Chapter 45

Applications of Nuclear Physics

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 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

The excited state lasts for a very short time The product nucleus is generally radioactive and decays by

beta emission

γ+→→+ ++ X*XXn 1A

Z

1A

Z

A

Z

1

0

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

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

neutronsYX*UUn 23692

23592

10 ++→→+

Fission Example: 235U

A typical fission reaction for uranium is

( )1 235 141 92 10 92 56 36 03n U Ba Kr n+ → + +

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

PLAYACTIVE 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, free-electron 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 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

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 turbine-

generator 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 Contains the fuel and radioactive fission products

Reactor building 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 HHHeHeHe

or

eHeHeH

Then

HeHH

eHHH

11

11

42

32

32

42

32

11

32

21

11

21

11

11

++→+

ν++→+

γ+→+

ν++→+

+

+

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

2 2 3 11 1 2 0

2 2 3 11 1 1 1

2 3 4 11 1 2 0

H H H n 327 MeV

H H H H 403 MeV

H H He n 1759 MeV

.

.

.

Q

Q

Q

+ → + =

+ → + =

+ → + =

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 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 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 Close to values required by Lawson criterion

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

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

PLAYACTIVE 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 Called background radiation About 0.13 rem/yr

Upper limit suggested by US government 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