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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
Fission Equation

Fission of
neutron
1
0
235
92
n

U
236U*


235U
by a slow (low energy)
236
92
U*
X
Y
neutrons
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:
1
0
n
235
92
U
141
56
Ba
92
36
Kr
1
0
3 n
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 (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
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


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
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
2 H is deuterium, and
1
may be written as 21D
1
1
1
1
H
2
1
1
1
2
1
H
3
2
H
H
H
e
He
Then
1
1
H
3
2
He
4
2
He
e
or
3
2
He
3
2
He
4
2
He
2
1
1
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 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
deuterium (D) and tritium (T)
2
1
D
2
1
D
3
2
2
1
D
2
1
D
3
1
2
1
D
3
1
T
1
0
Q
3.27 MeV
H
Q
4.03 MeV
1
0
Q
17.59 MeV
He
T
4
3
He
n
1
1
n
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



Needed to give nuclei enough energy to
overcome Coulomb forces
At these temperatures, the atoms are
ionized, forming a plasma
Plasma ion density, n


108 K
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
n
1014 s/cm3 for deuterium-tritium
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



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
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



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
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 halflife 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 ElectronLepton Number states that the
sum of electron-lepton numbers
before a reaction or a decay must
equal the sum of the electronlepton 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 Chamber
Example
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 GellMann 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
5K
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
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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?