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

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

1 235 236

0 92 92 *n U U X Y neutrons

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

1 235 141 92 1

0 92 56 36 03n U Ba Kr n

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 rodsabsorb 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

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

1 1 2

1 1 1

1 2 3

1 1 2

1 3 4

1 2 2

3 3 4 1

2 2 2 12

H H H e

H H He

Then

H He He e

or

He He He H

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)

2 2 3 1

1 1 2 0

2 2 3 1

1 1 1 1

2 3 4 1

1 1 3 0

3.27

4.03

17.59

D D He n Q MeV

D D T H Q MeV

D T He n Q MeV

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

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 be the elementary particles

Atom constituents

Proton, neutron, and electron

Were viewed as elementary because they are very stable

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

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 ΔE Δt ħ

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

Classification of Particles

Two broad categories

Classified by interactions

Hadrons

Interact through strong force

Composed of quarks

Leptons

Interact through weak force

Thought to be truly elementary

Some suggestions they may have some internal structure

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 ½

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

Proton Stability

Absolute conservation of baryon number indicates the proton must be absolutely stable Otherwise, it could decay into a

positron and a neutral pion Never been observed

Currently can say the proton has a half-life of at least 1031 years

Some theories indicate the proton can decay

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 Λ0 + K0

Then Λ0 - + 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 ½ 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

Quark Model

Three types u – up d – down s – strange c – charmed t – top b – bottom

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

number and strangeness

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

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

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 30.3 for quark summary

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

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 2.9 K

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?