From Ideas to Implementation

Core Module 9.4

A word from the creator

This Powerpoint presentation was prepared by Greg Pitt of Hurlstone Agricultural High School.

Please feel free to use this material as you see fit, but if you use substantial parts of this presentation,

leave this slide in the presentation.

Share resources with your fellow teachers and students.

*

* and quantitatively (see next section of syllabus) *

Cathode Ray Tubes and Charged Particles

The development of various types of cathode ray tubes beginning in the mid-19th century allowed the manipulation, using electric and magnetic fields, of streams of charged particles.

A very simple cathode ray tube

cathode


Observations of the behaviour of these charges led to an increased understanding of matter and the atom. Application of this understanding led to new technologies in the 20th century including the development of

• the oscilloscope

• television

• communications technologies

• the electron microscope

• photocopiers and fax machines


Charged particles entering a uniform magnetic field with a velocity at right angles to the field are deflected along a circular path.

The path is circular because the force on the moving charge is of a constant magnitude (qvB) and it is always perpendicular to the direction of the velocity, making it a centripetal force.

The maximum force is exerted on the charge when its velocity is perpendicular to the field.

velocity

magnet

cathode ray


This image shows the circular path of a positively charged particle in a uniform magnetic field into the page

Factors affecting the radius

• the greater the velocity the greater the radius

• the greater the particle mass the greater the radius

• the greater the magnetic field strength the smaller the radius

• the greater the charge of the particle the smaller the radius

Application

The mass spectrometer

Animation see: ChargeMotionBfield.avi


A cathode ray tube is a highly evacuated glass tube containing a positive and a negative electrode.

When a large DC potential difference is applied between the electrodes, the cathode releases electrons, forming a beam, which is attracted towards the positively charged electrode.

This beam of electrons is called a cathode ray.

A cathode ray is an electric current in a vacuum tube.


The electrons themselves, making up the cathode ray, cannot be seen.

This graphic shows how a cathode ray (electron beam) is made visible using a curved phosphor coated metal screen.

Electrons travelling through the tube strike the phosphorescent screen, causing it to emit green light, thus making the path of the electrons visible.

Cathode ray tubes and charged particlesThe magnet in this photo is just behind the cathode ray tube with one end pointing out of the page.What is the polarity of the magnet’s pole that is visible near the tube?It is a south pole.

X X X X X

X X X X X

X X X X X

X X X X X

X X X X X

–v

F

The cathode ray can be deflected from a straight-line path by a magnetic field, suggesting that the two were related in some way.The discovery of this effect in 1855 predates by some ten years the unification of electricity and magnetism by James Clerk Maxwell.

B


A moving charged particle, such as an electron, can be deflected by an electric field.

An electric field can be produced by a potential difference applied across a pair of parallel charged conducting plates.

The electron entering the field at right angles to the field is deflected along a parabolic trajectory in the field.

For animation see: ElectronDeflectionPlates2.mov

Debate Cathode Rays - Particles or Waves?

• Cathode rays – charged particles or em waves - debate in late 1800s

• Similar debate regarding light in the 1600s. Newton argued for particles. Huygens for waves. Young secured the wave model for light.

• Lenard predicted that cathode rays would travel with the velocity of light but Thomson (1884) determined the velocity of cathode rays to be less than 1/100 of the speed of light

• German and British rivalry between researchers concerning the nature of cathode rays. Germans a wave British particles.

• Ultimately there was to be truth in both.• J.J. Thomson was awarded the Nobel Prize in Physics in 1906 for

showing the electron to be a particle.• George Thomson (JJ’s son), was awarded the Nobel Prize in

Physics in 1937 for showing that the electron is a wave!

Striation Patterns in Low Pressure Discharge Tubes

first

These pictures show the same discharge tube with different high voltage sources.Left: Induction coilRight: Very high voltage transformer from a TV set

Maltese Cross Tube

firstIdentification of Properties

Electrons produced at the cathode are accelerated towards the cross, connected to the anode.The inertia of the electrons (due to their mass) carries them past the cross if they do not hit the metal cross itself.High energy electrons make the glass at the end of the tube glow.

Maltese Cross Tube


If an object is placed in the path of the cathode ray, a shadow of the object is cast on the glowing tube wall at the end.This showed that the cathode rays travelled in straight lines.

Tubes with Electric Plates - Cathode Ray Control


A potential difference applied across the charged electric plates causes the cathode ray to deflect to the right or the left, depending on the direction of the electric field produced.

charged plates

Tubes with Electric Plates - Cathode Ray Control


The deflection of electrons in the opposite direction to the electric field (away from the negative plate, towards the positive one) shows that electrons have a negative charge.

velocity

Fluorescent materials and cathode rays


These natural minerals fluoresce due to the absorption of UV radiation, which is subsequently emitted as visible light.

Cathode rays cause certain materials, called phosphors, to behave in a similar manner. This is the basis of screens on CROs, TV and CRT based computer monitors.

This demonstrates that cathode rays possess energy.

Paddle Wheel Discharge Tube and Cathode Rays


This cathode ray tube contains a small paddle wheel free to roll on its axle along glass tracks.

Cathode rays cause hit the paddle wheel, causing it to turn and move along the track.

This demonstrates that cathode rays have momentum.

Cathode Rays

first

(1) If an object is placed in the path of the cathode ray, a shadow of the object is cast on the glowing tube wall at the end. This showed that the cathode rays travelled in straight lines.

(2) The cathode ray can push a small paddle wheel up an incline, against the force of gravity. This showed that the cathode ray carried energy and could do work.

(3) The cathode ray can be deflected from a straight-line path by a magnetic field, suggesting that the two were related in some way. The discovery of this effect in 1855 predates by some ten years the unification of electricity and magnetism by James Clerk Maxwell.

(4) Cathode rays cause phosphorescent materials to give off light. This also shows that the cathode ray carries energy and can do work.

(5) Although there was some speculation that the cathode rays were negatively charged, it is not shown to be true by experiment until 1895, just two years before Thomson announced the discovery of the electron.

(6) J.J. Thomson is the first individual to succeed in deflecting the cathode ray with an electrical field. He did so in 1897. The cathode rays bend toward the positive pole, confirming that cathode rays are negatively charged.

Force on charged particle in magnetic field

Review• Electric charges experience no force if they are stationary in a uniform magnetic field

• Electric charges experience no force if they move with a velocity parallel to a uniform magnetic field

• Electric charges experience a maximum force when they move with a velocity perpendicular to a magnetic field

• The direction of the force is perpendicular to the velocity and the magnetic field direction

Quiz - force on charged particle in magnetic field

What is the direction of the force acting on the moving charged particles X and Y, both of which have the same magnitude charge?

X

Y

The force acting particle X is perpendicular out of the page

The force acting particle Y is perpendicular out of the pageBoth the charge and the direction of the velocity are opposite to X

What is the direction of the force acting on the moving charged particle Z?

ZThe force acting particle Y is perpendicular out of the pageIts magnitude is less than the force on X or Y.

Force on Charged Particle in Magnetic Field

F =qvBSin(θ)

The magnitude of the force (F) acting on a charged particle moving with velocity (v) in a magnetic field (B) is given by

The force (F) is measured in newtons (N)The velocity (v) is measured in metres/second (ms–1)The magnetic field (B) is measured in teslas (T)

Force on Charged Particle in Magnetic Field

F =qvBSin(θ)Solving Problems

Q1. An electron (mass 9.1 x 10-31 kg) moves with a velocity of 3 x 107 m/s perpendicular to a magnetic field of 2 teslas. The charge on an electron is -1.6 x 10-19 coulombs. What would be the force on the electron?

Q2. If a proton (mass 9.1 x 10-31 kg) entered the same field at the same speed of 3 x 107 m/s, compare its behaviour with that of the electron.

Q3. A magnetic field and an electric field are arranged perpendicular to each other. A stream of charged particles moving perpendicular to both fields remains undeflected when the electric field has a strength of 5 x 103 NC-1 and the magnetic field is 2 x 10-2 T. What is the speed of the particles? Explain how this is independent of the mass.

Q4. Compare (numerically) the mass to charge ratio of a beta particle and an alpha particle. State whether the mass or the charge of these particles has the greater effect on the radius of curvature of the particle in a magnetic field. Explain your answer.

Electric Field Strength - Point Charges

Qualitative description

• Electric fields are represented arrows to indicate the direction of the field.

• The closer the lines, the stronger the field represented.

• These diagrams show the electric fields surrounding positive and negative charges.

• The direction of an electric field is the direction of the force that it produces on a positive charge.

Quiz - Electric fields and point charges


Qualitatively describe the electric field surrounding a point positive charge.

The electric field surrounding an isolated point positive charge is radial. The field lines point away from the positive charge. The strength of the field decreases with distance from the charge.A diagram can be used to augment the description.

Qualitatively describe the electric field surrounding a point negative charge.

Electric Field Strength - Parallel Plates

The electric field between two parallel plates is uniform and has a direction from the positive to the negative plate.

+ –

+ –


The field becomes less uniform as the distance between the plates increases.The field near the edges of the plates is non-uniform.

The field direction is the direction of the force that would act on a positive charge placed in the field.

Quiz - Electric field between parallel plates

Solving Problems

Draw the electric field between the pair of square parallel plates seen edge on in the adjacent diagram.

Under what conditions is the field between the plates uniform?

E

The field is uniform providing the plates are parallel to each other and that the separation between the plates is small compared with the size (length of the sides) of the plate

Charged Plates and Electric Field Production

Quantitative description

E=Vd

The magnitude of the electric field (E) between two parallel plates is

Potential difference is measured in volts (V)Distance is measured in metres (m)Electric field strength is thus measured in volts/metre* (Vm–1)*the alternative unit newton/coulomb is identical

• proportional to the potential difference (V) between the plates

• inversely proportional to the separation (d) between them

Quiz - Electric field strength

Solving Problems

E=Vd

The distance between the two square plates shown edge on in the adjacent diagram is 2 mm.

The potential difference applied across the plates is 12 volts. What is the electric field strength?

The electric field strength is 6000 volts/metre

E=12

2×10–3

Thomson’s Experiment - Properties of Electrons

Charge to mass ratio of electron

• JJ Thomson used the vacuum tube above to determine the charge/mass ratio of the electron

• He adjusted electric and magnetic fields so that the forces they produced on the electrons cancelled each other [Electric F = qE, Magnetic F = qvB]

+ + + + +

– – – – –E

– vAn electron moves to the rightAn electric field is appliedWhich way must a magnetic field be applied to counter the force produced by the electric field?

Thomson’s Experiment - Properties of Electrons

Charge to mass ratio of electron

QuickTime™ and aCinepak decompressor

are needed to see this picture.

Deduce the direction of the magnetic field required to make the electrons travel in a straight line in the tube.Answer: into the page

Cathode Ray Tube - The Electron Gun

The electron gun in a cathode ray tube produces electrons.

• The cathode is heated by an electric current• Thermal vibrations give the electrons energy, releasing them

from the metal surface

Cathode Ray Tube - The Electron Gun

An electric field accelerates and focuses the electron beam

• What is the direction of the electric field in space in which the electrons are being accelerated?

• The electric field is to the left (positive to negative)

Cathode Ray Tube Operation

A stronger electric field, produced by the high voltage of the accelerating anode, accelerate the electron beam further

The kinetic energy of the fast moving electrons causes the screen phosphor to give off light.Movement of the electron beam in a vertical and horizontal direction is controlled by a combination of magnetic and electric fields.

Cathode Ray Tube - Electric Field

Charged particles experience a force due to an electric field

Electric field direction is by convention the direction of the force on a positive charge

E

+ force

–force

Electrons are therefore accelerated in the opposite direction to the electric field

Cathode Ray Tube - Fluorescent Screen

Electrons with high kinetic energies hit the phosphorescent screen, causing the atoms in the phosphor to produce light

Cathode Ray Tube and the Oscilloscope

Application

The oscilloscope is effectively a voltmeter capable of displaying variations in voltage (vertical axis) against time (horizontal axis). Any variable that can be measured electronically and converted to a voltage can be analysed with an oscilloscope. Many oscilloscopes now use computers to display the data rather than a dedicated instrument.

Oscilloscopes have played a key role in scientific research.

Cathode Ray Tube and the Oscilloscope

Application

Oscilloscopes contain a cathode ray tube that is less complex than a television picture tube

Cathode Ray Tube and the Electron Microscope

Application

Cathode ray tubes are the basis of the electron microscope.The electron microscope uses the wave properties of electrons to produce images of objects.The small wavelength permits a much greater resolution and hence magnification than a light microscope.Magnetic fields are used to focus and control the electron beam in the electron microscope.

Image: Desktop electron microscope

Cathode Ray Tube and the Electron Microscope

Application

Image: Electron microscope

Cathode Ray Tube and the Television Set

Application

Magnetic Fields and the Television Set

Application

The Oscilloscope and Experimental Physics

Discussion of development

• Cathode ray tubes are the basis of many cathode ray oscilloscopes.• Computer based oscilloscopes are now common, as is LCD screen use.• The development of the oscilloscope as a key tool for measurement propelled

research in many fields of science. Any variable that could be converted to a voltage could be displayed as a function of time on the oscilloscope screen.

• Such variables include electronic voltages, sound levels, light intensities, biological signals such as heart and brain activity.

Image: cathode ray oscilloscope

The Photocopy Machine

Discussion of application - see separate ppt on photocopier

Lightning Conductors

Discussion of application

Lightning conductors Lightning conductors are used on many buildings, towers and high voltage power lines.

Lightning Conductors

Discussion of application

See article “Lightning misses point” for an interesting example of how science can sometimes take things for granted - and get it wrong in the process! [Copied to notes page below]

Hertz and the Speed of Radio Waves

Radio waves and electromagnetic radiation

Hertz used interference between radio waves following two different measured paths to determine the wavelength of the waves. He knew the frequency and so was able to calculate the speed v = f, confirming that they were indeed electromagnetic waves.

Hertz and the Photoelectric Effect

A missed opportunity!

See notes page below

Production and Reception of Radio Waves

A First-hand Investigationfirst


References: Electromagnetic Waves, emwavgeneration.mov, emwavepropagating.mov

• If a charge is moved, ,a disturbance is created in the electric field lines associated with that charge

• The disturbance in the electric field propagates outward at the speed of light

Propagating disturbance moving to the right



• A simplified 2-D animation of the disturbance in the field is shown in this movie…

QuickTime™ and aAnimation decompressor




• If the charge oscillates, ,a field disturbance having wave properties is created

• The disturbance propagates outward at the speed of light



An electromagnetic wave is created by an oscillating dipole.A dipole is a pair of oppositely charged particles.An alternating dipole produces an electromagnetic wave with a frequency equal to that of the oscillations of the dipole.An AC voltage applied to a length of conductor becomes a dipole aerial.



An alternating current in an aerial creates an electromagnetic wave consisting of electric and magnetic fields perpendicular to each other.



This animation represents a propagating electromagnetic wave




Radio waves are a part of the electromagnetic spectrum



The output terminals of an induction coil act as a simple dipole transmitter, producing electromagnetic waves, including radio waves over a wide frequency range.



The radio waves can be detected with a radio receiver tuned off the station (so that the station signal does not swamp the weak radio waves from the induction coil)


• Reception of radio waves is dependent on the energy carried by the radio wave fields producing a current in a receiving antenna.

Receiver

Current in antenna

• Induction of a current occurs because the antenna is a conductor.• The antenna may be a simple length of wire, or sometimes a coil of wire

around an iron core, which can be moved by a tuning dial to alter the response of the antenna so that waves of different frequency can be received.

• The length of the antenna determines which frequencies are best received.


• Radio waves can be transmitted most easily along a line-of-sight path• Communication using microwaves requires line-of-sight repeater transmitters• The Earth’s ionosphere can be used to reflect the waves


• Almost all electronic devices produce electromagnetic radiation.• calculators, computers, cell phones, TVs, radios etc…

• Legislation requires computers to be shielded to prevent radio interference

• the shielding is usually a metal case enclosing the computer



AttenuationRadio waves, like all electromagnetic waves, obey the inverse square law.The further the receiver is from the source, the weaker the radio signal.


AttenuationThe intensity of the radio wave decreases as the square of the distance from the source.

transmitter

1 km2 km

3 km4 km

The Photoelectric Effect

Observation and Investigationfirst

Demonstration Two negatively charged electroscopes with polished zinc plates on top of them

Ultraviolet light shone onto one of the metal plates (the other one is the control) causes the electroscope it is resting on to lose its charge more rapidly than the control.Why is a control necessary?

A control is necessary because both electroscopes lose their charge. The important fact is that the UV light causes one to lose charge more rapidly.

U V



Photoelectrons are ordinary electrons Ultraviolet light produces photoelectronsThese are ejected from the zinc surface

ExplanationThe UV light causes electrons in the zinc to be ejected from the metal surface, resulting in a loss of negative charge from the metal, causing electrons to move from the electroscope to the zinc.

U V e e e

The electroscope is thus discharged - this is the photoelectric effect

e



An excellent quantitative simulation of the photoelectric effecthttp://home.a-city.de/walter.fendt/phe/photoeffect.htm



The photoelectric effect• The filter can be changed to select a specific wavelength from the source• Light above the threshold frequency will eject electrons from the cathode• A variable stopping voltage (note polarity) is adjusted to reduce the current to

zero• The stopping voltage is proportional to the incident light frequency• At a given frequency light, the current is proportional to the light intensity

stop

ping

vol

tage


The photoelectric effect and Albert EinsteinEinstein was awarded the Nobel Prize for his explanation of the photoelectric effect (not for relativity!)He proposed that• light consisted of quanta (later

called photons)• either ALL of a photon’s energy

was absorbed by an electron or NONE of it was

The Photoelectric Effect and Breathalysers

Application (ref: http://www.howstuffworks.com/breathalyzer3.htm)

• A lamp (A) produces a broadband (multiple-wavelength) IR beam.

• The IR beam passes through the sample chamber (D) and is focussed by a lens (E) onto a filter wheel (F).

• The filter wheel contains narrow band filters specific for the wavelengths of the bonds in ethanol. The light passing through each filter is detected by the photocell (G), where it is converted to an electrical pulse.

• The electrical pulse is relayed to a microprocessor, which interprets the pulses and calculates the BAC based on the absorption of infrared light.

Alcohol reacts with chemicals in the breathalyser, causing a colour change dependent on the amount of alcohol in the sample.The chemicals absorb varying amounts of the IR light, depending on their colour.

The Photoelectric Effect and Solar Cells

Application of photoelectric effect

• A photon enters the semiconductor

• It may be absorbed and raise an electron from the valence to the conduction band

• The absorption process generates electron-hole pairs

• Immediately after their creation, the electron and hole decay to energy states near the edges of their respective bands

A “solar cell” is more correctly called a photovoltaic cell

A photovoltaic cell converts light energy to electrical energy

The Photoelectric Effect and Photovoltaic Cells


Contact between p and n type semiconductors produces an electric field at the junction region.

The direction of this field is from the n-layer to the p-layer.

Electric field region


• At the p-n junction, conduction band electrons move from the n-layer to holes in the p-layer, creating a field

• Light falling on a p-n junction device, disturbs the electric field equilibrium

• Light energy produces free electrons in the p-layer allowing current to flow, establishing a voltage at the external terminals

• Thus light energy has produced a voltage providing electrical energy



An alternative explanation


The Photoelectric Effect and Photocells

Application

A “photocell” is probably better called a “photoconductive cell”A photoconductive cell is also known as a photoresistor it is the earliest photoelectric device developed.

Photoconductive cells are used to turn street lights on and off automatically, as counting devices on production lines, in various alarm systems, and in supermarkets as the sensor that scans codes on grocery items at checkout counters and in photography as the light meters used to measure the intensity of illumination.

Energy of light in modern photoconductive cell is used to free electrons from their valence bonds in a semiconductor material. At room temperature, 21°C (294.16K), the number of free charges in a semiconductor is relatively limited. Light-released electrons raises its conductivity. The resistance may change from several hundred thousand ohms in the dark to a few hundred ohms in sunlight. To increase the dark resistance and reduce the dark current, the conducting path is often laid down in a zigzag manner on a ceramic wafer.

A number of substances are photoconductive. Some of which are lead sulfide (PbS), lead selenide (PbSe), and lead telluride (PbTe) are sensitive to infrared radiation, whereas cadmium sulfide (CdS) has sensitivity to light in the visual range.

The Blackbody Radiation Model

In the second half of the 19th century, the study of heat lead to major scientific and industrial developments.

Scientists were interested in understanding the nature of radiation emitted by hot objects.

The dependence of the radiation on the temperatures of the objects was investigated and the amount of radiation emitted at different wavelengths for objects at different temperatures was determined...

Sun 15th Aug 2002

Blackbody Radiation – Planck and Einstein

Black body radiation curves at various temperatures

These graphs show the radiation emission curves for hot objects at different temperatures.

Note that…

• as the temperature increases, the peak wavelength emitted by the black body decreases

• as temperature increases, the total energy emitted increases, because the total area under the curve increases

The concept of a blackbody radiator was first defined by Kirchoff in 1860

The Blackbody Radiation Model

An ideal blackbody radiator has these properties... It• is a perfect absorber and emitter of radiation• re-emits all radiation incident on the blackbody• emits radiation with characteristics dependant only on the

temperature of the objectExamples closely approximating ideal blackbody radiators include...• the inside of a furnace (such as a

brick kiln or pottery kiln• the surface of the Sun• tiles on the space shuttle during re-

entry into the atmosphere

A blackbody was first defined by Kirchhoff in 1859-60 as an object that re-emits all of the radiant energy incident upon it. i.e., it is a perfect emitter and absorber of radiation. (http://astro.estec.esa.nl/SA-general/Projects/Planck/mplanck/mplanck.html)


Planck was able to account for the shape of the blackbody radiation curves by postulating that energy was emitted in discrete packets (“quanta”), rather than continuously as was the classical theory.This novel concept was to usher in quantum mechanics, the triumph of physics in the 20th century.Einstein was soon to use the quantum concept in explaining the photoelectric effect - but he never accepted the uncertainty inherent in quantum mechanics.

Max Planck


Assess and Analyse

The solid curve shows the blackbody spectrum of an object at 5000 KThe surface of the Sun is an approximation of such a blackbody emitter.The dotted line shows the intensity / frequency relationship predicted by the classical theory

The classical theory* was unable to account for the observed distribution of radiation intensity at different wavelengths.* A key concept of classical physics was that quantities were continuous and could take on any value


• electromagnetic radiation must be absorbed by electrons in the metal in discrete packets (quanta)

• electromagnetic radiation is quantised• an oscillating charge (e.g. electron) can accept or

lose energy in small discrete amounts with the quantum having an energy hf*

E=hf

U V e e e

e

In his 1905 explanation of the photoelectric effect, Einstein concluded that

* hf = Plank’s constant x frequency h = 6.6 x 10–34 Js


Therefore Einstein no longer thought of radiation as being continuous, as demanded by the wave model. He said it consisted of a series of "packets" of energy.This meant that radiation was being thought of as a "packet of energy" but also as a wave because it had a frequency. These later became known as photons.Planck had had no explanation for his quantum model for blackbody radiation but he knew it was necessary and that it worked - this is called an empirical result.

E=hf

U V e e e

eEinstein’s quantum explanation of the photoelectric effect thus provided an explanation for Planck’s quantum analysis of blackbody radiation.

The Particle Theory of Light

Photon energy and frequency

E=hf

c=fλ

Calculate the energy of a photon of red light having a wavelength of 700 nm.

Calculate the frequency of the light3 × 108 =f × 700 x 10−9

f =4.29 × 1014 Hz

E =6.626 × 10−34 × 4.49 × 1014

E = 2.84 × 10−19 J

[700 nm = 700 x 10–9 m]

Hence calculate the energy of the light photon

The Particle Theory of Light

Solving Problems

E=hf

c=fλ

The Einstein - Planck Debate

The nature of science research - social and political forces

There was no direct debate between Einstein and Planck.The intention of the syllabus outcome is unclearIt may refer to the different views Planck and Einstein took about scientists remaining in Germany during the WWI Nazi era and continuing to do scientific research.Planck, along with nearly a hundred leading German intellectuals signed a manifesto defending Germany’s war actions. Planck stayed on and directed the Kaiser Wilhelm Institute.Einstein left Germany. Although there was no direct correspondence between Einstein and Planck, consideration of the actions of each provides a case study of the complexity of evaluating the moral responsibility of science to social orders.See MS word article “Planck_Einstein_Debate.doc” for further comment.

Describing the de Broglie Model

De Broglie hypothesised that electrons might have wave properties.He reasoned that if photons have an equivalent mass (based on Einstein’s relativity theory relating mass and energy), and they had wave properties, that electrons, with a small mass, would conversely have wave properties.His hypothesis was confirmed by experiments demonstrating that an electron beam produced a diffraction pattern, very similar to x-ray diffraction, when passed through crystalline materials.

X-ray diffraction produced by potassium sulfate crystals[right]


Electron orbits

• De Broglie predicted that moving electrons would have wave properties• Wave properties restrict the orbits of electrons to specific, discrete values• Orbits not involving a whole number of electron wavelengths would produce

destructive interference

A possible electron orbit An impossible orbit


Electron orbits - background

De Broglie related work done by Planck and Einstein, producing a result that correctly predicted the wave properties of electrons and their associated wavelengths.

Electrons in Solids - Insulators

The electrons in insulators are all held firmly in chemical bonds (“shared between atoms” - syllabus)

The electrons are unable to move, hence these materials do not conduct electricity.

Diamonds are a good example of an electrical insulator.

Covalent compounds (for the benefit of chemistry students), or substances made of a mixture of such compounds, do not conduct electricity well - they are insulators. e.g. sugar, alcohol, wood, paper, glass, ceramics (except for superconducting ceramics).

Electrons in Solids - Insulators

In insulators such as diamond, the outer electrons are used in pairs to form chemical bonds between atoms and so these

electrons are not free to move through the material

C C C

C C C

Electrons in Solids - Conductors

Solids, that are conductors, have electrons in them that can readily move through the material. Most metals are very good electrical conductors because the outer electrons of the atoms are free to move from atom to atom. Even the colour of metals is due to this “sea of electrons”.

Electron conduction through metals under the action of an electric field.

Electrons in Solids - Conductors

Electrons in insulators cannot move through the materialThere is no sharp division between conductors and insulators

Metals have a lattice structure of immovable positive ions in a sea of electrons free to move through the structure

Electrons in Solids - Semiconductors

A pure single crystal of silicon

Sliced into disks for IC production

Becomes an integrated circuit (P2)

The Periodic Table - Semiconductors

14

Si

32

Ge

Comparison of number of charge carriers

Qualitative only

insulators have almost no free charge carriers

conductors have many charge carriers

Semiconductors have much fewer

charge carriers than conductors, but

more that insulators

conductorsinsulators semiconductors

Num

ber o

f cha

rge

carri

ers


Band structure and electrical resistance

Outer electrons in metals are already in the conduction band.It takes some energy to move electrons from the valence to the conduction band in semiconductors.Larger band gaps result in greater resistances of materials.



ExplanationAtomic vibration excites some electrons across the band gap into the conduction band.Corresponding holes are created in the valence band.Both holes and electrons act as charge carriers.As the temperature increases, the number of electron-hole pairs increases and the semiconductor conductivity increases.In metals, conductivity decreases with increasing temperature.

Electrical Conduction in Semiconductors

14

Si

32

Ge

Pure semiconductors are called intrinsic semiconductors

Intrinsic semiconductors are insulators at 0 K (absolute zero)

Above absolute zero the conductivity of intrinsic semiconductors increases with increasing temperature


Investigation - electrons, holes and conduction when an electric field is applied

–––

+++

Electrons and holes exist in equal numbers

When an electric field is applied…

electrons and holes move in opposite directions

electron

hole


Investigation - electrons, holes and conduction when an electric field is applied

–––

+++

–––

+++

–––

+++

–––

+++

–––

+++

This model applies to intrinsic semiconductors

The invention of the transistor

How shortcomings in available technology lead to the invention of the transistor

By the late 1950s, electrical engineers were aware of the potential of digital electronics.The first digital computers had been built already, using vacuum tube technology.Circuits being designed required exponentially increasing numbers of components. The first digital computer had over 18000 valves which meant there was a very short time between breakdowns.This was mediated against by the physical limitations of assembling such large numbers of components together.

Invention of the Transistor - Role of Germanium

Germanium use related to lack of ability to produce [silicon] of suitable purity

The first transistors were made of germanium, rather than silicon, because• germanium could be purified and worked at significantly lower temperatures• it was too difficult to produce pure crystals of silicon for semiconductor use

An early germanium transistor

The first [germanium] transistor

Germanium was the First Semiconductor Used

Why silicon became the preferred material for the transistor

Germanium transistors had disadvantages including• undesirable variation in performance with

temperature increase • their low power outputs (limited by temperature

constraints)• the relative rarity and hence expense of germanium• mechanical “point contact” between doped

semiconductors, resulted in a lack of ruggedness and reliability

Silicon and the transistor

Why silicon became the preferred material for the transistor

The later use of silicon in transistors• resulted in an increase in the operating

temperature of semiconductor devices• improved semiconductor power handling ability

(because of higher Toperating)• grown junctions later used in silicon transistors

increased ruggedness and reliability

Doping of semiconductors

How doping changes electrical properties

• The electrical properties of semiconductors can be changed by the addition of minute quantities of other elements into the crystal lattice

5

B15

P

• This process is called “doping”• Elements used for doping typically have either 3

or 5 outer electrons, and similar size atoms to the semiconductor material so that they substitute readily into the semiconductor crystal lattice

• The electrical properties change due to the creation of additional charge carriers - doped semiconductors are better conductors than intrinsic semiconductors because they contain more charge carriers per unit volume


P-type and N-type semiconductors and relative numbers of charge carriers

• The addition of dopants containing 5 outer electrons produces a semiconductor having more free electrons in the conduction band than an intrinsic semiconductor. There are more negative charge carriers than holes.


Intrinsic, p-type and n-type semiconductors

n-type semiconductor1 atom in 200 000 substituted

The old “group V” is now called the group 15 elements


P-type and N-type semiconductors and relative numbers of charge carriers

• The addition of dopants containing 3 outer electrons produces a semiconductor having holes than there are electrons in the conduction band. There are more positive charge carriers than electrons free to flow as current.


Intrinsic, p-type and n-type semiconductors

The old “group III” is now called the group 13 elements

Differences between thermionic and solid state

Why solid state replaced thermionic devices (vacuum tubes)

Solid state devices have generally replaced thermionic devices• Small size• Better economy of operation - lower power consumption • Greater speed• Reliability is much better (more rugged, lower temperatures)• Economical to produce• Mass-production techniques are possible

Solar cells and the photoelectric effect

Semiconductors, electric fields and current in solar cells

Click here for link

9.4.4 Investigations into the electrical properties of particular metals at different temperatures led to the identification of superconductivity and the exploration of possible applications...

William and Lawrence Bragg (father and son) were awarded the 1915 Nobel Prize for “their services in the analysis of crystal structure by means of X-rays”

They were Australian scientists working in Britain.

• The x-rays were reflected from layers within the crystal.• Reflected x-rays produced an interference pattern.• The pattern was recorded on photographic film.• Mathematical analysis of the diffraction pattern

permitted the crystal structure to be deduced.

William and Lawrence Bragg used a collimated beam of x-rays to investigate the crystal structure of materials, including metals.

The pattern produced depended on

• The wavelength of the x-rays• The distance between planes

of atoms in the crystal• The angle of incidence of the

x-rays on the crystal planes

X-ray crystallography apparatus - schematic

A typical x-ray crystallography diffraction interference pattern

[potassium sulfate]

The work of William and Lawrence Bragg was a key to understanding the crystal structure of

• Metals• Inorganic compounds (e.g. sodium chloride)

Later, the techniques developed by William and Lawrence Bragg were used to investigate the structure of

• Ceramics• DNA (by Rosalind Franklin, Crick and Watson)

Knowledge of the structure of metals and ceramics lead to the development of theoretical models for superconductivity and the discovery of high temperature superconductors.

The Impact of the Braggs’ Contribution to Understanding Crystal Structure

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• William and Lawrence Bragg developed the Bragg spectrometer

• (a) State which component of the electromagnetic spectrum the Bragg spectrometer used. (1 mark)

• (b) State specifically what their device was used to study and why visible light was not used for their spectrometer.(2 marks)

• Clarify the difference in behaviour of electrons when they flow in a metal at room temperature and when they flow in a superconductor below its critical (transition) temperature.(3 marks)

William and Lawrence Bragg pioneered x-ray diffraction techniques

that allowed the crystal structure of metals to be

investigated

1. Electrons interact with the lattice atoms when a collision occurs, and then the velocity of the electron abruptly and randomly changes direction as a result of collision and some energy is transferred to the lattice atoms, causing them to vibrate.

2. Thermal equilibrium exists throughout the conductor.

3. Conduction electrons do not interact with each other.

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• Metals have a large number of electrons in the conduction band relative to other materials.

• Electrons in the conduction band can move freely when an electric field is applied.

Lattice of positive ions

electron

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+Electric field

Random changes of direction of the motion of individual electrons is a result of collisions with vibrating atoms in the metallic crystal lattice.

Individual electrons move through a metal conductor at an average speed of a few centimetres per minute.They are said to “drift” through the metal.The average rate at which electrons move through the conductor is called the drift velocity.

A potential difference producing an electric field to the left…

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will cause the electrons to drift to the right.

Collisions of the conduction electrons with the atoms in the lattice cause the atoms to vibrate more.Vibration of atoms is heat energy.Increasing the current through a metal results in more collisions and hence greater vibration of the atoms in the lattice.

Hence the temperature of a metallic conductor increases as the current increases.If a metal conductor is cooled, there is less vibration and fewer collisions with the conduction electrons.This causes the resistance to decrease.



This animation models the drift of electrons through a conductor and the collisions of the electrons with the lattice ions

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For any given current, the electron drift velocity is

inversely proportional to the density of electrons

inversely proportional to the cross sectional area of wire

inversely proportional to the electronic charge

* This is hardly a “discuss” outcome!

but that’s what the syllabus says...

*

Review of band gaps and conduction

Metals have very small band gaps compared with insulators and semiconductors

Superconductivity Syllabus 9.4.4 Column 2



Pair formation (avi)

Superconductors are materials which, below a particular temperature called the transition temperature allow electrons to move through the crystal lattice with no loss of energy to the lattice - i.e. no heat loss.

Superconductivity Syllabus 9.4.4 Column 2 Bardeen, Cooper and Schrieffer proposed a theory [Now called the BCS Theory] of superconductivity in which electron pairs interact with the superconducting lattice in a process called electron-phonon interaction.

Superconductivity Syllabus 9.4.4 Column 2

Bardeen

Cooper

Superconductivity Syllabus 9.4.4 Column 2 Bardeen

Cooper

BCS Theory

• In 1957 a remarkably successful theory was developed to explain superconductivity

• The theory explains superconductivity as a result of electrons interacting and travelling in pairs within the crystal lattice

• This theory was developed by Bardeen, Cooper, and Schrieffer at the University of Illinois 46 years after the discovery of superconductivity

• They were awarded the Nobel Prize in 1972 (Bardeen also won the Nobel Prize in 1956 for inventing the transistor)

The electron creates a phonon, a wave disturbance, carrying momentum through the lattice as if it were a particle travelling through the lattice

A second electron passing by the moving region of positive charge density experiences an attractive electrostatic force causing it to increase its momentum i.e. it absorbs the phonon

Superconductivity involves pairs of electrons

The electrons exchange some momentum with each other through the phonon interaction

The second electron effectively travels freely in the virtual lattice wake of the leading electron

BCS theory predicts that under certain conditions, the attraction between the two electrons due to phonon exchanges can be slightly greater than the electrostatic repulsion between them

The effect of this attraction is that the electrons will be weakly bound together what is called a Cooper pair

pairs interact with the superconducting lattice in a process called electron-phonon interaction.

Superconductivity involves pairs of electrons

The conditions for production of superconductivity are

1. The temperature of the material must be low enough so that the number of random thermal phonons be small

2. The interaction between an electron and phonon must be large

3. The number of electrons in energy states capable of forming Cooper pairs must be large

4. The two electrons have antiparallel spins enabling them to form a pair

Conditions Needed for Superconductivity

Cooper pairs are constantly forming and breaking apart Many Cooper pairs occupy overlapping spaces within the

lattice (this is possible because as a pair, they have zero spin) permitting the interaction of many electrons in the pairing process

All Cooper pairs have the same quantum state and in the ground state, all electrons form bound pairs

All the Cooper pairs represent a highly ordered system and when an external electric field is applied, the pairs move through the lattice with each pair’s motion locked to that of every other pair so that none are involved in the random scattering within the lattice, which gives rise to electrical resistance

The Mechanism for Superconductivity

An external magnetic field interacts with the opposite spins of the Cooper pair, raising the energy of one and lowering the energy of the other

If the external field is large enough, both electrons will point in the same direction, destroying the Cooper pairs and hence the superconductivity of the material

Strong External Magnetic Fields Destroy Superconductivity

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Material Ir Ru Cd Zn Ga Al Sn Hg Pb Nb

Transition Temp(K)

0.1 0.50 0.56 0.85 1.08 1.20 3.72 4.15 7.19 9.46

• At temperatures approaching absolute zero, the resistance of many metals suddenly drops to zero

• The temperature at which this occurs is called the transition temperature

• They are said to have become superconductors• The temperature at which the transition to the

superconducting state is different for different metallic elements

• These materials are classified as low-temperature superconductors

Superconductivity of Elements

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• Some alloys have higher transition temperatures than the constituent elements

• Ceramic materials have been made with even higher transition temperatures than the metal alloys - these are called high-temperature superconductors

• There is a special interest in high-temperature superconductors, because the transition temperature can be attained using liquid nitrogen at a temperature of 77 K

Material Ir Ru Cd Zn Ga Al Sn Hg Pb Nb

Transition Temp(K)

0.1 0.50 0.56 0.85 1.08 1.20 3.72 4.15 7.19 9.46

Superconductivity of Alloys and Ceramics

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A small, strong permanent magnet, such as a neodymium magnet, placed above a superconductor hovers above the surface of the superconductor due to a force of repulsion.

The force is produced by the magnetic fields produced by the electric currents induced in the superconductor. The induced currents produce magnetic poles that mirror the levitated magnet’s poles.

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Superconductors

Magnetic Levitation

Superconductor

magnet

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Superconductors

Magnetic Levitation

QuestionIn your course, you performed an investigation to observe magnetic levitation and the way in which a magnet is held in position by a superconducting material.

Recount how you performed this investigation.

Answer

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Answer

Superconductors - Magnetic Levitation

QuestionIn the physics course, you performed an investigation to observe magnetic levitation and the way in which a magnet is held in position by a superconducting material. With reference to specific hazards, clarify procedures you put in place to minimise these hazards when carrying out this investigation.

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Answer

Superconductors

Magnetic Levitation

QuestionExplain why a magnet is able to hover above a superconducting material that has reached the temperature at which it is superconducting.

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A small, strong permanent neodymium magnet (gold colour), hovers above the surface of the dark coloured superconducting disk immersed in liquid nitrogen at 77 kelvins. The magnet remains suspended, even when stationary (no flux change) because the current in the superconductor keeps flowing once it is induced.

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A Japanese designed and built magnetically levitated train has travelled at speeds exceeding 520 kmh–1 using superconducting magnets on-board the train.

The magnets induce currents in the rails below them, causing a repulsion, which balances the force of gravity, allowing the train to move without direct contact with the track.

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Superconductivity and Maglev Trains

Superconductivity Syllabus Col. 3

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Superconductivity and Maglev Trains

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Key pointsMaglev has had slow development because of high infrastructure costsRunning costs are expected to be about a third that of traditional rail transport and 20% that of an aircraftCommercial maglev due to begin operation in 2003 from Shanghai to its airport (33 km link)Maglev trip Melb-Syd would be 8 hours[Copy/paste and print this article for clearer reading!]

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Key pointsTransrapid says maglev would be faster than the French TGV (300 km/h)(it’s a business - they WOULD say that!)

Two maglevs being considered in Germany - short distances only[no air competition!]

Two projects receiving funding in USNetherlands also considering maglev[Copy/paste and print this article for clearer reading!]

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• Electrical Grids - for the generation, transmission and storage of power, improving power supply quality (in generators, cables, transformers)

• Motors - DC and AC electric motors, propulsion systems• Bearings - for frictionless motion (flywheels, magnetic

levitation)• Magnet Systems - for current leads, MRI, beam focusing

magnets, very high field research magnets

Applications of Superconductivity

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Superconducting Transmission Lines

Since 10% to 15% of generated electricity is dissipated as heat due to resistive losses in transmission lines, the prospect of zero loss superconducting transmission lines is appealing.

A prototype superconducting transmission line was able to 1000 MW of power within a conductor of diameter 40 cm.

This is equivalent to the transmission of the entire output of a large electrical power station on a single conducting transmission line.

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Superconducting Motors

The world's first 1000 hp HTS industrial motor was successfully tested in July 2000 by Rockwell Automation Power Systems and American Superconductor

http://www.amsuper.com/navyupdate.htm

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Superconducting Transmission Lines

Superconducting wires would have the advantage of allowing energy to be transmitted using low voltage DC.High voltages are used to transmit energy to minimise resistive heat losses in the transmission lines.The use of superconductors would remove the need for large transformer banks and multiple high voltage AC transmission lines on towers as is used in the conventional electricity grid.

Efforts are being made to develop practical high temperature superconductors with transition temperatures higher than the boiling point of nitrogen to permit the transmission of energy at temperatures realistically and economically achievable on a large scale.

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Electromagnets using superconducting coils are used to produce very strong magnetic fields used in particle accelerators such as Fermilab

Superconductivity is Used to Make Super-strong Magnets

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Historical Advance of Tc

Useful reference: http://superconductors.org/

Transition Temperatures [or Critical Temperatures]

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Transition Temperatures

Historical Advance of Tc

The discovery of high-temperature superconductors, significantly changed the potential for applications of superconductivity.

Such materials are superconducting above the temperature of liquid nitrogen - a temperature readily achievable.

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Historical Perspective on Superconducting Transition Temperatures

Critical temperature

(kelvins)

Transition Temperatures

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Resistance characteristics of a high temperature superconductor

The resistance of superconductors becomes zero abruptly at Tc

Resistivity Drops to Zero at the Transition Temperature

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Resistance of a Superconductor

Real data - experimental error occurs in real science!

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Application of Superconductors to Power Transmission

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Electromagnets using superconducting coils are used to produce very strong magnetic fields used in medical magnetic resonance imaging

Superconductors are Used in MRI Machines

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Macroscopic Quantum State

• All electron pairs in a superconductor move through the lattice in unison.• The Cooper Electron Pairs retain this ordered structure while moving through the

crystal lattice in the presence of an external electric field. Thus each pair becomes locked into its position with others pairs, and as a result no random scattering of electron pairs may occur due to crystal imperfections (caused by a low degree of vibrational energy resulting from the low temperature).

• Zero resistivity may be defined as the absence of electron scattering from the crystal lattice and hence the superconductor now demonstrates zero resistivity.

• All Cooper Electron Pairs throughout the material effectively condense to a single quantum state, and the entire structure behaves as though an enormous quantum mechanical system. On the macroscopic level, the system is quantised and may be represented by a single wave function extending the entire material.

• It could be argued that because the electron pairs throughout the material are in a single quantum state, unlike any other state of matter - solid, liquid or gas - that superconductors could be considered a separate state of matter.

Are Superconductors a New State of Matter?

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Superconductivity is a Phenomenon Needing a Quantum Mechanical Model for its Explanation and as such it could be considered a new state of matter. It is called a Bose-Einstein condensate. Such a state is generally agreed to have properties justifying its being classified as a separate state of matter.

Phenomena requiring a quantum model for their explanation…

• Lasers

• Superfluidity - liquid helium

• Superconductivity

• Bose-Einstein condensates[includes superconductors]


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Phenomena Needing a Quantum Mechanical Model

Examples of BECs

• Helium atoms: superfluidity• Cooper pairs: superconductivity• Super-atoms at extremely low temperatures

(0.000 000 1 Kelvin)


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2000 Rubidium Atoms Forming a BEC

Scientists Have Created Other Bose-Einstein Condensates

END

Good Luck with your HSC

Return

* Retell a series of events

QuestionRecount* how you performed this investigation.

• a high temperature superconducting disk was placed in a container and the disk was just covered with liquid nitrogen

Liquid N2

HTS disk

HTS disk

Liquid N2

magnet

• the superconductor was left for a short time until it cooled to the temperature at which its resistance dropped to zero

• a strong magnet was then carefully placed, using plastic tweezers, just above the superconducting disk

• The magnet hovered above the HTS disk

Return

Question… clarify procedures you put in place to minimise these hazards…

* Clarify: make clear or plain

• Wear safety glasses to protect eyes from being splashed with liquid nitrogen or being exposed to freezing vapours

• Wear thick cotton gloves to protect hands in the case of spills, and to prevent their contact with very low temperature (cryogenic) materials in the experiment

• Handle the magnet with plastic tweezers when placing it near the cryogenic materials - this keeps hands at a safe distance and the plastic does not conduct heat well

• Wear thick, closed shoes to prevent spills coming into contact with the feet. Long pants should cover shoes.

QuestionExplain* why a magnet is able to hover above a superconducting material that has reached the temperature at which it is superconducting.

Return

* Relate cause and effect; make the relationships between things evident; provide why and/or how

The effect of magnetic levitation is caused by induced magnetic poles on the surface of the superconductor repelling the magnet, causing it to hover above the HTS surface

HTS disk

Liquid N2

magnetThe magnetic poles on the superconductor are produced by large currents induced on the superconductor surface by the flux changes produced by the magnet above. The currents are large because the HTS has no resistance at temperatures below Tc

N

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opposing poles

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rProduction and Perception

Visible light consists of light of wavelengths ranging from 400 to 700 nm

If all colours are present at equal intensities, the result we see is white

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A balance of red, green, and blue is also perceived as white

If the colours are present at equal intensities, the result we see is white

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A CRT or LCD can display all colours using just three coloured pixels

The reason this is possible is because the eye has cells that respond to red, green and blue wavelengths.

When we perceive a colour such as yellow, it is because the red and green sensing cells are being equally stimulated.

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Hot objects emit light over a range of frequencies

If the colours are present at equal intensities, the result we see is white

warm

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very hot

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An object at 5000 K emits light over all visible wavelengths, as well as longer and shorter wavelengths than visible light.

The balance of wavelengths present favours the longer parts of the spectrum resulting in a perceived colour that is yellow rather than white.

From Ideas to Implementation

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