Nuclear Energy
Seventh Edition


Nuclear Energy
An Introduction to the Concepts,
Systems, and Applications of
Nuclear Processes
Seventh Edition

Raymond L. Murray
Keith E. Holbert

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Notices
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Library of Congress Cataloging-in-Publication Data
Murray, Raymond LeRoy, 1920Nuclear energy : an introduction to the concepts, systems, and applications of nuclear processes / Raymond L.
Murray, Keith E. Holbert. – Seventh edition.
pages cm
Includes bibliographical references and index.
ISBN 978-0-12-416654-7 (alk. paper)
1. Nuclear engineering. 2. Nuclear energy. I. Holbert, Keith E. II. Title.
TK9145.M87 2014
621.48–dc23

2013039295


British Library Cataloguing-in-Publication Data
A catalogue record for this book is available from the British Library.
ISBN: 978-0-12-416654-7
For information on all Butterworth–Heinemann publications visit
our website at store.elsevier.com
Printed and bound in United States of America
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1


About the Authors

Raymond L. Murray (Ph.D., University of Tennessee, 1950) was a long-time faculty member in the
Department of Nuclear Engineering of North Carolina State University. Professor Murray studied
under J. Robert Oppenheimer at the University of California at Berkeley. In the Manhattan Project
of World War II, he contributed to the uranium isotope separation process at Berkeley and Oak Ridge.
In the early 1950s, he helped found the first university nuclear engineering program and the first
university nuclear reactor. During his 30 years of teaching and research in reactor analysis at North
Carolina State, he taught many of our leaders in universities and industry throughout the world.
He was the author of textbooks in physics and nuclear technology and the recipient of a number of
awards, including the Eugene P. Wigner Reactor Physicist Award of the American Nuclear Society
in 1994. He was a Fellow of the American Physical Society, a Fellow of the American Nuclear
Society, and a member of several honorary, scientific, and engineering societies. After retirement from
the university, Dr. Murray was a consultant on criticality for the Three Mile Island Recovery Program,
served as chairman of the North Carolina Radiation Protection Commission, and served as chairman of
the North Carolina Low-Level Radioactive Waste Management Authority. He provided an annual lecture at MIT for the Institute of Nuclear Power Operations.

xv


xvi

About the Authors

Keith E. Holbert (Ph.D., University of Tennessee, 1989) is presently an Associate Professor in the
School of Electrical, Computer and Energy Engineering at Arizona State University. His research

expertise is in the area of instrumentation and system diagnostics including radiation effects on sensors.
Dr. Holbert has performed tests on safety-related systems in more than a dozen nuclear power plants in
the United States. He has published more than 100 journal and conference papers, a textbook, and holds
one patent. Dr. Holbert is a registered professional (nuclear) engineer. He is a member of the American
Nuclear Society and a Senior Member of the IEEE. Dr. Holbert holds a Guest Scientist affiliation with
Los Alamos National Laboratory. As the Director of the Nuclear Power Generation Program at ASU,
Professor Holbert teaches undergraduate and graduate engineering courses on electric power generation (from all forms of energy), nuclear reactor theory and design, nuclear power plant controls and
diagnostics, reactor safety analysis, and health physics and radiation measurements. Dr. Holbert has
been the recipient of multiple teaching awards. Keith is a Christian, who ascribes to the doctrine that
God has entrusted humanity with good stewardship of His creation.


Preface
Professor Raymond L. Murray (1920–2011) authored six editions of this textbook until his death.
Standing on the shoulders of his work, I have humbly attempted to expand the coverage and depth
of the material while keeping with its original intent. As stated in the preface to the first edition
(1975), the book “is designed for use by anyone who wishes to know about the role of nuclear energy
in our society or to learn nuclear concepts for use in professional work.” The continued hope is that the
book will benefit both (future) nuclear professionals and interested members of the public.
For the first time in recent memory, the United States is projected to be energy independent by 2040,
largely due to increased domestic production of petroleum and natural gas. However, by many accounts,
humanity stands at a crossroads, with self-inflicted stresses due to population growth and anthropogenic
climate change. Simultaneously, the quality of life is enhanced through the availability of economic
energy sources. Trends show electricity being increasingly tapped as the end-use energy form. Another
challenge is the competitive collaboration between two critical resources—the energy-water nexus.
Nuclear reactors are planned that combat global warming, conserve nuclear fuel, support desalination, and produce hydrogen for transportation. The construction and plans for new nuclear power plants
continue worldwide despite the events at Fukushima in 2011. In what is called a nuclear revival, many
utilities in the United States have applied to the Nuclear Regulatory Commission for license extension
and approval for new reactor construction.
Besides nuclear power generation, associated technologies are utilized in a variety of applications

including nuclear medicine and smoke detectors. Furthermore, since the terrorist attacks of 2001, radiation detectors have been installed at ports of entry worldwide to intercept illicit shipments of
nuclear materials.
Like politics and religion, the subject of nuclear energy generates heated debate in certain circles.
Hence, a purpose of this book must be to bring factual information to the discussion. Topics that seem
to generate the most concern inevitably include the persistent nuclear waste issue, nuclear power plant
safety, radiation, and atomic weapons. Therefore, the authors are compelled to devote coverage to these
(sometimes controversial) areas.
Those familiar with earlier editions will quickly realize that the ordering of chapters in the last twothirds of the textbook has changed noticeably. Part I retains its focus on foundational nuclear concepts.
Part II is now devoted to topics concerning radiation and its generation, effects, and utilization; whereas
Part III is aligned to nuclear power generation. Besides changes to the organizational structure, significant amounts of up-to-date nuclear data have been added (e.g., see Appendix A), thereby increasing
the utility of this book as a reference.
Student learning is enhanced by performing calculations and analyses on nuclear quantities. This
edition provides Exercises, solvable by handheld calculator, with final answers given in Appendix B.
In addition, MATLAB programs and Excel spreadsheets for the solution of computer exercises in the
text can be downloaded from />Persons providing valuable ideas and information are recognized at appropriate places in the book.
The author welcomes any constructive comments and corrections to the text ().
Keith E. Holbert
Tempe, Arizona, 2013

xvii


PART

Basic concepts

I

In the study of the practical applications of nuclear energy we must consider the properties of
individual particles of matter—their “microscopic” features—as well as the character of matter

in its ordinary form, a “macroscopic” (large-scale) view. Examples of the small-scale properties
are masses of atoms and nuclear particles, their effective sizes for interaction with each other,
and the number of particles in a certain volume. The combined behavior of large numbers of
individual particles is expressed in terms of properties such as mass density, charge density,
electrical conductivity, thermal conductivity, and elastic constants. We continually seek
consistency between the microscopic and macroscopic views.
Since all processes involve interactions of particles, it is necessary to develop a background
understanding of the basic physical facts and principles that govern such interactions. In Part I
we shall examine the concept of energy, describe the models of atomic and nuclear structure,
discuss radioactivity and nuclear reactions in general, review the ways radiation reacts with
matter, and concentrate on two important nuclear processes: fission and fusion.


CHAPTER

Energy

1

CHAPTER OUTLINE
1.1 Forces and Energy ............................................................................................................................3
1.2 Units of Measure ..............................................................................................................................5
1.3 Thermal Energy ................................................................................................................................6
1.4 Radiant Energy .................................................................................................................................7
1.5 The Equivalence of Matter and Energy ...............................................................................................9
1.6 Energy and the World .....................................................................................................................11
1.7 Summary .......................................................................................................................................11
1.8 Exercises .......................................................................................................................................12
1.9 Computer Exercise .........................................................................................................................13
References ...........................................................................................................................................13

Further Reading ....................................................................................................................................14

Our material world is composed of many substances distinguished by their chemical, mechanical, and
electrical properties. They are found in nature in various physical states—the familiar solid, liquid, and
gas, along with the ionic plasma. However, the apparent diversity of kinds and forms of material is reduced
by the knowledge that there are only a little more than 100 distinct chemical elements and that the chemical
and physical features of substances depend merely on the strength of force bonds between atoms.
In turn, the distinctions between the elements of nature arise from the number and arrangement of
basic particles: electrons, protons, and neutrons. At both the atomic and nuclear levels, the structure of
elements is determined by internal forces and energy.

1.1 FORCES AND ENERGY
A limited number of basic forces exist: gravitational, electrostatic, electromagnetic, and nuclear. Associated with each of these is the ability to do work. Thus, energy in different forms may be stored,
released, transformed, transferred, and “used” in both natural processes and man-made devices. It is
often convenient to view nature in terms of only two basic entities: particles and energy. Even this
distinction can be removed, because we know that matter can be converted into energy and vice versa.
Let us review some principles of physics needed for the study of the release of nuclear energy and its
conversion into thermal and electrical forms. We recall that if a constant force F is applied to an object
to move it a distance s, the amount of work W done is the product W ¼ Fs. As a simple example, we pick
up a book from the floor and place it on a table. Our muscles provide the means to lift against the force
of gravity on the book. We have done work on the object, which now possesses stored energy (potential
energy), because it could do work if allowed to fall back to the original level. Now a force F acting on a

3


4

CHAPTER 1 Energy


mass m provides an acceleration a, given by Newton’s law F ¼ ma. Starting from rest, the object gains a
speed v, and at any instant has energy of motion (kinetic energy) in amount
1
EK ¼ mv2
ð1:1Þ
2
For objects falling under the force of gravity, we find that the potential energy is reduced as the kinetic
energy increases, but the sum of the two energy types remains constant. This is an example of the principle of conservation of energy. Let us apply this principle to a practical situation and perform some
illustrative calculations.
As we know, falling water provides one primary source for generating electrical energy. In a hydroelectric plant, river water is collected by a dam and allowed to fall through a considerable height h,
known as the head. The potential energy of water is thus converted into kinetic energy. The water
is directed to strike the blades of a hydraulic turbine, which turns an electric generator.
The potential energy of a mass m located at the top of a dam is EP ¼ Fh, being the work done to place
it there. The force is the weight F ¼ mg, where g is the acceleration of gravity. Thus, the potential
energy is
Ep ¼ mgh

ð1:2Þ

EXAMPLE 1.1
Find the velocity of water descending through a dam with a 50 m head. Ignoring friction, the
potential energy in kinetic form would appear at the bottom, that is, EP ¼ EK. Using gravitational
acceleration at the Earth’s surface* g0 ¼ 9.81 m/s2, the water speed would be
rffiffiffiffiffiffiffiffi rffiffiffiffiffiffiffiffi rffiffiffiffiffiffiffiffiffiffiffiffiffi
ffi
2EK
2EP
2mg0 h pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
v¼
¼

¼
¼ 2ð9:81 m=s2 Þð50 mÞ ¼ 31:3 m=s
m
m
m

Energy takes on various forms, classified according to the type of force that is acting. The water in
the hydroelectric plant experiences the force of gravity, and thus gravitational energy is involved. It is
transformed into mechanical energy of rotation in the turbine, which is then converted to electrical
energy by the generator. At the terminals of the generator, there is an electrical potential difference,
which provides the force to move charged particles (electrons) through the network of the electrical
supply system. The electrical energy may then be converted into mechanical energy as in motors, into
light energy as in light bulbs, into thermal energy as in electrically heated homes, or into chemical
energy as in a storage battery.
The automobile also provides familiar examples of energy transformations. The burning of gasoline
releases the chemical energy of the fuel in the form of heat, part of which is converted to energy of
*The standard acceleration of gravity is 9.80665 m/s2. For discussion and simple illustrative purposes, such numbers are
rounded off to a few significant digits. Only when accuracy is important will more figures or decimals be used. The principal
source of physical constants, conversion factors, and nuclear properties is the CRC Handbook of Chemistry and Physics
(Haynes et al., 2011).


1.2 Units of measure

5

motion of mechanical parts, while the rest is transferred to the atmosphere and highway. The vehicle’s
alternator provides electricity for control and lighting. In each of these examples, energy is changed
from one form to another but is not destroyed. The conversion of heat to other forms of energy is governed by two laws, the first and second laws of thermodynamics. The first law states that energy is
conserved; the second specifies inherent limits on the efficiency of the energy conversion.

Energy can be classified according to the primary source. We have already noted two sources of
energy: falling water and the burning of the chemical fuel gasoline, which is derived from petroleum,
one of the main fossil fuels. To these we can add solar energy; the energy from winds, tides, or the
sea motion; and heat from within the Earth. Finally, we have energy from nuclear reactions (i.e.,
the “burning” of nuclear fuel).

1.2 UNITS OF MEASURE
For many purposes, we use the metric system of units, more precisely designated as SI or Syste`me
Internationale. In this system (see NIST in the chapter’s references), the base units are the kilogram
(kg) for mass, the meter (m) for length, the second (s) for time, the mole (mol) for amount of substance,
the ampere (A) for electric current, the kelvin (K) for thermodynamic temperature, and the candela (cd)
for luminous intensity. Table 1.1 summarizes these SI base units and important derived quantities.
Table 1.1 SI Base and Derived Quantities and Units
Quantity

Unit

Unit Symbol

Unit Dimension(s)

Length
Mass
Time
Electric current
Thermodynamic temperature
Amount of substance
Luminous intensity
Frequency
Force

Pressure
Energy, work, heat
Power
Electric charge
Electric potential
Electric capacitance
Magnetic flux
Magnetic flux density
Absorbed dose
Dose equivalent
Activity

meter
kilogram
second
ampere
kelvin
mole
candela
hertz
newton
pascal
joule
watt
coulomb
volt
farad
weber
tesla
gray

sievert
becquerel

m
kg
s
A
K
mol
cd
Hz
N
Pa
J
W
C
V
F
Wb
T
Gy
Sv
Bq

1/s
kg Á m/s2 ¼ J/m
N/m2 ¼ kg/(m Á s2)
N Á m ¼ kg Á m2/s2
J/s ¼ kg Á m2/s3
AÁs

J/C ¼ W/A ¼ kg Á m2/(s3 Á A)
C/V
VÁs
Wb/m2
J/kg
J/kg
1/s


6

CHAPTER 1 Energy

In addition, the liter (L) and metric ton (tonne) are in common use (1 L ¼ 10–3 m3; 1 tonne ¼ 1000 kg).
However, for understanding earlier literature, one requires knowledge of other systems. Table A.3 in
Appendix A lists useful conversions from British units to SI units.
The transition in the United States from British units to SI units has been much slower than expected.
To ease understanding by the typical reader, a dual display of numbers and their units are frequently given
in this book. Familiar and widely used units such as the centimeter, the barn, the curie, and the rem are
maintained.
In dealing with forces and energy at the level of molecules, atoms, and nuclei, it is conventional to
use another energy unit, the electronvolt (eV). Its origin is electrical in character, being the amount of
kinetic energy that would be imparted to an electron (charge 1.602 Â 10–19 coulombs) if it were accelerated through a potential difference of 1 volt. Because the work done on 1 coulomb would be 1 J, we
see that 1 eV ¼ 1.602 Â 10–19 J. The unit is of convenient size for describing atomic reactions. For
instance, to remove one electron from the hydrogen atom requires 13.6 eV of energy. However, when
dealing with nuclear forces, which are very much larger than atomic forces, it is preferable to use the
million-electronvolt unit (MeV). To separate the neutron from the proton in the nucleus of heavy
hydrogen, for example, requires an energy of about 2.2 MeV (i.e., 2.2 Â 106 eV).

1.3 THERMAL ENERGY

Of special importance to us is thermal energy, as the form most readily available from the sun, from
burning of ordinary fuels, and from the nuclear fission process. First, we recall that a simple definition
of the temperature of a substance is the number read from a measuring device such as a thermometer in
intimate contact with the material. If energy is supplied, the temperature rises (e.g., energy from the sun
warms the air during the day). Each material responds to the supply of energy according to its internal
molecular or atomic structure, characterized on a macroscopic scale by the specific heat cp. If an
amount of thermal energy Q is added to the material mass without a change of state, a temperature
rise, DT, is induced in accordance with
Q ¼ mcp DT

ð1:3Þ

EXAMPLE 1.2
At constant pressure, the specific heat for water at 15  C and 1 atmosphere is cp ¼ 4.186 J/(g Á  C).
Thus, it requires 4.186 joules (J) of energy to raise the temperature of 1 gram of water by 1 degree
Celsius (1  C).
From our modern knowledge of the atomic nature of matter, we readily appreciate the idea that
energy supplied to a material increases the motion of the individual particles of the substance. Temperature can thus be related to the average kinetic energy of the atoms. For example, in a gas such as air,
the average energy of translational motion of the molecules E is directly proportional to the absolute
temperature T, through the relation
3
E ¼ kT
2

ð1:4Þ


1.4 Radiant energy

7


where k is Boltzmann’s constant, 1.38 Â 10–23 J/K. (Recall that the Kelvin scale has the same spacing of
degrees as the Celsius scale, but its zero is at À273.15  C.)
EXAMPLE 1.3
To gain an appreciation of molecules in motion, let us find the typical speed of oxygen molecules at
room temperature 20  C, or 293 K. The molecular weight of O2 is 32, and because one unit of atomic
weight corresponds to 1.66 Â 10–27 kg, the mass of the oxygen molecule is 5.30 Â 10–26 kg. Now
Á
3
3À
E ¼ kT ¼ 1:38 Â 10À23 J=K ð293 KÞ ¼ 6:07 Â 10À21 J
2
2
and thus from Equation (1.1) the speed is
qffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
À
Á À
Áffi
 ¼ 2 6:07 Â 10À21 J = 5:30 Â 10À26 kg ¼ 479 m=s
v ¼ 2E=m

Closely related to energy is the physical entity power, P, which is the rate at which work is done.
Hence, the power may be expressed in terms of the time derivative of energy
P¼

d
E
dt

ð1:5Þ


For a constant power, the energy is simply the product of the power and the time period, T, that is,
E ¼ PT.
EXAMPLE 1.4
To illustrate, let the mass flow rate m_ of water in the hydropower plant of Example 1.1 be 2 Â 106 kg/s.
As power is the time rate of change of energy, the power available is
P¼

À
ÁÀ
Á
d
_ ¼ 2 Â 106 kg=s 9:81 m=s2 ð50 mÞ ¼ 9:81 Â 108 J=s
EP ¼ mgh
dt

For convenience, the unit joule per second is called the watt (W). Our plant thus involves
9.8 Â 108 W. We can conveniently express this in kilowatts (l kW ¼ 103 W) or megawatts
(1 MW ¼ 106 W). Such multiples of units are used because of the enormous range of magnitudes of
quantities in nature, from the submicroscopic to the astronomical. Table 1.2 gives the standard set
of prefixes for the system of units.

1.4 RADIANT ENERGY
Another form of energy is electromagnetic or radiant energy. We recall that this energy may be released
by heating of solids, as in the wire of an incandescent light bulb; by electrical oscillations, as in radio or
television transmitters; or by atomic interactions, as in the sun. The radiation can be viewed in either of


8


CHAPTER 1 Energy

Table 1.2 Prefixes for Numbers and Abbreviations
Yotta
Zetta
Exa
Peta
Tera
Giga
Mega
Kilo
Hecto
Deca

Y
Z
E
P
T
G
M
k
h
da

1024
1021
1018
1015
1012

109
106
103
102
101

deci
centi
milli
micro
nano
pico
femto
atto
zepto
yocto

d
c
m
m
n
p
f
a
z
y

10–1
10–2

10–3
10–6
10–9
10–12
10–15
10–18
10–21
10–24

two ways—as a wave or as a particle—depending on the process under study. In the wave view, it is a
combination of electric and magnetic vibrations moving through space. In the particle view, it is a compact moving uncharged object, the photon, which is a bundle of pure energy, having mass only by virtue
of its motion. Regardless of its origin, all radiation can be characterized by its frequency, which is
related to speed and wavelength. Letting c be the speed of light, l its wavelength, and n its frequency,
we have{
c ¼ lv

ð1:6Þ

EXAMPLE 1.5
Find the frequency of yellow light of wavelength 5.89 Â 10–7 m. The speed of light in a vacuum is
c ¼ 3 Â 108 m/s; thus yellow light frequency is
c
3 Â 108 m=s
v¼ ¼
¼ 5:09 Â 1014 Hz
l 5:89 Â 10À7 m
X-rays and gamma rays are electromagnetic radiation arising from the interactions of atomic and
nuclear particles, respectively. They have energies and frequencies much higher than those of visible
light. Figure 1.1 presents the electromagnetic spectrum comparing the frequencies and wavelengths of
the various constituents such as visible light from 390 to 750 nm; however, the boundaries and ranges

of the components are not fixed. Of particular interest are the ionizing wavelengths, which begin within
the ultraviolet (UV) region ($10 eV). Later, we surmise that this is the reason some UV rays cause
skin cancer.
To appreciate the relationship of states of matter, atomic and nuclear interactions, and energy, let us
visualize an experiment in which we supply energy to a sample of water from a source of energy that is
{

We need both Roman and Greek characters, identifying the latter by name the first time they are used, thus l (lambda) and n
(nu). The Greek alphabet is compiled in Table A.1 for reference. The reader must be alert to symbols used for more than one
quantity.


1.5 The equivalence of matter and energy

9

FIGURE 1.1
Electromagnetic spectrum (ROYGBIV: red, orange, yellow, green, blue, indigo, violet).

as large and as sophisticated as we wish. Thus, we increase the degree of internal motion and eventually
dissociate the material into its most elementary components. Suppose in Figure 1.2 that the water is
initially ice at nearly absolute zero temperature, where water (H2O) molecules are essentially at rest.
As we add thermal energy to increase the temperature to 0  C or 32  F, molecular movement increases
to the point at which the ice melts to become liquid water, which can flow rather freely. To cause a
change from the solid state to the liquid state, a definite amount of energy (termed the heat of fusion)
is required. In the case of water, this latent heat is 334 J/g. In the temperature range in which water is
liquid, thermal agitation of the molecules permits some evaporation from the surface. At the boiling
point, 100  C or 212  F at atmospheric pressure, the liquid turns into the gaseous form as steam. Again,
energy is required to cause the change of state, with a heat of vaporization of 2258 J/g. Further heating,
by use of special high temperature equipment, causes dissociation of water into atoms of hydrogen (H)

and oxygen (O). By electrical means, electrons can be removed from hydrogen and oxygen atoms,
leaving a mixture of charged ions and electrons. Through nuclear bombardment, the oxygen nucleus
can be broken into smaller nuclei, and in the limit of temperatures in the billions of degrees, the
material can be decomposed into an assembly of electrons, protons, and neutrons.

1.5 THE EQUIVALENCE OF MATTER AND ENERGY
The connection between energy and matter is provided by Einstein’s theory of special relativity. It predicts that the mass of any object increases with its speed. Letting the mass when the object is stationary
be m0, the rest mass; letting m be the mass when it is at speed v; and noting that the speed of light in a
vacuum is c, then the relativistic mass is


10

CHAPTER 1 Energy

Increased energy supplied and increasing temperature

Solid ice

Liquid water

Steam

Dissociated H and O

Electrons, protons,
and neutrons

FIGURE 1.2
Effect of added energy to water.


m0
m ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1 À ðv=cÞ2

ð1:7Þ

For motion at low speed (e.g., 500 m/s), the relativistic mass is almost identical to the rest mass,
because v/c and its square are very small. Although the theory has the status of natural law, its rigor
is not required except for particle motion at high speed (i.e., when v is at least several percent of c). The
relation shows that a material object can have a speed no higher than c.
The implication of Einstein’s formula is that any object has a rest mass energy
E 0 ¼ m 0 c2

ð1:8Þ

ET ¼ mc2

ð1:9Þ

when motionless, and a total energy

The difference being EK the kinetic energy, that is
E T ¼ E 0 þ EK

ð1:10Þ

The kinetic energy imparted to a particle by the application of force according to Einstein is
EK ¼ ðm À m0 Þc2


ð1:11Þ


1.7 Summary

11

For low speeds, v ( c, EK is approximately 12 mv20 , the classical relation (see Exercise 1.7).
EXAMPLE 1.6
Let us compute the rest energy for an electron of mass 9.109 Â 10–31 kg
À
ÁÀ
Á2
E0 ¼ m0 c2 ¼ 9:109 Â 10À31 kg
2:998 Â 108 m=s ¼ 8:19 Â 10À14 J
.
À
Á À
Á
¼ 8:19 Â 10À14 J
1:602 Â 10À13 J=MeV ¼ 0:511 MeV

For one unit of atomic mass, 1.66 Â 10–27 kg, which is close to the mass of a hydrogen atom, the
corresponding energy is 931.5 MeV (see Exercise 1.14).
Thus we see that matter and energy are equivalent, with the factor c2 relating the amounts of each.
This suggests that matter can be converted into energy and that energy can be converted into matter.
Although Einstein’s relationship is completely general, it is especially important in calculating
the release of energy by nuclear means. We find that the energy yield from a kilogram of nuclear fuel
is more than a million times that from chemical fuel. To prove this startling statement, we first
find the result of the complete transformation of 1 kilogram of matter into energy, namely,

(1 kg)(3.0 Â 108 m/s)2 ¼ 9 Â 1016 J. The nuclear fission process, as one method of converting mass into
energy, is relatively inefficient, because the burning of 1 kg of uranium involves the conversion of only
0.87 g of matter into energy. This corresponds to approximately 7.8 Â 1013 J/kg of the uranium consumed. The enormous magnitude of this energy release can be appreciated only by comparison with
the energy of combustion of a familiar fuel such as gasoline, 5 Â 107 J/kg. The ratio of these numbers,
1.5 Â 106, reveals the tremendous difference between nuclear and chemical energies.
Calculations involving Einstein’s theory of relativity are readily accomplished using a MATLAB
program ALBERT, described in Computer Exercise 1.A.

1.6 ENERGY AND THE WORLD
All of the activities of human beings depend on energy, as we realize when we consider the dimensions
of the world’s energy problem. The efficient production of food requires machines, fertilizer, and
water, each making use of energy in a different way. Energy is vital to transportation, protection against
the weather, and the manufacturing of all goods. An adequate long-term supply of energy is therefore
essential for humanity’s survival. The world energy problem has many dimensions: the increasing cost
to acquire fuels as they become more scarce; the potential for global climate change resulting from
burning fossil fuels; the effects on safety and health of the by-products of energy consumption; the
inequitable distribution of energy resources among regions and nations; and the discrepancies between
current energy use and human expectations throughout the world.

1.7 SUMMARY
Associated with each basic type of force is an energy, which may be transformed to another form for
practical use. The addition of thermal energy to a substance causes an increase in temperature, the
measure of particle motion. Electromagnetic radiation arising from electrical devices, atoms, or nuclei


12

CHAPTER 1 Energy

may be considered to be composed of waves or of photons. Matter can be converted into energy

and vice versa according to Einstein’s formula E ¼ mc2. The energy of nuclear fission is millions of
times as large as that from chemical reactions. Energy is fundamental to all human endeavors and,
indeed, survival.

1.8 EXERCISES
1.1 Find the kinetic energy of a basketball player of mass 75 kg as he moves down the floor at a speed
of 8 m/s.
1.2 Recalling the conversion formulas for temperature,
5
C ¼ ðF À 32Þ
9

9
F ¼ C þ 32
5

where C and F are degrees in respective systems, convert each of the following: (a) 68  F,
(b) 500  F, (c) À273  C, (d) 1000  C, (e) À40 C.
1.3 If the specific heat of iron is 450 J/(kg Á  C), how much energy is required to bring 0.5 kg of iron
from 0  C to 100  C?
1.4 Find the speed corresponding to the average energy of nitrogen gas molecules (N2, 28 units of
atomic weight) at room temperature.
1.5 Find the power in kilowatts of an automobile rated at 200 horsepower. In a drive for 4 h at average
speed 45 mph, how many kWh of energy are required?
1.6 Find the frequency of a gamma-ray photon of wavelength 1.5 Â 10–12 m.
1.7 (a) For very small velocities compared with the velocity of light, show that the relativistic formula
for kinetic energy is ½m0v2. Hint: Use the series expansion (1 þ x)n ¼ 1 þ nx þ . . . (b) Find the
approximate relativistic mass increase of a car with rest mass 1000 kg moving at 20 m/s.
1.8 Noting that the electronvolt is 1.60 Â 10–19 J, how many joules are released in the fission of one
uranium nucleus, which yields 190 MeV?

1.9 Applying Einstein’s formula for the equivalence of mass and energy, E ¼ mc2, how many
kilograms of matter are converted into energy in Exercise 1.8?
1.10 If the atom of uranium-235 has mass of (235)(1.66 Â 10–27) kg, what amount of equivalent energy
does it have?
1.11 Using the results of Exercises 1.8, 1.9, and 1.10, what fraction of the mass of a U-235 nucleus is
converted into energy when fission takes place?
1.12 Show that to obtain a power of 1 W from fission of uranium, it is necessary to cause 3.3 Â 1010
fission events per second. Assume that each fission releases 190 MeV of useful energy.
1.13 Using the rest mass of each, compute the rest mass energy in MeV for (a) a proton and (b) a
neutron. Compare to values given in Table A.2.


References

13

1.14 Using the mass of 1.6605389 Â 10–27 kg for one atomic unit, calculate the equivalent energy
(in MeV) to 5 significant digits.
1.15 (a) If the fractional mass increase caused by relativity is DE/E0, show that
v=c ¼

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1 À ð1 þ DE=E0 ÞÀ2

(b) At what fraction of the speed of light does a particle have a mass that is 1% higher than the rest
mass? 10%? 100%?
1.16 The heat of combustion of hydrogen by the reaction 2H þ O ¼ H2O is quoted as
34.18 kilogram calories per gram of hydrogen. (a) Find how many Btu per pound this is with
the conversions 1 Btu ¼ 0.252 kcal, 1 lb ¼ 454 grams. (b) Find how many joules per gram this is
noting 1 cal ¼ 4.184 J. (c) Calculate the heat of combustion in eV per H2 molecule.

Note: Recall the number of particles per gram of molecular weight, Avogadro’s number,
NA ¼ 6.02 Â 1023.
1.17 Derive an analytical expression for finding the velocity of a relativistic particle given its kinetic
energy and rest mass.
1.18 Graph the percentage error in the kinetic energy computed from the classic mechanics
expression as compared to the full relativistic formula as a function of the fraction of the speed
of light (v/c).

1.9 COMPUTER EXERCISE
1.A Properties of particles moving at high velocities are related in a complicated way according
to Einstein’s theory of special relativity. To obtain answers easily, the MATLAB program
ALBERT (after Dr. Einstein) can be used to treat the following quantities: velocity,
momentum, total energy, kinetic energy, and ratio of mass to rest mass. Given one of these, for a
selected particle, ALBERT calculates the others. Test the program with various inputs,
including (a) an electron with velocity 0.5c, (b) a proton with 1000 MeV total energy, (c) a
neutron with 0.025 eV kinetic energy, (d) deuteron with m/m0 ¼ 1.01, and (e) alpha with
momentum 10–19 kg Á m/s.

References
Haynes, W.M. et al., (Ed.), 2011. CRC Handbook of Chemistry and Physics, ninety second ed. CRC Press. A standard source of data on many subjects.
National Institute of Standards and Technology (NIST), The NIST Reference on Constants, Units, and Uncertainty.
Information on SI units and fundamental physical constants.


14

CHAPTER 1 Energy

Further reading
Alsos Digital Library for Nuclear Issues. . Large collection of references.

American Institute of Physics, Center for History of Physics, Einstein. www.aip.org/history/einstein.
American Nuclear Society, 1986. Glossary of Terms in Nuclear Science and Technology. American Nuclear
Society.
American Nuclear Society, www.ans.org: Nuclear News, Radwaste Solutions, Nuclear Technology, Nuclear Science and Engineering, Fusion Science and Technology, and Transactions of the American Nuclear Society.
Online contents pages and selected articles or abstracts of technical papers.
American Nuclear Society public information. www.ans.org/pi. Essays on selected topics (e.g., radioisotope).
Asimov, I., 1982. Asimov’s Biographical Encyclopedia of Science and Technology: The Lives and Achievements
of 1510 Great Scientists from Ancient Times to the Present, second revised ed. Doubleday & Co.
Bloomfield, L., How Everything Works. www.howeverythingworks.org.
California Energy Commission, Energy Story. />Ehmann, W.D., Vance, D.E., 1991. Radiochemistry and Nuclear Methods of Analysis. John Wiley & Sons. Covers
many of the topics of this book in greater length.
Encyclopedia Britannica online. www.britannica.com. Brief articles are free; full articles require
paid membership.
Halliday, D., Walker, J., Resnick, R.E., 2007. Fundamentals of Physics Extended, seventh ed. John Wiley & Sons.
Textbook for college science and engineering students.
How Stuff Works. www.howstuffworks.com. Brief explanations of familiar devices and concepts, including many
of the topics of this book.
Internet Detective. www.vts.intute.ac.uk/detective. A tutorial on browsing for quality information on the Internet.
Knief, R.A., 1992. Nuclear Engineering: Theory and Technology of Commercial Nuclear Power, second ed.
Taylor & Francis. Comprehensive textbook that may be found in technical libraries.
Mayo, R.M., 1998. Introduction to Nuclear Concepts for Engineers. American Nuclear Society. College textbook
emphasizing nuclear processes.
McGraw-Hill, 2004. McGraw-Hill Concise Encyclopedia of Physics. McGraw-Hill.
Murray, R.L., Cobb, G.C., 1970. Physics: Concepts and Consequences. Prentice-Hall. Non-calculus text for liberal
arts students.
Nave, C., HyperPhysics. />Particle Data Group of Lawrence Berkeley National Laboratory, The Particle Adventure: Fundamentals of Matter
and Force. www.particleadventure.org.
PBS, 2005. Einstein’s Big Idea. www.pbs.org/wgbh/nova/einstein.
Physical Science Resource Center. www.compadre.org/psrc. Links provided by American Association of Physics
Teachers; select “browse resources.”

PhysLink. www.physlink.com. Select Reference for links to sources of many physics constants, conversion factors, and other data.
Radiation Information Network. www.physics.isu.edu/radinf. Numerous links to sources.
Rahn, F.J., Adamantiades, A.G., Kenton, J.E., Braun, C., 1991. A Guide to Nuclear Power Technology:
A Resource for Decision Making. Krieger Publishing Co (reprint of 1984 edition). A book for persons with
some technical background; almost a thousand pages of fine print; a host of tables, diagrams, photographs,
and references.
Tipler, P.A., Mosca, G., 2007. Physics for Scientists and Engineers, sixth ed. W.H. Freeman. Calculus-based
college textbook.
Wikipedia. . Millions of articles in free encyclopedia. Subject to edit by anyone and thus
may contain misinformation.
WWW Virtual Library. www.vlib.org. Links to virtual libraries in engineering, science, and other subjects.


CHAPTER

Atoms and nuclei

2

CHAPTER OUTLINE
2.1 Atomic Theory ..............................................................................................................................15
2.2 Gases ..........................................................................................................................................17
2.3 The Atom and Light .......................................................................................................................19
2.4 Laser Beams ................................................................................................................................22
2.5 Nuclear Structure .........................................................................................................................22
2.6 Sizes and Masses of Nuclei ..........................................................................................................23
2.7 Binding Energy .............................................................................................................................25
2.8 Summary ......................................................................................................................................28
2.9 Exercises .....................................................................................................................................28
2.10 Computer Exercises ......................................................................................................................29

References ...........................................................................................................................................30
Further Reading ....................................................................................................................................30

A complete understanding of the microscopic structure of matter and the exact nature of the forces
acting on that matter is yet to be realized. However, excellent models have been developed to predict
behavior to an adequate degree of accuracy for most practical purposes. These models are descriptive
or mathematical, often based on analogy with large-scale processes, on experimental data, or on
advanced theory.

2.1 ATOMIC THEORY
The most elementary concept is that matter is composed of individual particles—atoms—that retain
their identity as elements in ordinary physical and chemical interactions. Thus, a collection of helium
atoms that forms a gas has a total weight that is the sum of the weights of the individual atoms. Also,
when two elements combine to form a compound (e.g., if carbon atoms combine with oxygen atoms to
form carbon monoxide molecules), the total weight of the new substance is the sum of the weights of
the original elements.
There are more than 100 known elements. Most are found in nature; some are artificially produced.
Each is given a specific number in the periodic table of the elements; examples are hydrogen (H) 1,
helium (He) 2, oxygen (O) 8, and uranium (U) 92. The symbol Z is assigned to the atomic number,
which is also the number of electrons in the atom and determines its chemical properties. The periodic
table is shown in Figure 2.1.
Generally, the further an element is in the periodic table, the heavier its atoms. The atomic weight M is
the weight in grams of a definite number of atoms, 6.02 Â 1023, which is Avogadro’s number, NA.

15


16

CHAPTER 2 Atoms and nuclei


FIGURE 2.1
Periodic table of the elements.

Although we often use the terms atomic weight and atomic mass interchangeably, atomic mass describes
the mass of a single atom of a particular isotope, whereas atomic weight provides a weighted average
mass for an element based on the abundance of its constituent isotopes. For the elements just mentioned,
the values of M are approximately H, 1.008; He, 4.003; O, 16.00; and U, 238.0. Atomic weight is
expressed using grams/mole or atomic mass units (u), and atomic mass is quantified using atomic mass
units (u). Accurate values of atomic weights of all the elements are given in Table A.4 in Appendix A.
If an element has a nonnatural abundance of its isotopes (i.e., the elemental material is either
enriched or depleted), it is necessary to compute the atomic weight of the element (M) from the
weighted sum of all the atomic masses of the isotopes (Mj) rather than use the tabulated M value found
in a reference. In such cases, the isotopic abundance may be expressed either as an atom abundance or
fraction (gj), or as a weight or mass fraction (oj). This distinction leads to two formulas for determining
the elemental atomic weight:
X
M ¼
gj Mj
X oj
1
¼
Mj
M

ð2:1Þ


2.2 Gases


17

We can easily find the number of atoms per cubic centimeter in a substance if its density r (rho) in
grams per cubic centimeter is known. This procedure can be expressed as a convenient formula for
finding N, the atomic number density for any material
N¼

rNA
M

ð2:2Þ

The relationship holds for compounds as well, if M is taken as the molecular weight.

EXAMPLE 2.1
For natural uranium with a density of 19 g/cm3, we find an atom density of
À
Á
r NA ð19 g=cm3 Þ 6:02 Â 1023 atoms=mol
atoms
¼ 0:048 Â 1024
NU ¼ U ¼
MU
238 g=mol
cm3
The use of numbers times 1024 will turn out to be convenient later.

EXAMPLE 2.2
For a compound such as water, H2O, the molecular weight is first found,
MH2 O ¼ 2MH þ MO ¼ ð2Þð1:008Þ þ 15:999 ¼ 18:02 g=mol

Using the customary water density of r ¼ 1.0 g/cm3, the molecular density is
À
Á
rH2 O NA ð1:0 g=cm3 Þ 6:022 Â 1023 atoms=mol
molecules
¼ 0:0334 Â 1024
¼
NH2 O ¼
MH2 O
18:02 g=mol
cm3
With two atoms of hydrogen for every water molecule, the hydrogen atomic density is twice the
molecular density of water, that is, NH ¼ 2NH2 O ¼ 0:0668 Â 1024 atoms=cm3 ; whereas the oxygen
density is numerically equivalent to the water concentration, NO ¼ NH2 O .

2.2 GASES
Substances in the gaseous state are described approximately by the perfect or ideal gas law, relating
pressure (p), volume (V), and absolute temperature (T),
pV ¼ nkT

ð2:3Þ


18

CHAPTER 2 Atoms and nuclei

where n is the number of particles and k is Boltzmann’s constant. An increase in the temperature of the
gas as a result of heating causes greater molecular motion, which results in an increase of particle bombardment of a container wall and thus of pressure on the wall.
The gas particles, each of mass m, have a variety of speeds v in accord with Maxwell’s

gas theory, as shown in Figure 2.2. Maxwell’s formula for the number of molecules per unit
speed is
nð v Þ ¼

n0 4pv2
ð2pkT=mÞ

3=2

À
Á
exp Àmv2 =2kT

ð2:4Þ

where n0 is the total number of molecules. The most probable speed, at the peak of this Maxwellian
distribution, depends on temperature according to the relation (see Exercise 2.16)
vp ¼

pffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2kT=m

ð2:5Þ

while the average speed is
rffiffiffiffiffiffiffiffi
8kT
2
¼ pffiffiffi vp
v ¼

pm
p

ð2:6Þ

The kinetic theory of gases provides a basis for calculating properties such as the specific heat.
Recalling from Section 1.3 that the average energy of gas molecules is proportional to the temperature,
E ¼ 32 kT, we can deduce, as in Exercise 2.4, that the specific heat of a gas consisting only of single
atoms (monoatomic) is cV ¼ 32 k=m, where m is the mass of one atom. Thus, we see an intimate relationship between mechanical and thermal properties of materials.

FIGURE 2.2
Maxwellian distribution of molecular speeds.


2.3 The atom and light

19

2.3 THE ATOM AND LIGHT
Until the twentieth century, the internal structure of atoms was unknown, but it was believed that electric
charge and mass were uniform. Rutherford supervised some crucial experiments in which gold atoms
were bombarded by charged particles. He deduced in 1911 that most of the mass and positive charge
of an atom were concentrated in a nucleus of radius only approximately 10–5 times that of the atom,
and thus occupying a volume of approximately 10–15 times that of the atom (see Exercises 2.2 and
2.12). The new view of atoms paved the way for Bohr to find an explanation for the production of light.
It is well known that the color of a heated solid or gas changes as the temperature is increased,
tending to go from the red end of the visible region toward the blue end (i.e., from long wavelengths
to short wavelengths). The measured distribution of light among the different wavelengths at a
certain temperature can be explained by the assumption that light is in the form of photons. These
are absorbed and emitted with definite amounts of energy E that are proportional to the frequency

n, according to
E ¼ hv
where h is Planck’s constant, 6.63 Â 10

–34

ð2:7Þ

J Á s.

EXAMPLE 2.3
The energy corresponding to yellow light of frequency of 5.1 Â 1014 Hz is
À
ÁÀ
Á
E ¼ hv ¼ 6:63 Â 10À34 J Á s 5:1 Â 1014 sÀ1 ¼ 3:4 Â 10À19 J
This is seen to be a very minute amount of energy.
Bohr (1913) first explained the emission and absorption of light from incandescent hydrogen gas
with a novel model of the hydrogen atom. He assumed that the atom consists of a single electron moving at constant speed in a circular orbit about a nucleus—the proton—as shown in Figure 2.3. Each
particle has an electric charge of 1.6 Â 10–19 coulombs (C), but the positively charged proton has a mass

FIGURE 2.3
Hydrogen atom.


20

CHAPTER 2 Atoms and nuclei

Electron “jump”

Light of energy
hv = E2 − E1

+

n=1
n=2 n=3

n=4

E1
E2
E3

Possible
orbits

E4

FIGURE 2.4
Electron orbits in hydrogen (Bohr theory).

that is 1836 times that of the negatively charged electron. The radius of the orbit is set by the equality of
electrostatic force, attracting the two charges toward each other, to centripetal force, required to keep
the electron on a circular path. If sufficient energy is supplied to the hydrogen atom from the outside,
the electron is caused to jump to a larger orbit of definite radius. At some later time, the electron falls
back spontaneously to the original orbit, and energy is released in the form of a photon of light. The
photon energy hn is equal to the difference between energies in the two orbits. The smallest orbit has a
radius R1 ¼ 0.53 Â 10–10 m, whereas the others have radii increasing as the square of integers, n, which
are called principal quantum numbers. Thus if n is 1, 2, 3, . . . ,7, the radius of the n-th orbit is

R n ¼ n2 R1

ð2:8Þ

Figure 2.4 shows the allowed electron orbits in hydrogen. The energy of the atom system when the
electron is in the first orbit is E1 ¼ À13.6 eV, where the negative sign means that energy must be supplied to remove the electron to a great distance and leave the hydrogen as a positive ion. The energy
when the electron is in the nth orbit is
En ¼ E1 =n2

ð2:9Þ

The various discrete levels are shown in Figure 2.5.
The electronic structure of the other elements is described by the shell model, in which a limited
number of electrons can occupy a given orbit or shell. The atomic number Z is unique for each chemical
element and represents both the number of positive charges on the central massive nucleus of the atom
and the number of electrons in orbits around the nucleus. The maximum allowed numbers of electrons
in orbits as Z increases for the first few shells are 2, 8, and 18. The number of electrons in the outermost,
or valence, shell determines the chemical behavior of elements. For example, oxygen with Z ¼ 8 has
two electrons in the inner shell, six in the outer. Thus, oxygen has an affinity for elements with two
electrons in the valence shell. The formation of molecules from atoms by electron sharing is illustrated
by Figure 2.6, which shows the water molecule.