium Pd 46 106.42

phosphorus P 15 30.9738

platinum Pt 78 195.08

plutonium Pu 94 244*

polonium Po 84 209*

potassium K 19 39.098

praseodymium Pr 59 140.91

promethium Pm 61 145*

protactinium Pa 91 231.036

radium Ra 88 226.025

radon Rn 86 222*

rhenium Re 75 186.21

rhodium Rh 45 102.91

roentgenium Rg 111 272*

rubidium Rb 37 85.47

ruthenium Ru 44 101.07

rutherfordium Rf 104 261*

samarium Sm 62 150.36

scandium Sc 21 44.956

seaborgium Sg 106 263*

selenium Se 34 78.96

silicon Si 14 28.086

silver Ag 47 107.868

sodium Na 11 22.9898

strontium Sr 38 87.62

sulfur S 16 32.066

tantalum Ta 73 180.948

technetium Tc 43 99*

tellurium Te 52 127.60

terbium Tb 65 158.925

thallium Tl 81 204.38

thorium Th 90 232.038

thulium Tm 69 168.934

tin Sn 50 118.71

titanium Ti 22 47.867

tungsten W 74 183.84

ununbium Uub 112 285*

ununtrium Uut 113 284*

ununquadium Uuq 114 289*

ununpentium Uup 115 288*

ununhexium Uuh 116 292*

uranium U 92 238.03

vanadium V 23 50.94

xenon Xe 54 131.29

ytterbium Yb 70 173.04

yttrium Y 39 88.906

zinc Zn 30 65.39

zirconium Zr 40 91.22

273

Symbols for Physical Quantities

Appendix III

acceleration aangular acceleration αangular frequency, 2πf ωangular momentum Langular velocity ωarea Abreadth bcircular wavenumber kdiameter d, Ddistance s, Ldynamic viscosity ηenergy E, Wforce Ffrequency f, νheight hkinetic energy Ek, Tlength lmass mmass density ρmoment of force M

moment of inertia I, Jmomentum pperiod Tplane angle θ, φ, α,

β, etc.potential energy Ep, Vpower Ppressure pradius r, Rreduced mass µrelative density dsolid angle Ω, ωthickness dtime ttorque Tvelocity vvolume Vwavelength λwavenumber σweight W, Fg

The Greek Alphabet

A α alphaB β betaΓ γ gamma∆ δ deltaE ε epsilonZ ζ zetaH η etaΘ θ thetaI ι iotaK κ kappaΛ λ lambdaM µ mu

N ν nuΞ ξ xiO ο omikronΠ π piP ρ rhoΣ σ sigmaT τ tauΥ υ upsilonΦ φ phiX χ chiΨ ψ psiΩ ω omega

Appendix IV

Length

To convert into multiply by

inches meters 0.0254feet meters 0.3048yards meters 0.9144miles kilometers 1.60934nautical miles kilometers 1.85200nautical miles miles 1.15078kilometers miles 0.621371kilometers nautical miles 0.539957meters inches 39.3701meters feet 3.28084meters yards 1.09361

Area

To convert into multiply by

square inches square centimeters 6.4516square inches square meters 6.4516 × 10–4

square feet square meters 9.2903 × 10–2

square yards square meters 0.836127square miles square kilometers 2.58999square miles acres 640acres square meters 4046.86acres square miles 1.5625 × 10–3

square centimeters square inches 0.155square meters square feet 10.7639square meters square yards 1.19599square meters acres 2.47105 × 10–4

square meters square miles 3.86019 × 10–7

square kilometers square miles 0.386019

Volume

To convert into multiply by

cubic inches liters 1.63871 × 10–2

cubic inches cubic meters 1.63871 × 10–5

cubic feet liters 28.3168cubic feet cubic meters 0.0283168cubic yard cubic meters 0.764555gallon (US) liters 3.785438gallon (US) cubic meters 3.785438 × 10–3

gallon (US) gallon (UK) 0.83268

274

Conversion Factors

Appendix V

Mass

To convert into multiply by

pounds kilograms 0.453592pounds tonnes 4.53592 × 10–4

hundredweight (short) kilograms 45.3592hundredweight (short) tonnes 0.0453592tons (short) kilograms 907.18tons (short) tonnes 0.90718kilograms pounds 2.204623kilograms hundredweights (short) 0.022046kilograms tons (short) 1.1023 × 10–3

tonnes pounds 2204.623tonnes hundredweights (short) 22.0462tonnes tons (short) 0.90718

The short ton is used in the USA and is equal to 2000 pounds. The shorthundredweight (also known as the cental) is 100 pounds.

The long ton, which is used in the UK, is equal to 2240 pounds (1016.047kg). The long hundredweight is 112 pounds (50.802 kg). 1 long ton equals20 long hundredweights.

Force

To convert into multiply by

pounds force newtons 4.44822pounds force kilograms force 0.453592pounds force dynes 444822pounds force poundals 32.174poundals newtons 0.138255poundals kilograms force 0.031081poundals dynes 13825.5poundals pounds force 0.031081dynes newtons 10–5

dynes kilograms force 1.01972 × 10–6

dynes pounds force 2.24809 × 10–6

dynes poundals 7.2330 × 10–5

kilograms force newtons 9.80665kilograms force dynes 980665kilograms force pounds force 2.20462kilograms force poundals 70.9316newtons kilograms 0.101972newtons dynes 100000newtons pounds force 0.224809newtons poundals 7.2330

275

Appendix V

Conversion Factors

Work and energy

To convert into multiply by

British Thermal Units joules 1055.06British Thermal Units calories 251.997British Thermal Units kilowatt-hours 2.93071 × 10–4

kilowatt-hours joules 3600000kilowatt-hours calories 859845kilowatt-hours British Thermal Units 3412.14calories joules 4.1868calories kilowatt-hours 1.16300 × 10–6

calories British Thermal Units 3.96831 × 10–3

joules calories 0.238846joules kilowatt hours 2.7777 × 10–7

joules British Thermal Units 9.47813 × 10–4

joules electron volts 6.2418 × 1018

joules ergs 107

electronvolts joules 1.6021 × 10–19

ergs joules 10–7

Pressure

To convert into multiply by

atmospheres pascals* 101325bars pascals 100000pounds per square pascals 68894.76inch

pounds per square kilograms per square 703.068inch meter

pounds per square atmospheres 0.068046inch

kilograms per square pascals 9.80661meter

kilograms per square pounds per square 1.42234 × 10–3

meter inchkilograms per square atmospheres 9.67841 × 10–5

meterpascals kilograms per square 0.101972

meterpascals pounds per square 1.45038 × 10–4

inchpascals atmospheres 9.86923 × 10–6

*1 pascal = 1 newton per square meter

Appendix V

276

Conversion Factors

277

General physics resources:

American Physical Society www.physicscentral.com

American Association of Physics Teachers www.psrc-online.org

American Institute of Physics www.aip.org

Atomic, nuclear, and particle physics:

Brookhaven National Laboratory (BNL) www.bnl.gov

CERN (European Laboratory for Particle www.cern.chPhysics)

Fermi National Accelerator Laboratory www.fnal.gov(Fermilab)

JET (Joint European Torus) www.jet.efd.org

JINR (Joint Institute for Nuclear Researchin Dubna, Russia) www.jinr.ru

Lawrence Berkeley National Laboratory www.lbl.gov(LBNL)

Los Alamos National Laboratory www.lanl.gov

Stanford Linear Accelerator Center (SLAC) www.slac.stanford.edu

UCLA Particle Beam Physics Laboratory http://pbpl.physics.ucla.edu

History of physics:

Center for History of Physics www.aip.org/history

Biographies:

Nobel Prizes http://nobelprize.org

Web Sites

Appendix VI

278

Comprehensive texts covering physics:

Cutnell, John D. and Kenneth W. Johnson. Physics. 6th ed. New York: Wiley, 2003.

Giancoli, Douglas C. Physics: Principles with Applications. 5th ed. New York: PrenticeHall, 1997.

Other sources:

Barrow, John D. The World within the World. Oxford, U.K.: Oxford University Press,1988.

Chown, Marcus. The Magic Furnace: The Search for the Origins of Atoms. London:Jonathan Cape, 1999.

Emsley, John. Nature’s Building Blocks: An A–Z Guide to the Elements. Oxford, U.K.:Oxford University Press, 2001.

Feynman, Richard P. QED: The Strange Theory of Light and Matter. Princeton, N.J.:Princeton University Press, 1985.

Gribbin, John. Companion to the Cosmos. London: Weidenfeld & Nicolson, 1996.

Gribbin, John. Q is for Quantum. London: Weidenfeld & Nicolson, 1998.

Hawking, Stephen. A Brief History of Time. New York: Bantam, 1988.

Penrose, Sir Roger. The Road to Reality: The Mathematics and Physics of the Universe.London: Vintage, 2002.

Stewart, Ian. Does God Play Dice? The New Mathematics of Chaos. 2nd ed. London:Penguin, 1997.

’t Hooft, Gerard. In Search of the Ultimate Building Blocks. Cambridge, U.K.:Cambridge University Press, 1997.

Weinberg, Steven. The First Three Minutes: A Modern View of the Origin of theUniverse. London: André Deutsch, 1977.

Weinberg, Steven. The Discovery of Subatomic Particles. New York: ScientificAmerican Library, 1983.

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