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Chapter 30
Nuclear Energy
and
Elementary Particles
Processes of Nuclear Energy

Fission


Fusion


A nucleus of large mass number splits into
two smaller nuclei
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
neutron
235U
by a slow (low energy)
236
n 235
U

92
92 U*  X  Y  neutrons
1
0
 236U*
is an intermediate, short-lived state
 X and Y are called fission fragments

Many combinations of X and Y satisfy the
requirements of conservation of energy and
charge
Sequence of Events in Fission
The 235U nucleus captures a thermal (slowmoving) 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
QUICK QUIZ 30.1
In the first atomic bomb, the energy released
was equivalent to about 30 kilotons of TNT,
where a ton of TNT releases an energy of
4.0 × 109 J. The amount of mass converted
into energy in this event is nearest to: (a) 1
g, (b) 1 mg, (c) 1 g, (d) 1 kg, (e) 20
kilotons
QUICK QUIZ 30.1 ANSWER
(c). The total energy released was E = (30
×103 ton)(4.0 × 109 J/ton) = 1.2 × 1014 J.
The mass equivalent of this quantity of
energy is:
E
1.2  1014 J
3
m 2 
 1.3  10 kg ~ 1g
8
2
c
(3.0  10 m/s)
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 g
of U can release energy equal to about 20000 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


When K < 1, the reactor is said to be
subcritical


The chain reaction is self-sustaining
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



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


If K >1, the heat produced in the runaway reaction can
melt the reactor
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 –
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 –
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 turbinegenerator 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



Reactor building


Contains the fuel and radioactive fission products
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
1
1
2

The proton-proton
H

H

H

e

1
1
1
cycle is a series of
1
2
3
three nuclear
1H 1H 2 He  
reactions believed to
Then
operate in the Sun
1
3
4

 Energy liberated is
1H 2 He  2 He  e  
primarily in the form
or
of gamma rays,
positrons and
3
3
4
1
1
2 He  2 He  2 He 1H1H
neutrinos

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


Comparitively few radioactive byproducts 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
deutrium and tritium
2
2
3
1
H

H

H

1
1
2
0 n Q  3.27 MeV

H H H H Q  4.03 MeV
2
1
2
1
3
1
1
1
H H He  n
2
1
3
1
4
3
1
0
Q  17.59 MeV
Considerations for a Fusion
Reactor, cont
Tritium is radioactive and must be
produced artifically
 The Coulomb repulsion between two
charged nuclei must be overcome
before they can fuse

Requirements for Successful
Thermonuclear Reactor

High temperature ~ 108 K



Plasma ion density, n


Needed to give nuclei enough energy to overcome
Coulomb forces
At these temperatures, the atoms are ionized,
forming a plasma
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
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
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 manifestions
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
Antiparticles

For every particle, there is an antiparticle



An antiparticle has the same mass as the particle, but
the opposite charge
The positron (electron’s antiparticle) was discovered
by Anderson in 1932


From Dirac’s version of quantum mechanics that
incorporated special relativity
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
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 existance of the
particle were done by studying cosmic rays in
the 1930’s
 Actually discovered multiple particles



Pi meson (pion)
Muon

Not a meson
Pion

There are three varieties of pions

+ and 

0


Mass of 139.6 MeV/c2
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
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 existance of the virtual photon
would 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

Feynman Diagram – Proton
and Neutron
The exchange is via the
nuclear force
 The existance 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 board categories
 Classified by interactions

Hadrons – interact through strong force
 Leptons – interact through weak force

Hadrons
Interact through the strong force
 Two subclasses


Mesons



Baryons




Decay finally into electrons, positrons, neutrinos and
photons
Integer spins
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
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 electronlepton 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, taulepton numbers must be conserved

Muon- and tau-lepton numbers are assigned
similarly to electron-lepton numbers
QUICK QUIZ 30.2
Which of the following reactions cannot occur?

( b) n  p  e  v e
(c)   e  v e  v (d)     v 




QUICK QUIZ 30.2 ANSWER
(a). This reaction fails to conserve charge and
cannot occur.
QUICK QUIZ 30.3
Which of the following reactions cannot occur?
(a) p  p  2
(b)   p  n  
0
(c)   n  K  

(d)   p  K  

0



QUICK QUIZ 30.3 ANSWER
(b). This reaction fails to conserve charge
and cannot occur.
QUICK QUIZ 30.4
Suppose a claim is made that the
decay
of
a
_
+
neutron is given by n  p + e . Which of
the following conservation laws are
violated by this proposed decay scheme?
(a) energy, (b) linear momentum, (c) spin
angular momentum, (d) electric charge, (e)
lepton number, (f) baryon number.
QUICK QUIZ 30.4 ANSWER
(c), (e). The proton and the electron each
have spin s = ½ . The two possible resultant
spins after decay are 1 (spins aligned) or 0
(spins anti-aligned). Neither equal the spin of
a neutron, s = ½ , so spin angular momentum
is not conserved. The are no leptons present
before the proposed decay and one lepton
(the electron) present after decay. Thus, the
decay also fails to conserve lepton number.
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, the 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 interaction does not
Bubble Chamber
Example
The dashed lines
represent neutral
particles
 At the bottom,
- + p  Λ0 + K0
 Then Λ0  - + p
and
 K0   + µ- + µ

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 symmetic 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
Stangeness 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 GellMann and Zweig
Original Quark Model

Three types




Associated with each quark is an antiquark


The antiquark has opposite charge, baryon
number and strangeness
Quarks have fractional electrical charges


u – up
d – down
s – originally sideways, now strange
+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 discrepencies 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/Ψ 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

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 red quark is
attracted to an
antired 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 unlike colors attract


Different colors 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 shortranged 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 matter particles
 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 manifestions 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
Cosmic Background Radiation
(CBR)
CBR is 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?
Is it possible to unify electroweak and strong
forces?
Why do quark and leptons form similar but
distinct families?
Why do quarks carry fractional charge?
What determines the masses of fundamental
particles?
Do leptons and quarks have a substructure?