Chapter 30

Nuclear Energy and

Elementary Particles

Processes of Nuclear Energy Fission

A nucleus of large mass number splits into two smaller nuclei

Fusion Two light nuclei fuse to form a

heavier nucleus Large amounts of energy are

released in either case

Nuclear Fission A heavy nucleus splits into two

smaller nuclei The total mass of the products is less

than the original mass of the heavy nucleus

First observed in 1939 by Otto Hahn and Fritz Strassman following basic studies by Fermi

Lisa Meitner and Otto Frisch soon explained what had happened

Fission Equation Fission of 235U by a slow (low energy)

neutron

236U* is an intermediate, short-lived state Lasts about 10-12 s

X and Y are called fission fragments Many combinations of X and Y satisfy the

requirements of conservation of energy and charge

More About Fission of 235U About 90 different daughter nuclei

can be formed Several neutrons are also

produced in each fission event Example:

The fission fragments and the neutrons have a great deal of KE following the event

Sequence of Events in Fission The 235U nucleus captures a thermal (slow-

moving) neutron This capture results in the formation of

236U*, and the excess energy of this nucleus causes it to undergo violent oscillations

The 236U* nucleus becomes highly elongated, and the force of repulsion between the protons tends to increase the distortion

The nucleus splits into two fragments, emitting several neutrons in the process

Sequence of Events in Fission – Diagram

Energy in a Fission Process Binding energy for heavy nuclei is about

7.2 MeV per nucleon Binding energy for intermediate nuclei

is about 8.2 MeV per nucleon Therefore, the fission fragments have

less mass than the nucleons in the original nuclei

This decrease in mass per nucleon appears as released energy in the fission event

Energy, cont An estimate of the energy released

Assume a total of 240 nucleons Releases about 1 MeV per nucleon

8.2 MeV – 7.2 MeV Total energy released is about 240 Mev

This is very large compared to the amount of energy released in chemical processes

Chain Reaction Neutrons are emitted when 235U

undergoes fission These neutrons are then available to

trigger fission in other nuclei This process is called a chain reaction

If uncontrolled, a violent explosion can occur

The principle behind the nuclear bomb, where 1 kg of U can release energy equal to about 20 000 tons of TNT

Chain Reaction – Diagram

Nuclear Reactor A nuclear reactor is a system designed to

maintain a self-sustained chain reaction The reproduction constant, K, is defined

as the average number of neutrons from each fission event that will cause another fission event The maximum value of K from uranium

fission is 2.5 In practice, K is less than this

A self-sustained reaction has K = 1

K Values When K = 1, the reactor is said to be

critical The chain reaction is self-sustaining

When K < 1, the reactor is said to be subcritical The reaction dies out

When K > 1, the reactor is said to be supercritical A run-away chain reaction occurs

Basic Reactor Design Fuel elements

consist of enriched uranium

The moderator material helps to slow down the neutrons

The control rods absorb neutrons

Reactor Design Considerations – Neutron Leakage

Loss (or “leakage”) of neutrons from the core

These are not available to cause fission events

The fraction lost is a function of the ratio of surface area to volume Small reactors have larger percentages lost If too many neutrons are lost, the reactor

will not be able to operate

Reactor Design Considerations – Neutron Energies Slow neutrons are more likely to cause fission

events Most neutrons released in the fission process

have energies of about 2 MeV In order to sustain the chain reaction, the

neutrons must be slowed down A moderator surrounds the fuel

Collisions with the atoms of the moderator slow the neutrons down as some kinetic energy is transferred

Most modern reactors use heavy water as the moderator

Reactor Design Considerations – Neutron Capture

Neutrons may be captured by nuclei that do not undergo fission Most commonly, neutrons are

captured by 238U The possibility of 238U capture is lower

with slow neutrons The moderator helps minimize the

capture of neutrons by 238U

Reactor Design Considerations – Power Level Control A method of control is needed to adjust the

value of K to near 1 If K >1, the heat produced in the runaway reaction

can melt the reactor Control rods are inserted into the core to

control the power level Control rods are made of materials that are

very efficient at absorbing neutrons Cadmium is an example

By adjusting the number and position of the control rods, various power levels can be maintained

Pressurized Water Reactor – Diagram

Pressurized Water Reactor – Operation Notes This type of reactor is commonly used

in electric power plants in the US Fission events in the reactor core supply

heat to the water contained in the primary system The primary system is a closed system

This water is maintained at a high pressure to keep it from boiling

The hot water is pumped through a heat exchanger

Pressurized Water Reactor – Operation Notes, cont The heat is transferred to the water

contained in a secondary system This water is converted into steam The steam is used to drive a turbine-

generator to create electric power The water in the secondary system is

isolated from the water in the primary system This prevents contamination of the secondary

water and steam by the radioactive nuclei in the core

Reactor Safety – Containment Radiation exposure, and its potential health

risks, are controlled by three levels of containment

Reactor vessel Contains the fuel and radioactive fission

products Reactor building

Acts as a second containment structure should the reactor vessel rupture

Location Reactor facilities are in remote locations

Reactor Safety – Loss of Water If the water flow was interrupted, the nuclear

reaction could stop immediately However, there could be enough residual heat

to build up and melt the fuel elements The molten core could also melt through the containment

vessel and into the ground Called the China Syndrome If the molten core struck ground water, a steam explosion

could spread the radioactive material to areas surrounding the power plant

Reactors are built with emergency cooling systems that automatically flood the core if coolant is lost

Reactor Safety – Radioactive Materials Disposal of waste material

Waste material contains long-lived, highly radioactive isotopes

Must be stored over long periods in ways that protect the environment

Present solution is sealing the waste in waterproof containers and burying them in deep salt mines

Transportation of fuel and wastes Accidents during transportation could expose the public

to harmful levels of radiation Department of Energy requires crash tests and

manufacturers must demonstrate that their containers will not rupture during high speed collisions

Nuclear Fusion Nuclear fusion occurs when two

light nuclei combine to form a heavier nucleus

The mass of the final nucleus is less than the masses of the original nuclei This loss of mass is accompanied by a

release of energy

Fusion in the Sun All stars generate energy through fusion The Sun, along with about 90% of other

stars, fuses hydrogen Some stars fuse heavier elements

Two conditions must be met before fusion can occur in a star The temperature must be high enough The density of the nuclei must be high

enough to ensure a high rate of collisions

Proton-Proton Cycle The proton-proton cycle

is a series of three nuclear reactions believed to operate in the Sun

Energy liberated is primarily in the form of gamma rays, positrons and neutrinos

21H is deuterium, and

may be written as 21D

Fusion Reactors Energy releasing fusion reactions are

called thermonuclear fusion reactions A great deal of effort is being directed

at developing a sustained and controllable thermonuclear reaction

A thermonuclear reactor that can deliver a net power output over a reasonable time interval is not yet a reality

Advantages of a Fusion Reactor Inexpensive fuel source

Water is the ultimate fuel source If deuterium is used as fuel, 0.06 g of

it can be extracted from 1 gal of water for about 4 cents

Comparatively few radioactive by-products are formed

Considerations for a Fusion Reactor The proton-proton cycle is not feasible

for a fusion reactor The high temperature and density required

are not suitable for a fusion reactor The most promising reactions involve

deuterium (D) and tritium (T)

Considerations for a Fusion Reactor, cont Deuterium is available in almost

unlimited quantities in water and is inexpensive to extract

Tritium is radioactive and must be produced artificially

The Coulomb repulsion between two charged nuclei must be overcome before they can fuse

Requirements for Successful Thermonuclear Reactor High temperature 108 K

Needed to give nuclei enough energy to overcome Coulomb forces

At these temperatures, the atoms are ionized, forming a plasma

Plasma ion density, n The number of ions present

Plasma confinement time, The time the interacting ions are maintained at

a temperature equal to or greater than that required for the reaction to proceed successfully

Lawson’s Criteria Lawson’s criteria states that a net

power output in a fusion reactor is possible under the following conditions n 1014 s/cm3 for deuterium-tritium n 1016 s/cm3 for deuterium-deuterium

The plasma confinement time is still a problem

Magnetic Confinement One magnetic

confinement device is called a tokamak

Two magnetic fields confine the plasma inside the doughnut

A strong magnetic field is produced in the windings

A weak magnetic field is produced in the toroid

The field lines are helical, spiral around the plasma, and prevent it from touching the wall of the vacuum chamber

Some Fusion Reactors TFTR

Tokamak Fusion Test Reactor Princeton Central ion temperature of 510 million

degrees C The n values were close to Lawson criteria

JET Tokamak at Abington, England 6 x 1017 DT fusions per second were

achieved

Current Research in Fusion Reactors

NSTX – National Spherical Torus Experiment Produces a spherical plasma with a hole in the center Is able to confine the plasma with a high pressure

ITER – International Thermonuclear Experimental Reactor

An international collaboration involving four major fusion programs is working on building this reactor

It will address remaining technological and scientific issues concerning the feasibility of fusion power

Other Methods of Creating Fusion Events Inertial laser confinement

Fuel is put into the form of a small pellet It is collapsed by ultrahigh power lasers

Inertial electrostatic confinement Positively charged particles are rapidly

attracted toward an negatively charged grid Some of the positive particles collide and

fuse

Elementary Particles Atoms

From the Greek for “indivisible” Were once thought to the elementary

particles Atom constituents

Proton, neutron, and electron Were viewed as elementary because

they are very stable

Discovery of New Particles New particles

Beginning in 1937, many new particles were discovered in experiments involving high-energy collisions

Characteristically unstable with short lifetimes

Over 300 have been cataloged A pattern was needed to understand all

these new particles

Quarks Physicists recognize that most particles

are made up of quarks Exceptions include photons, electrons and a

few others The quark model has reduced the array

of particles to a manageable few The quark model has successfully

predicted new quark combinations that were subsequently found in many experiments

Fundamental Forces All particles in nature are subject

to four fundamental forces Strong force Electromagnetic force Weak force Gravitational force

Strong Force Is responsible for the tight binding of

the quarks to form neutrons and protons

Also responsible for the nuclear force binding the neutrons and the protons together in the nucleus

Strongest of all the fundamental forces Very short-ranged

Less than 10-15 m

Electromagnetic Force Is responsible for the binding of

atoms and molecules About 10-2 times the strength of

the strong force A long-range force that decreases

in strength as the inverse square of the separation between interacting particles

Weak Force Is responsible for instability in certain

nuclei Is responsible for beta decay

A short-ranged force Its strength is about 10-6 times that of

the strong force Scientists now believe the weak and

electromagnetic forces are two manifestations of a single force, the electroweak force

Gravitational Force A familiar force that holds the planets,

stars and galaxies together Its effect on elementary particles is

negligible A long-range force It is about 10-43 times the strength of the

strong force Weakest of the four fundamental forces

Explanation of Forces Forces between particles are often

described in terms of the actions of field particles or quanta For electromagnetic force, the photon

is the field particle The electromagnetic force is

mediated, or carried, by photons

Forces and Mediating Particles (also see table 30.1)

Interaction (force)Mediating Field Particle

Strong Gluon

Electromagnetic Photon

Weak W and Z0

Gravitational Gravitons

Paul Adrien Maurice Dirac 1902 – 1984 Instrumental in

understanding antimatter

Aided in the unification of quantum mechanics and relativity

Contributions to quantum physics and cosmology

Nobel Prize in 1933

Antiparticles For every particle, there is an antiparticle

From Dirac’s version of quantum mechanics that incorporated special relativity

An antiparticle has the same mass as the particle, but the opposite charge

The positron (electron’s antiparticle) was discovered by Anderson in 1932

Since then, it has been observed in numerous experiments

Practically every known elementary particle has a distinct antiparticle

Exceptions – the photon and the neutral pi particles are their own antiparticles

Hideki Yukawa 1907 – 1981 Predicted the

existence of mesons

Nobel Prize in 1949

Mesons Developed from a theory to explain the

strong nuclear force Background notes

Two atoms can form a covalent bond by the exchange of electrons

In electromagnetic interactions, charged particles interact by exchanging a photon

A new particle was proposed to explain the strong nuclear force It was called a meson

Mesons, cont The proposed particle would have a

mass about 200 times that of the electron

Efforts to establish the existence of the particle were done by studying cosmic rays in the 1930’s

Actually discovered multiple particles Pi meson (called pion) Muon

Plays no role in the strong interaction

Pion There are three varieties of pions

+ and - Mass of 139.6 MeV/c2

0

Mass of 135.0 MeV/c2

Pions are very unstable - decays into a muon and an

antineutrino with a lifetime of about 2.6 x10-8 s

Richard Feynmann 1918 – 1988 Contributions include

Work on the Manhattan Project Invention of diagrams to

represent particle interactions Theory of weak interactions Reformation of quantum

mechanics Superfluid helium Challenger investigation

Shared Nobel Prize in 1965

Feynman Diagrams A graphical representation of the

interaction between two particles Feynman diagrams are named for

Richard Feynman who developed them

Feynman Diagram – Two Electrons The photon is the field

particle that mediates the interaction

The photon transfers energy and momentum from one electron to the other

The photon is called a virtual photon

It can never be detected directly because it is absorbed by the second electron very shortly after being emitted by the first electron

The Virtual Photon The existence of the virtual photon

would be expected to violate the law of conservation of energy But, due to the uncertainty principle

and its very short lifetime, the photon’s excess energy is less than the uncertainty in its energy

The virtual photon can exist for short time intervals, such that E t

Feynman Diagram – Proton and Neutron The exchange is via the

nuclear force The existence of the pion

is allowed in spite of conservation of energy if this energy is surrendered in a short enough time

Analysis predicts the rest energy of the pion to be 130 MeV / c2

This is in close agreement with experimental results

Classification of Particles Two broad categories Classified by interactions

Hadrons – interact through strong force

Leptons – interact through weak force

Hadrons Interact through the strong force Two subclasses

Mesons Decay finally into electrons, positrons, neutrinos and

photons Integer spins

Baryons Masses equal to or greater than a proton Noninteger spin values Decay into end products that include a proton

(except for the proton) Composed of quarks

Leptons Interact through weak force All have spin of 1/2 Leptons appear truly elementary

No substructure Point-like particles

Scientists currently believe only six leptons exist, along with their antiparticles Electron and electron neutrino Muon and its neutrino Tau and its neutrino

Conservation Laws A number of conservation laws are

important in the study of elementary particles

Two new ones are Conservation of Baryon Number Conservation of Lepton Number

Conservation of Baryon Number Whenever a baryon is created in a

reaction or a decay, an antibaryon is also created

B is the Baryon Number B = +1 for baryons B = -1 for antibaryons B = 0 for all other particles

The sum of the baryon numbers before a reaction or a decay must equal the sum of baryon numbers after the process

Conservation of Lepton Number There are three conservation laws,

one for each variety of lepton Law of Conservation of Electron-

Lepton Number states that the sum of electron-lepton numbers before a reaction or a decay must equal the sum of the electron-lepton number after the process

Conservation of Lepton Number, cont

Assigning electron-lepton numbers Le = 1 for the electron and the electron neutrino Le = -1 for the positron and the electron antineutrino Le = 0 for all other particles

Similarly, when a process involves muons, muon-lepton number must be conserved and when a process involves tau particles, tau-lepton numbers must be conserved Muon- and tau-lepton numbers are assigned

similarly to electron-lepton numbers

Strange Particles Some particles discovered in the 1950’s

were found to exhibit unusual properties in their production and decay and were given the name strange particles

Peculiar features include Always produced in pairs Although produced by the strong interaction,

they do not decay into particles that interact via the strong interaction, but instead into particles that interact via weak interactions

They decay much more slowly than particles decaying via strong interactions

Strangeness To explain these unusual properties, a new

law, conservation of strangeness, was introduced Also needed a new quantum number, S The Law of Conservation of Strangeness states

that the sum of strangeness numbers before a reaction or a decay must equal the sum of the strangeness numbers after the process

Strong and electromagnetic interactions obey the law of conservation of strangeness, but the weak interactions do not

Bubble ChamberExample The dashed lines

represent neutral particles

At the bottom, - + p 0 + K0

Then 0 - + p and

K0 + µ- + µ

Murray Gell-Mann 1929 – Worked on

theoretical studies of subatomic particles

Nobel Prize in 1969

The Eightfold Way Many classification schemes have been

proposed to group particles into families These schemes are based on spin, baryon

number, strangeness, etc. The eightfold way is a symmetric pattern

proposed by Gell-Mann and Ne’eman There are many symmetrical patterns that

can be developed The patterns of the eightfold way have

much in common with the periodic table Including predicting missing particles

An Eightfold Way for Baryons

A hexagonal pattern for the eight spin 1/2 baryons

Strangeness vs. charge is plotted on a sloping coordinate system

Six of the baryons form a hexagon with the other two particles at its center

An Eightfold Way for Mesons

The mesons with spins of 0 can be plotted

Strangeness vs. charge on a sloping coordinate system is plotted

A hexagonal pattern emerges

The particles and their antiparticles are on opposite sides on the perimeter of the hexagon

The remaining three mesons are at the center

Quarks Hadrons are complex particles with size

and structure Hadrons decay into other hadrons There are many different hadrons Quarks are proposed as the elementary

particles that constitute the hadrons Originally proposed independently by Gell-

Mann and Zweig

Original Quark Model Three types

u – up d – down s – originally sideways, now strange

Associated with each quark is an antiquark The antiquark has opposite charge,

baryon number and strangeness

Original Quark Model, cont Quarks have fractional electrical

charges +1/3 e and –2/3 e

All ordinary matter consists of just u and d quarks

Original Quark Model – Rules All the hadrons at the time of the

original proposal were explained by three rules Mesons consist of one quark and one

antiquark This gives them a baryon number of 0

Baryons consist of three quarks Antibaryons consist of three

antiquarks

Additions to the Original Quark Model – Charm Another quark was needed to account

for some discrepancies between predictions of the model and experimental results

Charm would be conserved in strong and electromagnetic interactions, but not in weak interactions

In 1974, a new meson, the J/ was discovered that was shown to be a charm quark and charm antiquark pair

More Additions – Top and Bottom Discovery led to the need for a more

elaborate quark model This need led to the proposal of two new

quarks t – top (or truth) b – bottom (or beauty)

Added quantum numbers of topness and bottomness

Verification b quark was found in a Y meson in 1977 t quark was found in 1995 at Fermilab

Numbers of Particles At the present, physicists believe

the “building blocks” of matter are complete Six quarks with their antiparticles Six leptons with their antiparticles See table 30.5

Color Isolated quarks

Physicist now believe that quarks are permanently confined inside ordinary particles

No isolated quarks have been observed experimentally

The explanation is a force called the color force

Color force increases with increasing distance This prevents the quarks from becoming isolated

particles

Colored Quarks Color “charge” occurs in red, blue,

or green Antiquarks have colors of antired,

antiblue, or antigreen Color obeys the Exclusion Principle A combination of quarks of each

color produces white (or colorless) Baryons and mesons are always

colorless

Quark Structure of a Meson

A green quark is attracted to an antigreen quark

The quark – antiquark pair forms a meson

The resulting meson is colorless

Quark Structure of a Baryon

Quarks of different colors attract each other

The quark triplet forms a baryon

The baryon is colorless

Quantum Chromodynamics (QCD) QCD gave a new theory of how quarks

interact with each other by means of color charge

The strong force between quarks is often called the color force

The strong force between quarks is carried by gluons Gluons are massless particles There are 8 gluons, all with color charge

When a quark emits or absorbs a gluon, its color changes

More About Color Charge Like colors repel and opposite colors attract

Different colors also attract, but not as strongly as a color and its anticolor

The color force between color-neutral hadrons is negligible at large separations The strong color force between the constituent

quarks does not exactly cancel at small separations

This residual strong force is the nuclear force that binds the protons and neutrons to form nuclei

QCD Explanation of a Neutron-Proton Interaction

Each quark within the proton and neutron is continually emitting and absorbing virtual gluons

Also creating and annihilating virtual quark-antiquark pairs

When close enough, these virtual gluons and quarks can be exchanged, producing the strong force

Weak Interaction The weak interaction is an extremely

short-ranged force This short range implies the mediating

particles are very massive The weak interaction is responsible for

the decay of c, s, b, and t quarks into u and d quarks

Also responsible for the decay of and leptons into electrons

Weak Interaction, cont The weak interaction is very important

because it governs the stability of the basic particles of matter

The weak interaction is not symmetrical Not symmetrical under mirror reflection Not symmetrical under charge exchange

Electroweak Theory The electroweak theory unifies

electromagnetic and weak interactions

The theory postulates that the weak and electromagnetic interactions have the strength at very high particle energies Viewed as two different

manifestations of a single interaction

The Standard Model A combination of the electroweak theory

and QCD form the standard model Essential ingredients of the standard

model The strong force, mediated by gluons, holds the

quarks together to form composite particles Leptons participate only in electromagnetic and

weak interactions The electromagnetic force is mediated by photons The weak force is mediated by W and Z bosons

The Standard Model – Chart

Mediator Masses Why does the photon have no mass

while the W and Z bosons do have mass? Not answered by the Standard Model The difference in behavior between low

and high energies is called symmetry breaking

The Higgs boson has been proposed to account for the masses

Large colliders are necessary to achieve the energy needed to find the Higgs boson

Grand Unification Theory (GUT) Builds on the success of the

electroweak theory Attempted to combine electroweak

and strong interactions One version considers leptons and

quarks as members of the same family

They are able to change into each other by exchanging an appropriate particle

The Big Bang This theory of cosmology states that

during the first few minutes after the creation of the universe all four interactions were unified All matter was contained in a quark soup

As time increased and temperature decreased, the forces broke apart

Starting as a radiation dominated universe, as the universe cooled it changed to a matter dominated universe

A Brief History of the Universe

George Gamow

1904 – 1968 Among the first to

look at the first half hour of the universe

Predicted: Abundances of

hydrogen and helium Radiation should still

be present and have an apparent temperature of about 5 K

Cosmic Background Radiation (CBR) CBR represents the

cosmic “glow” left over from the Big Bang

The radiation had equal strengths in all directions

The curve fits a blackbody at ~3K

There are small irregularities that allowed for the formation of galaxies and other objects

Connection Between Particle Physics and Cosmology

Observations of events that occur when two particles collide in an accelerator are essential to understanding the early moments of cosmic history

There are many common goals between the two fields

Some Questions Why so little antimatter in the Universe? Do neutrinos have mass?

How do they contribute to the dark mass in the universe?

Explanation of why the expansion of the universe is accelerating?

Is there a kind of antigravity force acting between widely separated galaxies?

Is it possible to unify electroweak and strong forces?

Why do quark and leptons form similar but distinct families?

More Questions Are muons the same as electrons, except

for their mass? Why are some particles charged and

others neutral? Why do quarks carry fractional charge? What determines the masses of

fundamental particles? Do leptons and quarks have a

substructure?