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.

Introduction

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.

Section 45.1

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.

For fast neutrons in some materials, elastic collisions dominate.

These materials are called moderators since they moderate the originally energetic neutrons very efficiently. Moderator nuclei should be of low mass so that a large amount of kinetic energy is

transferred to them in elastic collisions. Materials such as paraffin and water are good moderators for neutrons.

Section 45.1

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.

Section 45.1

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.

1 1 10

A A AZ Z Zn X X* X ã+ ++ → → +

Section 45.1

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.

Multiplying the mass defect by c2 gives the numerical value of the released energy. This energy is in the form of kinetic energy associated with the motion of the

neutrons and the daughter nuclei after the fission event.

Section 45.2

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.

Section 45.2

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 ++→→+

Section 45.2

Fission Example: 235U

A typical fission reaction for uranium is

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

Section 45.2

Distribution of Fission Products

The most probable products have mass numbers A 95 and A 140.

There are also 2 to 3 neutrons released per event.

Section 45.2

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.

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.

Section 45.2

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.

Section 45.3

Chain Reaction – Diagram

Section 45.3

Enrico Fermi

1901 – 1954

Italian physicist

Nobel Prize in 1938 for producing transuranic elements by neutron irradiation and for his discovery of nuclear reactions brought about by thermal neutrons

Other contributions include theory of beta decay, free-electron theory of metal, development of world’s first fission reactor (1942)

Section 45.3

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

Section 45.3

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.

Section 45.3

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.

Section 45.3

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.

Section 45.3

Pressurized Water Reactor – Diagram

Section 45.3

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.

Section 45.3

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.

Section 45.3

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.

Section 45.3

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.

Section 45.3Section 45.3

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.

Section 45.3

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

Section 45.3

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.

Section 45.3

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.

Section 45.4

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.

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, positrons, gamma rays 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++→+

+

+

Section 45.4

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.

Section 45.4

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.

Section 45.4

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

+ → + =

+ → + =

+ → + =

Section 45.4

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.

Section 45.4

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.

Can be accomplished raising the temperature of the fuel to approximately 108 K.

At this temperature, the atoms are ionized and the system contains a collection of electrons and nuclei, referred to as a plasma.

Section 45.4

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 Pgen lines with the Plost line give the Tignit.

Section 45.4

Requirements for Successful Thermonuclear Reactor

High temperature ~ 108 K

Needed to give nuclei enough energy to overcome Coulomb forces

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.

Section 45.4

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.

Section 45.4

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.

Section 45.4

Confinement Techniques

Magnetic confinement

Uses magnetic fields to confine the plasma

Inertial confinement

Particles’ inertia keeps them confined very close to their initial positions.

Section 45.4

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.

Section 45.4

Fusion Reactors Using Magnetic Confinement

TFTR – Tokamak Fusion Test Reactor

Close to values required by Lawson criterion

JET – Joint European Torus

Reaction rates of 6 x 1017 D-T fusions per second were reached

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.

Fusion operation is expected to begin in 2018.

Section 45.4

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.

Section 45.4

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.

Section 45.4

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)

Construction was completed in early 2009

Will include 192 laser beams focused on D-T pellets The lasers were fired in March 2009 and broke the megajoule record for lasers.

They delivered 1.1 MJ to a target

Fusion ignition tests are planned for 2010.

Section 45.4

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.

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.

Fusion Reactor Design, cont.

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.

Section 45.4

Fusion Reactor Design, Diagram

Section 45.4

Some Advantages of Fusion

Low cost and abundance of fuel

Deuterium

Impossibility of runaway accidents

Decreased radiation hazards

Section 45.4

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

Section 45.4

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

Section 45.5

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.

Section 45.5

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

Section 45.5

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.

Section 45.5

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.

Section 45.5

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

Section 45.5

RBE Factors, A Sample

Section 45.5

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

Section 45.5

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.

Section 45.5

SI Units, Table

Section 45.5

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

Section 45.6

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.

Section 45.6

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.

Section 45.6

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.

Section 45.6

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.

Section 45.6

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.

Section 45.6

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.

Section 45.6

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.

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

Section 45.6

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.

Section 45.7

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.

Section 45.7