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Chapter 45
Applications of Nuclear
Physics
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 both
cases
Interactions Involving
Neutrons



Because of their charge neutrality, neutrons
are not subject to Coulomb forces
As a result, they do not interact electrically
with electrons or the nucleus
Neutrons can easily penetrate deep into an
atom and collide with the nucleus
Fast Neutrons



A fast neutron has energy greater than
approximately 1 MeV
During its many collisions when traveling
through matter, the neutron gives up some of
its kinetic energy to a nucleus
For fast neutrons in some materials, elastic
collisions dominate

These materials are called moderators since
they moderate the originally energetic neutrons
very efficiently
Thermal Neutrons

Most neutrons bombarding a moderator will
become thermal neutrons



They are in thermal equilibrium with the
moderator material
Their average kinetic energy at room temperature
is about 0.04 eV
This corresponds to a neutron root-mean-square
speed of about 2 800 m/s

Thermal neutrons have a distribution of speeds
Neutron Capture


Once the energy of a neutron is sufficiently low,
there is a high probability that it will be captured by a
nucleus
The neutron capture equation can be written as
1
0


n AZ XAZ1 X*AZ1 X  
The excited state lasts for a very short time
The product nucleus is generally radioactive and decays by
beta emission
Nuclear Fission



A heavy nucleus splits into two smaller nuclei
Fission is initiated when a heavy nucleus
captures a thermal neutron
The total mass of the daughter nuclei is less
than the original mass of the parent nucleus

This difference in mass is called the mass defect
Short History of Fission

First observed in 1938 by Otto Hahn and Fritz
Strassman following basic studies by Fermi


Bombarding uranium with neutrons produced
barium and lanthanum
Lise Meitner and Otto Frisch soon explained
what had happened


After absorbing a neutron, the uranium nucleus
had split into two nearly equal fragments
About 200 MeV of energy was released
Fission Equation: 235U

Fission of 235U by a thermal neutron
236
n 235
U

92
92 U*  X  Y  neutrons
1
0
 236U*

is an intermediate, excited state that exists
for about 10-12 s before splitting
X and Y are called fission fragments

Many combinations of X and Y satisfy the
requirements of conservation of energy and charge
Fission Example: 235U

A typical fission
reaction for uranium is
141
92
1
n  235
U

Ba

Kr

3

92
56
36
0n
1
0
Distribution of Fission
Products


The most probable
products have mass
numbers A  140 and A
 95
There are also an
average of 2.5 neutrons
released per event
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

Releases about 1 MeV per nucleon





8.2 MeV – 7.2 MeV
Assume a total of 235 nucleons
Total energy released is about 235 MeV
This is the disintegration energy, Q
This is very large compared to the amount of
energy released in chemical processes
Chain Reaction

Neutrons are emitted when 235U undergoes
fission



An average of 2.5 neutrons
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
When controlled, the energy can be put to
constructive use
Chain Reaction – Diagram
Active Figure 45.3

Use the active figure to
observe the chain
reaction
PLAY
ACTIVE FIGURE
Enrico Fermi




1901 – 1954
Italian physicist
Nobel Prize in 1938 for
producing transuranic
elements by neutron
irradiation
Other contributions include
theory of beta decay, freeelectron theory of metal,
development of world’s first
fission reactor (1942)
Moderator

The moderator slows the neutrons

The slower neutrons are more likely to react with
235U than 238U



The probability of neutron capture by 238U is high
when the neutrons have high kinetic energies
Conversely, the probability of capture is low when the
neutrons have low kinetic energies
The slowing of the neutrons by the moderator
makes them available for reactions with 235U while
decreasing their chances of being captured by
238U
Reactor Fuel

Most reactors today use uranium as fuel

Naturally occurring uranium is 99.3% 238U and
0.7% 235U
 238U


almost never fissions
It tends to absorb neutrons producing neptunium and
plutonium
Fuels are generally enriched to at least a few
percent 235U
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 average 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
Pressurized Water Reactor –
Diagram
Pressurized Water Reactor –
Notes


This type of reactor is the most common in use in
electric power plants in the US
Fission events in the uranium in the fuel rods raise
the temperature of the water contained in the
primary loop



The primary system is a closed system
This water is maintained at a high pressure to keep
it from boiling
This water is also used as the moderator to slow
down the neutrons
Pressurized Water Reactor –
Notes, cont.




The hot water is pumped through a heat
exchanger
The heat is transferred by conduction 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
Pressurized Water Reactor –
Notes, final

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
A fraction of the neutrons produced in fission
leak out before inducing other fission events

An optimal surface area-to-volume ratio of the fuel
elements is a critical design feature
Basic Design of a Reactor
Core




Fuel elements consist of
enriched uranium
The moderator material
helps to slow down the
neutrons
The control rods absorb
neutrons
All of these are surrounded
by a radiation shield
Control Rods


To control the power level, control rods are inserted
into the reactor core
These rods are made of materials that are very
efficient in absorbing neutrons


Cadmium is an example
By adjusting the number and position of the control
rods in the reactor core, the K value can be varied
and any power level can be achieved

The power level must be within the design of the reactor
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
Prevents radioactive material from contaminating the
environment
Location

Reactor facilities are in remote locations
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
At present, the most promising solution seems to be
sealing the waste in waterproof containers and burying
them in deep geological repositories
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: 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

H H H  e  
1
1
1
1
2
1
H 21H32 He  
1
1
Then
H 32 He  42 He  e   
1
1
or
3
2
He  32 He  42 He 11H11H
Fusion in the Sun


These reactions occur in the core of a star
and are responsible for the energy released
by the stars
High temperatures are required to drive these
reactions

Therefore, they are known as thermonuclear
fusion reactions
Fusion Reactions, final


All of the reactions in the proton-proton cycle
are exothermic
An overview of the cycle is that four protons
combine to form an alpha particle and two
positrons
Advantages of a Fusion
Reactor

Inexpensive fuel source



Water is the ultimate fuel source
If deuterium is used as fuel, 0.12 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 and tritium
H  21H  32 H  01n Q  3.27 MeV
2
1
H  H  H  H Q  403
. MeV
2
1
2
1
3
1
1
1
H  31H  42 He  01n Q  1759
. MeV
2
1
Considerations for a Fusion
Reactor, cont.


Tritium is radioactive and must be produced
artificially
The Coulomb repulsion between two charged
nuclei must be overcome before they can
fuse

A major problem in obtaining energy from fusion
reactions
Potential Energy Function



The potential energy is
positive in the region r > R,
where the Coulomb
repulsive force dominates
It is negative where the
nuclear force dominates
The problem is to give the
nuclei enough kinetic
energy to overcome this
repulsive force
Critical Ignition Temperature


The temperature at
which the power
generation rate in any
fusion reaction exceeds
the lost rate is called
the critical ignition
temperature, Tignit
The intersections of the
gen lines with the lost
line give the Tignit
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 interval during which energy injected into the
plasma remains in the plasma
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

These are the
minima on the
curves
Requirements, Summary


The plasma temperature must be very high
To meet Lawson’s criterion, the product n
must be large



For a given value of n, the probability of fusion
between two particles increases as  increases
For a given value of , the collision rate increases
as n increases
Confinement is still a problem
Confinement Techniques

Magnetic confinement


Uses magnetic fields to confine the plasma
Inertial confinement

Particles’ inertia keeps them confined very close
to their initial positions
Magnetic Confinement


One magnetic confinement
device is called a tokamak
Two magnetic fields confine
the plasma inside the donut



A strong magnetic field is
produced in the windings
A weak magnetic field is
produced by the toroidal
current
The field lines are helical,
they spiral around the
plasma, and prevent it from
touching the wall of the
vacuum chamber
Fusion Reactors Using
Magnetic Confinement

TFTR – Tokamak Fusion Test Reactor


NSTX – National Spherical Torus Experiment



Close to values required by Lawson criterion
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
Inertial Confinement


Uses a D-T target that has a very high
particle density
Confinement time is very short


Therefore, because of their own inertia, the
particles do not have a chance to move from their
initial positions
Lawson’s criterion can be satisfied by
combining high particle density with a short
confinement time
Laser Fusion





Laser fusion is the most
common form of inertial
confinement
A small D-T pellet is struck
simultaneously by several
focused, high intensity laser
beams
This large input energy
causes the target surface to
evaporate
The third law reaction
causes an inward
compression shock wave
This increases the
temperature
Fusion Reactors Using Inertial
Confinement

Omega facility



University of Rochester (NY)
Focuses 24 laser beams on the target
National Ignition Facility




Lawrence Livermore National Lab (CA)
Currently under construction
Will include 192 laser beams focused on D-T
pellets
Fusion ignition tests are planned for 2010
Fusion Reactor Design –
Energy

In the D-T reaction, the
alpha particle carries
20% of the energy and
the neutron carries 80%

The neutrons are about
14 MeV
Active Figure 45.12


Use the active figure to
observe different fusion
reactions
Measure the energy
released
PLAY
ACTIVE FIGURE
Fusion Reactor Design,
Particles




The alpha particles are primarily absorbed by the
plasma, increasing the plasma’s temperature
The neutrons are absorbed by the surrounding
blanket of material where their energy is extracted
and used to generate electric power
One scheme is to use molten lithium to capture the
neutrons
The lithium goes to a heat-exchange loop and
eventually produces steam to drive turbines
Fusion Reactor Design,
Diagram
Some Advantages of Fusion

Low cost and abundance of fuel



Deuterium
Impossibility of runaway accidents
Decreased radiation hazards
Some Anticipated Problems
with Fusion


Scarcity of lithium
Limited supply of helium


Helium is needed for cooling the superconducting
magnets used to produce the confinement fields
Structural damage and induced radiation
from the neutron bombardment
Radiation Damage


Radiation absorbed by matter can cause
damage
The degree and type of damage depend on
many factors


Type and energy of the radiation
Properties of the matter
Radiation Damage, cont.

Radiation damage in the metals used in the
reactors comes from neutron bombardment



They can be weakened by high fluxes of energetic
neutrons producing metal fatigue
The damage is in the form of atomic displacements,
often resulting in major changes in the properties of
the material
Radiation damage in biological organisms is
primarily due to ionization effects in cells

Ionization disrupts the normal functioning of the cell
Types of Damage in Cells

Somatic damage is radiation damage to any
cells except reproductive ones



Can lead to cancer at high radiation levels
Can seriously alter the characteristics of specific
organisms
Genetic damage affects only reproductive
cells

Can lead to defective offspring
Damage Dependence on
Penetration

Damage caused by radiation also depends
on the radiation’s penetrating power

Alpha particles cause extensive damage, but
penetrate only to a shallow depth



Due to their charge, they will have a strong interaction
with other charged particles
Neutrons do not interact with material and so
penetrate deeper, causing significant damage
Gamma rays can cause severe damage, but often
pass through the material without interaction
Units of Radiation Exposure

The roentgen (R) is defined as



That amount of ionizing radiation that produces
an electric charge of 3.33 x 10-10 C in 1 cm3 of air
under standard conditions
Equivalently, that amount of radiation that
increases the energy of 1 kg of air by 8.76 x 10-3 J
One rad (radiation absorbed dose)

That amount of radiation that increases the
energy of 1 kg of absorbing material by 1 x 10-2 J
More Units

The RBE (relative biological effectiveness)



The number of rads of x-radiation or gamma
radiation that produces the same biological
damage as 1 rad of the radiation being used
Accounts for type of particle which the rad itself
does not
The rem (radiation equivalent in man)

Defined as the product of the dose in rad and the
RBE factor

Dose in rem = dose in rad x RBE
RBE Factors, A Sample
Radiation Levels

Natural sources – rocks and soil, cosmic rays



Upper limit suggested by US government



Called background radiation
About 0.13 rem/yr
0.50 rem/yr
Excludes background
Occupational



5 rem/yr for whole-body radiation
Certain body parts can withstand higher levels
Ingestion or inhalation is most dangerous
Radiation Levels, cont.

50% mortality rate


About 50% of the people exposed to a dose of
400 to 500 rem will die
New SI units of radiation dosages


The gray (Gy) replaces the rad
The sievert (Sv) replaces the rem
SI Units, Table
Radiation Detectors,
Introduction


Radiation detectors exploit the interactions
between particles and matter to allow a
measurement of the particles’ characteristics
Things that can be measured include:




Energy
Momentum
Charge
Existence
Early Detectors

Photographic emulsion


The path of the particle corresponds to points at
which chemical changes in the emulsion have
occurred
Cloud chamber


Contains a gas that has been supercooled
Energetic particles ionize the gas along the
particles’ paths
Early Detectors, Cont.

Bubble chamber



Uses a liquid maintained
near its boiling point
Ions produced by
incoming charged
particles leave bubble
tracks
The picture is an
artificially colored bubble
chamber photograph
Contemporary Detectors

Ion chamber



Electron-ion pairs are
generated as radiation
passes through a gas and
produces an electric signal
The current is proportional
to the number of pairs
produced
A proportional counter is
an ion chamber that detects
the presence of the particle
and measures its energy
Geiger Counter




A Geiger counter is the most
common form of an ion
chamber used to detect
radiation
When a gamma ray or
particle enters the thin
window, the gas is ionized
The released electrons
trigger a current pulse
The current is detected and
triggers a counter or speaker
Geiger Counter, cont.


The Geiger counter easily detects the
presence of a particle
The energy lost by the particle in the counter
is not proportional to the current pulse
produced

Therefore, the Geiger counter cannot be used to
measure the energy of a particle
Other Detectors

The semiconductor-diode detector



A reverse-bias p-n junction
As a particle passes through the junction, a brief pulse
of current is created and measured
The scintillation counter



Uses a solid or liquid material whose atoms are easily
excited by radiation
The excited atoms emit photons as they return to
their ground state
With a photomultiplier, the photons can be converted
into an electrical signal
Other Detectors, cont.

Track detectors


Various devices used to view the tracks or paths
of charged particles directly
The energy and momentum of these energetic
particles are found from the curvature of their path
in a magnetic field of known magnitude and
direction
Other Detectors, Final

Spark chamber


A counting device that consists of an array of
conducting parallel plates and is capable of
recording a three-dimensional track record
Drift chamber


A newer version of the spark chamber
Has thousands of high-voltage wires throughout
the space of the detector
Applications of Radiation

Tracing

Radioactive particles can be used to trace chemicals
participating in various reactions




Example, 131I to test thyroid action
Also to analyze circulatory system
Also useful in agriculture and other applications
Materials analysis

Neutron activation analysis uses the fact that when a
material is irradiated with neutrons, nuclei in the
material absorb the neutrons and are changed to
different isotopes
Applications of Radiation,
cont.

Radiation therapy



Radiation causes the most damage to rapidly
dividing cells
Therefore, it is useful in cancer treatments
Food preservation

High levels of radiation can destroy or
incapacitate bacteria or mold spores