04/21/07 Ch. 14 Medical Applications of Nuclear Technologies
04/28/07 N/A FINAL EXAM N/A
MEGR 3090 INTRODUCTION TO NUCLEAR ENGINEERING FINAL EXAM: SATURDAY, APRIL 28, 2007
8:30 - 10:45 A.M. TEXT: Introduction to Nuclear Science & Engineering, Schultis & Faw, published by Marcel-Dekker, ISBN/ISSN 0-8247-0834-2 (available as e-book at Atkins Library) All tests and exams are open book. There will be 2 tests that will count 25% each; selected homework problems will count a total of 25%; and the final exam will count 25% of the final grade. INSTRUCTOR: Dr. Dennis K. Williams, P.E. PHONES: 704-246-4189 (OFFICE) EMAIL: [email protected] OFFICE HOURS: By Appointment; please feel free to contact me outside of class, preferably by email or at my office number between the hours of 9:00 a.m. and 4:30 p.m. Monday through Friday. Every attempt will be made to answer any questions that the student may have by email or by phone. If an appointment needs to be made to resolve any ques-tions, please identify your needs to me as far in advance as possible. COURSE DESCRIPTION: Intended for majors in the fields of mechanical engineering, civil engineering, biology, chemistry, and physics who are seeking a basic introduction to the field of nuclear science and engineering. The course will introduce the student to fundamental concepts of nuclear engineering, nuclear energetics, radioactivity, binary nuclear reactions, reactor theory, and medical applications of nuclear technology. An interdisciplinary approach that combines chem-istry, physics, engineering, biology and mathematics to the study of introductory topics surrounding modern nuclear technology will be em-ployed. GRADES: A 91 – 100 B 81 – 90 C 71 – 80 D 61 - 70 F less than 61
FUNDAMENTALS OF NUCLEARSCIENCE AND ENGINEERING
J. KENNETH SHULTISRICHARD E. FAW
Kansas State UniversityManhattan, Kansas, U.S.A.
M A R C E L
MARCEL DEKKER, INC. NEW YORK • BASEL
D E K K E R
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ISBN: 0-8247-0834-2
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Nuclear engineering and the technology developed by this discipline began andreached an amazing level of maturity within the past 60 years. Although nuclearand atomic radiation had been used during the first half of the twentieth century,mainly for medical purposes, nuclear technology as a distinct engineering disciplinebegan after World War II with the first efforts at harnessing nuclear energy forelectrical power production and propulsion of ships. During the second half of thetwentieth century, many innovative uses of nuclear radiation were introduced in thephysical and life sciences, in industry and agriculture, and in space exploration.
The purpose of this book is two-fold as is apparent from the table of contents.The first half of the book is intended to serve as a review of the important resultsof "modern" physics and as an introduction to the basic nuclear science neededby a student embarking on the study of nuclear engineering and technology. Laterin this book, we introduce the theory of nuclear reactors and its applications forelectrical power production and propulsion. We also survey many other applicationsof nuclear technology encountered in space research, industry, and medicine.
The subjects presented in this book were conceived and developed by others.Our role is that of reporters who have taught nuclear engineering for more yearsthan we care to admit. Our teaching and research have benefited from the effortsof many people. The host of researchers and technicians who have brought nu-clear technology to its present level of maturity are too many to credit here. Onlytheir important results are presented in this book. For their efforts, which havegreatly benefited all nuclear engineers, not least ourselves, we extend our deepestappreciation. As university professors we have enjoyed learning of the work of ourcolleagues. We hope our present and future students also will appreciate these pastaccomplishments and will build on them to achieve even more useful applicationsof nuclear technology. We believe the uses of nuclear science and engineering willcontinue to play an important role in the betterment of human life.
At a more practical level, this book evolved from an effort at introducing anuclear engineering option into a much larger mechanical engineering program atKansas State University. This book was designed to serve both as an introductionto the students in the nuclear engineering option and as a text for other engineeringstudents who want to obtain an overview of nuclear science and engineering. We
Copyright 2002 by Marcel Dekker, Inc. All Rights Reserved.
believe that all modern engineering students need to understand the basic aspectsof nuclear science engineering such as radioactivity and radiation doses and theirhazards.
Many people have contributed to this book. First and foremost we thank ourcolleagues Dean Eckhoff and Fred Merklin, whose initial collection of notes for anintroductory course in nuclear engineering motivated our present book intendedfor a larger purpose and audience. We thank Professor Gale Simons, who helpedprepare an early draft of the chapter on radiation detection. Finally, many revisionshave been made in response to comments and suggestions made by our students onwhom we have experimented with earlier versions of the manuscript. Finally, thecamera copy given the publisher has been prepared by us using I^TEX, and, thus,we must accept responsibility for all errors, typographical and other, that appearin this book.
J. Kenneth Shultis and Richard E. Faw
Copyright 2002 by Marcel Dekker, Inc. All Rights Reserved.
Contents
1 Fundamental Concepts1.1 Modern Units
1.1.1 Special Nuclear Units1.1.2 Physical Constants
1.2 The Atom1.2.1 Atomic and Nuclear Nomenclature1.2.2 Atomic and Molecular Weights1.2.3 Avogadro's Number1.2.4 Mass of an Atom1.2.5 Atomic Number Density1.2.6 Size of an Atom1.2.7 Atomic and Isotopic Abundances1.2.8 Nuclear Dimensions
1.3 Chart of the Nuclides1.3.1 Other Sources of Atomic/Nuclear Information
2 Modern Physics Concepts2.1 The Special Theory of Relativity
2.1.1 Principle of Relativity2.1.2 Results of the Special Theory of Relativity
2.2 Radiation as Waves and Particles2.2.1 The Photoelectric Effect2.2.2 Compton Scattering2.2.3 Electromagnetic Radiation: Wave-Particle Duality2.2.4 Electron Scattering2.2.5 Wave-Particle Duality
2.3 Quantum Mechanics2.3.1 Schrodinger's Wave Equation2.3.2 The Wave Function2.3.3 The Uncertainty Principle2.3.4 Success of Quantum Mechanics
2.4 Addendum 1: Derivation of Some Special Relativity Results2.4.1 Time Dilation
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2.4.2 Length Contraction2.4.3 Mass Increase
2.5 Addendum 2: Solutions to Schrodinger's Wave Equation2.5.1 The Particle in a Box2.5.2 The Hydrogen Atom2.5.3 Energy Levels for Multielectron Atoms
Atomic/Nuclear Models3.1 Development of the Modern Atom Model
3.1.1 Discovery of Radioactivity3.1.2 Thomson's Atomic Model: The Plum Pudding Model3.1.3 The Rutherford Atomic Model3.1.4 The Bohr Atomic Model3.1.5 Extension of the Bohr Theory: Elliptic Orbits3.1.6 The Quantum Mechanical Model of the Atom
3.2 Models of the Nucleus3.2.1 Fundamental Properties of the Nucleus3.2.2 The Proton-Electron Model3.2.3 The Proton-Neutron Model3.2.4 Stability of Nuclei3.2.5 The Liquid Drop Model of the Nucleus3.2.6 The Nuclear Shell Model3.2.7 Other Nuclear Models
Nuclear Energetics4.1 Binding Energy
4.1.1 Nuclear and Atomic Masses4.1.2 Binding Energy of the Nucleus4.1.3 Average Nuclear Binding Energies
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5.3.4 Positron Decay5.3.5 Electron Capture5.3.6 Neutron Decay5.3.7 Proton Decay5.3.8 Internal Conversion5.3.9 Examples of Energy-Level Diagrams
5.4 Characteristics of Radioactive Decay5.4.1 The Decay Constant5.4.2 Exponential Decay5.4.3 The Half-Life5.4.4 Decay Probability for a Finite Time Interval5.4.5 Mean Lifetime5.4.6 Activity5.4.7 Half-Life Measurement5.4.8 Decay by Competing Processes
5.5 Decay Dynamics5.5.1 Decay with Production5.5.2 Three Component Decay Chains5.5.3 General Decay Chain
5.6 Naturally Occurring Radionuclides5.6.1 Cosmogenic Radionuclides5.6.2 Singly Occurring Primordial Radionuclides5.6.3 Decay Series of Primordial Origin5.6.4 Secular Equilibrium
5.7 Radiodating5.7.1 Measuring the Decay of a Parent5.7.2 Measuring the Buildup of a Stable Daughter
6 Binary Nuclear Reactions6.1 Types of Binary Reactions
6.1.1 The Compound Nucleus6.2 Kinematics of Binary Two-Product Nuclear Reactions
6.2.1 Energy/Mass Conservation6.2.2 Conservation of Energy and Linear Momentum
6.4 Applications of Binary Kinematics6.4.1 A Neutron Detection Reaction6.4.2 A Neutron Production Reaction6.4.3 Heavy Particle Scattering from an Electron
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6.6.1 Fission Products6.6.2 Neutron Emission in Fission6.6.3 Energy Released in Fission
6.7 Fusion Reactions6.7.1 Thermonuclear Fusion6.7.2 Energy Production in Stars6.7.3 Nucleogenesis
7 Radiation Interactions with Matter7.1 Attenuation of Neutral Particle Beams
7.1.1 The Linear Interaction Coefficient7.1.2 Attenuation of Uncollided Radiation7.1.3 Average Travel Distance Before an Interaction7.1.4 Half-Thickness7.1.5 Scattered Radiation7.1.6 Microscopic Cross Sections
7.2 Calculation of Radiation Interaction Rates7.2.1 Flux Density7.2.2 Reaction-Rate Density7.2.3 Generalization to Energy- and Time-Dependent Situations7.2.4 Radiation Fluence7.2.5 Uncollided Flux Density from an Isotropic Point Source
8.2 Scintillation Detectors8.3 Semiconductor lonizing-Radiation Detectors8.4 Personal Dosimeters
8.4.1 The Pocket Ion Chamber8.4.2 The Film Badge8.4.3 The Thermoluminescent Dosimeter
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8.5 Measurement Theory8.5.1 Types of Measurement Uncertainties8.5.2 Uncertainty Assignment Based Upon Counting Statistics8.5.3 Dead Time8.5.4 Energy Resolution
9 Radiation Doses and Hazard Assessment9.1 Historical Roots9.2 Dosimetric Quantities
9.2.1 Energy Imparted to the Medium9.2.2 Absorbed Dose9.2.3 Kerma9.2.4 Calculating Kerma and Absorbed Doses9.2.5 Exposure9.2.6 Relative Biological Effectiveness9.2.7 Dose Equivalent9.2.8 Quality Factor9.2.9 Effective Dose Equivalent9.2.10 Effective Dose
9.3 Natural Exposures for Humans9.4 Health Effects from Large Acute Doses
9.4.1 Effects on Individual Cells9.4.2 Deterministic Effects in Organs and Tissues9.4.3 Potentially Lethal Exposure to Low-LET Radiation
9.5 Hereditary Effects9.5.1 Classification of Genetic Effects9.5.2 Summary of Risk Estimates9.5.3 Estimating Gonad Doses and Genetic Risks
9.6 Cancer Risks from Radiation Exposures9.6.1 Dose-Response Models for Cancer9.6.2 Average Cancer Risks for Exposed Populations
9.7 Radon and Lung Cancer Risks9.7.1 Radon Activity Concentrations9.7.2 Lung Cancer Risks
10 Principles of Nuclear Reactors10.1 Neutron Moderation10.2 Thermal-Neutron Properties of Fuels10.3 The Neutron Life Cycle in a Thermal Reactor
10.3.1 Quantification of the Neutron Cycle10.3.2 Effective Multiplication Factor
10.4 Homogeneous and Heterogeneous Cores10.5 Reflectors10.6 Reactor Kinetics
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10.6.1 A Simple Reactor Kinetics Model10.6.2 Delayed Neutrons10.6.3 Reactivity and Delta-k10.6.4 Revised Simplified Reactor Kinetics Models10.6.5 Power Transients Following a Reactivity Insertion
10.7 Reactivity Feedback10.7.1 Feedback Caused by Isotopic Changes10.7.2 Feedback Caused by Temperature Changes
10.9 Addendum 1: The Diffusion Equation10.9.1 An Example Fixed-Source Problem10.9.2 An Example Criticality Problem10.9.3 More Detailed Neutron-Field Descriptions
10.10 Addendum 2: Kinetic Model with Delayed Neutrons10.11 Addendum 3: Solution for a Step Reactivity Insertion
11 Nuclear Power11.1 Nuclear Electric Power
11.1.1 Electricity from Thermal Energy11.1.2 Conversion Efficiency11.1.3 Some Typical Power Reactors11.1.4 Coolant Limitations
11.2 Pressurized Water Reactors11.2.1 The Steam Cycle of a PWR11.2.2 Major Components of a PWR
11.3 Boiling Water Reactors11.3.1 The Steam Cycle of a BWR11.3.2 Major Components of a BWR
11.4 New Designs for Central-Station Power11.4.1 Certified Evolutionary Designs11.4.2 Certified Passive Design11.4.3 Other Evolutionary LWR Designs11.4.4 Gas Reactor Technology
11.5 The Nuclear Fuel Cycle11.5.1 Uranium Requirements and Availability11.5.2 Enrichment Techniques11.5.3 Radioactive Waste11.5.4 Spent Fuel
11.6 Nuclear Propulsion11.6.1 Naval Applications11.6.2 Other Marine Applications11.6.3 Nuclear Propulsion in Space
12 Other Methods for Converting Nuclear Energy to Electricity12.1 Thermoelectric Generators
12.1.1 Radionuclide Thermoelectric Generators
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12.3 AMTEC Conversion12.4 Stirling Converters12.5 Direct Conversion of Nuclear Radiation
12.5.1 Types of Nuclear Radiation Conversion Devices12.5.2 Betavoltaic Batteries
12.6 Radioisotopes for Thermal Power Sources12.7 Space Reactors
12.7.1 The U.S. Space Reactor Program12.7.2 The Russian Space Reactor Program
13 Nuclear Technology in Industry and Research13.1 Production of Radioisotopes13.2 Industrial and Research Uses of Radioisotopes and Radiation13.3 Tracer Applications
Appendix D: Decay Characteristics of Selected Radionuclides
Copyright 2002 by Marcel Dekker, Inc. All Rights Reserved.
Chapter 1
Fundamental Concepts
The last half of the twentieth century was a time in which tremendous advances inscience and technology revolutionized our entire way of life. Many new technolo-gies were invented and developed in this time period from basic laboratory researchto widespread commercial application. Communication technology, genetic engi-neering, personal computers, medical diagnostics and therapy, bioengineering, andmaterial sciences are just a few areas that were greatly affected.
Nuclear science and engineering is another technology that has been transformedin less than fifty years from laboratory research into practical applications encoun-tered in almost all aspects of our modern technological society. Nuclear power,from the first experimental reactor built in 1942, has become an important sourceof electrical power in many countries. Nuclear technology is widely used in medicalimaging, diagnostics and therapy. Agriculture and many other industries make wideuse of radioisotopes and other radiation sources. Finally, nuclear applications arefound in a wide range of research endeavors such as archaeology, biology, physics,chemistry, cosmology and, of course, engineering.
The discipline of nuclear science and engineering is concerned with quantify-ing how various types of radiation interact with matter and how these interactionsaffect matter. In this book, we will describe sources of radiation, radiation inter-actions, and the results of such interactions. As the word "nuclear" suggests, wewill address phenomena at a microscopic level, involving individual atoms and theirconstituent nuclei and electrons. The radiation we are concerned with is generallyvery penetrating and arises from physical processes at the atomic level.
However, before we begin our exploration of the atomic world, it is necessary tointroduce some basic fundamental atomic concepts, properties, nomenclature andunits used to quantify the phenomena we will encounter. Such is the purpose ofthis introductory chapter.
1.1 Modern UnitsWith only a few exceptions, units used in nuclear science and engineering are thosedefined by the SI system of metric units. This system is known as the "InternationalSystem of Units" with the abbreviation SI taken from the French "Le SystemeInternational d'Unites." In this system, there are four categories of units: (1) baseunits of which there are seven, (2) derived units which are combinations of the baseunits, (3) supplementary units, and (4) temporary units which are in widespread
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Table 1.1. The SI system of units arid their four categories.
Base SI units:Physical quantitylengthmasstimeelectric currentthermodynamic temperatureluminous intensityquantity of substance
Examples of Derived SIPhysical quantityforcework, energy, quantity of heatpowerelectric chargeelectric potential differenceelectric resistancemagnetic fluxmagnetic flux densityfrequencyradioactive decay ratepressurevelocitymass densityareavolumemolar energyelectric charge density
Unit namenautical mileknotangstromhectarebarstandard atmospherebarncurieroentgengraysievert
Symbol
mkgsAKcdmol
Symbol
NJWcVftWbTHzBqPa
Symbolraclsr
Symbol
AhabaratmbCiRGySv
Formula
kg m sN mJ s-1
A sW A'1
V A-1
V sWb m"2
s-1
s-1
N m-'2
in s"1
kg m~^om
in3
J mor1
C m-3
Value in SI unit1852 m1852/3600 rn s~[
0.1 nm = ICT10 rn1 hm2 = 104 m2
0.1 MPa0.101325 MPa10~24 cm2
3.7 x 10H) Bq2.58 x 10~4 C kg"1
1 J kg-1
Source: NBS Special Publication 330, National Bureau of Standards, Washington, DC, 1977.
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use for special applications. These units are shown in Table 1.1. To accommodatevery small and large quantities, the SI units and their symbols are scaled by usingthe SI prefixes given in Table 1.2.
There are several units outside the SI which are in wide use. These include thetime units day (d), hour (h) and minute (min); the liter (L or I); plane angle degree(°), minute ('), and second ("); and, of great use in nuclear and atomic physics,the electron volt (eV) and the atomic mass unit (u). Conversion factors to convertsome non-Si units to their SI equivalent are given in Table 1.3.
Finally it should be noted that correct use of SI units requires some "grammar"on how to properly combine different units and the prefixes. A summary of the SIgrammar is presented in Table 1.4.
Table 1.2. SI prefixes. Table 1.3. Conversion factors.
2.834952 x 10~2 kg4.535924 X lO^1 kg9.071 847 x 102 kg
9.806650 N a
4.448222 N8.896444 X 103 N
6.894757 x 103 Pa4.788026 x 101 Pa1.013250 x 105 Paa
2.49082 x 102 Pa3.38639 x 103 Pa1.33322 x 102 Pa1 x 105 Paa
1.60219 x 10~19 J4.184 Ja
1.054350 X 103 J3.6 x 106 Ja
8.64 x 1010 Ja
"Exact converson factor.
Source: Standards for Metric Practice, ANSI/ASTME380-76, American National Standards Institute,New York, 1976.
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Table 1.4. Summary of SI grammar.
Grammar Comments
capitalization
space
plural
raised dots
solidis
mixing units/names
prefix
double vowels
hyphens
numbers
A unit name is never capitalized even if it is a person's name. Thuscurie, not Curie. However, the symbol or abbreviation of a unitnamed after a person is capitalized. Thus Sv, not sv.
Use 58 rn, not 58m .
A symbol is never pluralized. Thus 8 N, not 8 Ns or 8 Ns.
Sometimes a raised dot is used when combining units such as N-m2-s;however, a single space between unit symbols is preferred as inN m2 s.
For simple unit combinations use g/cm3 or g cm~3. However, formore complex expressions, N m~2 s""1 is much clearer than N/m2/s.
Never mix unit names and symbols. Thus kg/s, not kg/second orkilogram/s.
Never use double prefixes such as ^g; use pg. Also put prefixes inthe numerator. Thus km/s, not m/ms.
When spelling out prefixes with names that begin with a vowel, su-press the ending vowel on the prefix. Thus megohm and kilohm, notmegaohm and kiloohm.
Do not put hyphens between unit names. Thus newton meter, notnewton-meter. Also never use a hyphen with a prefix. Hence, writemicrogram not micro-gram.
For numbers less than one, use 0.532 not .532. Use prefixes to avoidlarge numbers; thus 12.345 kg, not 12345 g. For numbers with morethan 5 adjacent numerals, spaces are often used to group numeralsinto triplets; thus 123456789.12345633, not 123456789.12345633.
1.1.1 Special Nuclear UnitsWhen treating atomic and nuclear phenomena, physical quantities such as energiesand masses are extremely small in SI units, and special units are almost alwaysused. Two such units are of particular importance.
The Electron VoltThe energy released or absorbed in a chemical reaction (arising from changes inelectron bonds in the affected molecules) is typically of the order of 10~19 J. Itis much more convenient to use a special energy unit called the electron volt. Bydefinition, the electron volt is the kinetic energy gained by an electron (mass me
and charge —e) that is accelerated through a potential difference AV of one volt= 1 W/A = 1 (J s~1)/(C s-1) = 1 J/C. The work done by the electric field is-e&V = (1.60217646 x 1(T19 C)(l J/C) = 1.60217646 x 10~19 J = 1 eV. Thus
1 eV= 1.602 176 46 x 10~19 J.
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solidis
If the electron (mass me) starts at rest, then the kinetic energy T of the electronafter being accelerated through a potential of 1 V must equal the work done on theelectron, i.e.,
T = \m^ = -eAV = I eV. (1.1)Zi
The speed of the electron is thus v = ^/2T/me ~ 5.93 x 105 m/s, fast by oureveryday experience but slow compared to the speed of light (c ~ 3 x 108 m/s).
The Atomic Mass UnitBecause the mass of an atom is so much less than 1 kg, a mass unit more appropriateto measuring the mass of atoms has been defined independent of the SI kilogrammass standard (a platinum cylinder in Paris). The atomic mass unit (abbreviatedas amu, or just u) is defined to be 1/12 the mass of a neutral ground-state atomof 12C. Equivalently, the mass of Na
12C atoms (Avogadro's number = 1 mole) is0.012 kg. Thus, 1 amu equals (1/12)(0.012 kg/JVa) = 1.6605387 x 10~27 kg.
1.1.2 Physical ConstantsAlthough science depends on a vast number of empirically measured constants tomake quantitative predictions, there are some very fundamental constants whichspecify the scale and physics of our universe. These physical constants, such as thespeed of light in vacuum c, the mass of the neutron me, Avogadro's number 7Va,etc., are indeed true constants of our physical world, and can be viewed as auxiliaryunits. Thus, we can measure speed as a fraction of the speed of light or mass as amultiple of the neutron mass. Some of the important physical constants, which weuse extensively, are given in Table 1.5.
1.2 The AtomCrucial to an understanding of nuclear technology is the concept that all matter iscomposed of many small discrete units of mass called atoms. Atoms, while oftenviewed as the fundamental constituents of matter, are themselves composed of otherparticles. A simplistic view of an atom is a very small dense nucleus, composed ofprotons and neutrons (collectively called nucleons), that is surrounded by a swarm ofnegatively-charged electrons equal in number to the number of positively-chargedprotons in the nucleus. In later chapters, more detailed models of the atom areintroduced.
It is often said that atoms are so small that they cannot been seen. Certainly,they cannot with the naked human eye or even with the best light microscope.However, so-called tunneling electron microscopes can produce electrical signals,which, when plotted, can produce images of individual atoms. In fact, the sameinstrument can also move individual atoms. An example is shown in Fig. 1.1. Inthis figure, iron atoms (the dark circular dots) on a copper surface are shown beingmoved to form a ring which causes electrons inside the ring and on the coppersurface to form standing waves. This and other pictures of atoms can be found onthe web at http://www.ibm.com/vis/stm/gallery.html.
Although neutrons and protons are often considered as "fundamental" particles,we now know that they are composed of other smaller particles called quarks held
Copyright 2002 by Marcel Dekker, Inc. All Rights Reserved.
m sub n Note, what is shown is the mass of an electron (m sub e); not the mass of a neutron.
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Table 1.5. Values of some important physical constants as internationally recom-mended in 1998.
Constant Symbol Value
Speed of light (in vacuum)
Electron charge
Atomic mass unit
Electron rest mass
Proton rest mass
Neutron rest mass
Planck's constant
Avogadro's constant
Boltzmann constant
Ideal gas constant (STP)Electric constant
2.99792458 x 108 m s~l
1.60217646 x 10'19 C
1.6605387 x 10~27 kg(931.494013 MeV/c2)
9.1093819 x 10~31 kg(0.51099890 MeV/c2)(5.48579911 x 10~4 u)
1.6726216 x 10~27 kg(938.27200 MeV/c2)(1.0072764669 u)
1.6749272 x 10~27 kg(939.56533 MeV/c2)(1.0086649158 u)
6.6260688 x 10~34 J s4.1356673 x 10~15 eV s
6.0221420 x 1023 mol"1
1.3806503 x 10~23 J K~ ]
(8.617342 x 10~5 eV K"1)
8.314472 J mor1 K"1
8.854187817 x 10~12 F m"1
Source: P.J. Mohy and B.N. Taylor, "CODATAFundamental Physical Constants," Rev. Modern
Recommended Values of thePhysics, 72, No. 2, 2000.
together by yet other particles called gluons. Whether quarks arid gluons are them-selves fundamental particles or are composites of even smaller entities is unknown.Particles composed of different types of quarks are called baryons. The electron andits other lepton kin (such as positrons, neutrinos, and muons) are still thought, bycurrent theory, to be indivisible entities.
However, in our study of nuclear science and engineering, we can viewr the elec-tron, neutron and proton as fundamental indivisible particles, since the compositenature of nucleons becomes apparent only under extreme conditions, such as thoseencountered during the first minute after the creation of the universe (the "bigbang") or in high-energy particle accelerators. We will not deal with such giganticenergies. Rather, the energy of radiation we consider is sufficient only to rearrangeor remove the electrons in an atom or the neutrons and protons in a nucleus.
1.2.1 Atomic and Nuclear NomenclatureThe identity of an atom is uniquely specified by the number of neutrons N andprotons Z in its nucleus. For an electrically neutral atom, the number of electronsequals the number of protons Z, which is called the atomic number. All atoms ofthe same element have the same atomic number. Thus, all oxygen atoms have 8protons in the nucleus while all uranium atoms have 92 protons.
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Figure 1.1. Pictures of iron atoms on a copper surface being moved toform a ring inside of which surface copper electrons are confined and formstanding waves. Source: IBM Corp.
However, atoms of the same element may have different numbers of neutrons inthe nucleus. Atoms of the same element, but with different numbers of neutrons,are called isotopes. The symbol used to denote a particular isotope is
where X is the chemical symbol and A = Z + TV, which is called the mass number.For example, two uranium isotopes, which will be discussed extensively later, are2g|U and 2g2U. The use of both Z and X is redundant because one specifies theother. Consequently, the subscript Z is often omitted, so that we may write, forexample, simply 235U and 238U.1
1To avoid superscripts, which were hard to make on old-fashioned typewriters, the simpler formU-235 and U-238 was often employed. However, with modern word processing, this form shouldno longer be used.
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Symbol for identifying specific isotopes of an element.
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Because isotopes of the same element have the same number and arrangementof electrons around the nucleus, the chemical properties of such isotopes are nearlyidentical. Only for the lightest isotopes (e.g., 1H, deuterium 2H, and tritium 3H)are small differences noted. For example, light water 1H2O freezes at 0 °C whileheavy water 2H2O (or D2O since deuterium is often given the chemical symbol D)freezes at 3.82 °C.
A discussion of different isotopes arid elements often involves the following basicnuclear jargon.
nuclide: a term used to refer to a particular atom or nucleus with a specific neutronnumber N and atomic (proton) number Z. Nuclides are either stable (i.e.,unchanging in time unless perturbed) or radioactive (i.e., they spontaneouslychange to another nuclide with a different Z and/or N by emitting one ormore particles). Such radioactive nuclides are termed rachonuclides.
isobar: nuclides with the same mass number A = N + Z but with different numberof neutrons N and protons Z. Nuclides in the same isobar have nearly equalmasses. For example, isotopes which have nearly the same isobaric mass of14 u include ^B. ^C, ^N, and ^O.
isotone: nuclides with the same number of neutrons Ar but different number ofprotons Z. For example, nuclides in the isotone with 8 neutrons include ^B.^C. J f N and *f O.
isorner: the same nuclide (same Z and A") in which the nucleus is in different long-lived excited states. For example, an isomer of "Te is 99mTe where the mdenotes the longest-lived excited state (i.e., a state in which the nucleons inthe nucleus are not in the lowest energy state).
1.2.2 Atomic and Molecular WeightsThe atomic weight A of an atom is the ratio of the atom's mass to that of one neutralatom of 12C in its ground state. Similarly the molecular weight of a molecule is theratio of its molecular mass to one atom of 12C. As ratios, the atomic and molecularweights are dimensionless numbers.
Closely related to the concept of atomic weight is the atomic mass unit, whichwe introduced in Section 1.1.1 as a special mass unit. Recall that the atomic massunit is denned such that the mass of a 12C atom is 12 u. It then follows that themass M of an atom measured in atomic mass units numerically equals the atom'satomic weight A. From Table 1.5 we see 1 u ~ 1.6605 x 10~27 kg. A detailedlisting of the atomic masses of the known nuclides is given in Appendix B. Fromthis appendix, we see that the atomic mass (in u) and. hence, the atomic weight ofa nuclide almost equals (within less than one percent) the atomic mass number Aof the nuclide. Thus for approximate calculations, we can usually assume A — A.
Most naturally occurring elements are composed of two or more isotopes. Theisotopic abundance 7, of the /-th isotope in a given element is the fraction of theatoms in the element that are that isotope. Isotopic abundances are usually ex-pressed in atom percent and are given in Appendix Table A.4. For a specifiedelement, the elemental atomic weight is the weighted average of the atomic weights
Copyright 2002 by Marcel Dekker, Inc. All Rights Reserved.
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one-twelfth of a
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one-twelfth of an
of all naturally occurring isotopes of the element, weighted by the isotopic abun-dance of each isotope, i.e.,
where the summation is over all the isotopic species comprising the element. Ele-mental atomic weights are listed in Appendix Tables A. 2 and A. 3.
Example 1.1: What is the atomic weight of boron? From Table A.4 we findthat naturally occurring boron consists of two stable isotopes 10B and nB withisotopic abundances of 19.1 and 80.1 atom-percent, respectively. From AppendixB the atomic weight of 10B and UB are found to be 10.012937 and 11.009306,respectively. Then from Eq. (1.2) we find
AB = (7io-4io +7n./4ii)/100
= (0.199 x 10.012937) + (0.801 x 11.009306) = 10.81103.
This value agrees with the tabulated value AB = 10.811 as listed in Tables A.2and A.3.
1.2.3 Avogadro's NumberAvogadro's constant is the key to the atomic world since it relates the number ofmicroscopic entities in a sample to a macroscopic measure of the sample. Specif-ically, Avogadro's constant 7Va ~ 6.022 x 1023 equals the number of atoms in 12grams of 12C. Few fundamental constants need be memorized, but an approximatevalue of Avogadro's constant should be.
The importance of Avogadro's constant lies in the concept of the mole. Amole (abbreviated mol) of a substance is denned to contain as many "elementaryparticles" as there are atoms in 12 g of 12C. In older texts, the mole was oftencalled a "gram-mole" but is now called simply a mole. The "elementary particles"can refer to any identifiable unit that can be unambiguously counted. We can, forexample, speak of a mole of stars, persons, molecules or atoms.
Since the atomic weight of a nuclide is the atomic mass divided by the mass ofone atom of 12C, the mass of a sample, in grams, numerically equal to the atomicweight of an atomic species must contain as many atoms of the species as thereare in 12 grams (or 1 mole) of 12C. The mass in grams of a substance that equalsthe dimensionless atomic or molecular weight is sometimes called the gram atomicweight or gram molecular weight. Thus, one gram atomic or molecular weight ofany substance represents one mole of the substance and contains as many atoms ormolecules as there are atoms in one mole of 12C, namely Na atoms or molecules.That one mole of any substance contains Na entities is known as Avogadro's lawand is the fundamental principle that relates the microscopic world to the everydaymacroscopic world.
Copyright 2002 by Marcel Dekker, Inc. All Rights Reserved.
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19.9
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Example 1.2: How many atoms of 10B are there in 5 grams of boron? FromTable A. 3, the atomic weight of elemental boron AB = 10.811. The 5-g sampleof boron equals m/ AB moles of boron, and since each mole contains Na atoms,the number of boron atoms is
Na = = (5 g)(0.6022 x 10" atoms/mo.) = y
AB (10.811 g/mol)
From Table A. 4, the isotopic abundance of 10B in elemental boron is found tobe 19.9%. The number Nw of 10B atoms in the sample is, therefore, A/io =(0.199)(2.785 x 1023) = 5.542 x 1022 atoms.
1.2.4 Mass of an AtomWith Avogadro's number many basic properties of atoms can be inferred. Forexample, the mass of an individual atom can be found. Since a mole of a groupof identical atoms (with a mass of A grams) contains 7Va atoms, the mass of anindividual atom is
M (g/atom) = A/Na ~ A/Na. (1.3)
The approximation of A by A is usually quite acceptable for all but the most precisecalculations. This approximation will be used often throughout this book.
In Appendix B. a comprehensive listing is provided for the masses of the knownatom. As will soon become apparent, atomic masses are central to quantifying theenergetics of various nuclear reactions.
Example 1.3: Estimate the mass on an atom of 238U. From Eq. (1.3) we find
238 (g/mol)6.022 x 1023 atoms/mol
= 3.952 x 10 g/atom.
From Appendix B, the mass of 238U is found to be 238.050782 u which numericallyequals its gram atomic weight A. A more precise value for the mass of an atomof 238U is, therefore,
,238in ___ 238.050782 (g/mol)M(238U) = I,w ' = 3.952925 x IQ~" g/atom.v ; 6.022142 x 1023 atoms/mol &/
Notice that approximating A by A leads to a negligible error.
1.2.5 Atomic Number DensityIn many calculations, we will need to know the number of atoms in 1 cm3 of asubstance. Again, Avogadro's number is the key to finding the atom density. For ahomogeneous substance of a single species and with mass density p g/cm3, 1 cm3
Copyright 2002 by Marcel Dekker, Inc. All Rights Reserved.
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contains p/A moles of the substance and pNa/A atoms. The atom density N isthus
N (atoms/cm3) - (1.4)
To find the atom density Ni of isotope i of an element with atom density N simplymultiply N by the fractional isotopic abundance 7^/100 for the isotope, i.e., Ni —
Equation 1.4 also applies to substances composed of identical molecules. In thiscase, N is the molecular density and A the gram molecular weight. The number ofatoms of a particular type, per unit volume, is found by multiplying the moleculardensity by the number of the same atoms per molecule. This is illustrated in thefollowing example.
Example 1.4: What is the hydrogen atom density in water? The molecularweight of water AH Q = 1An + 2Ao — 2A# + AO = 18. The molecular densityof EbO is thus
A r / T T _ pH2°Na (I g cm"3) x (6.022 x 1023 molecules/mol)7V(ri2O) = : = ; :V ' ^H20 18g/mol
= 3.35 x 1022 molecules/cm3.
The hydrogen density 7V(H) = 27V(H2O) = 2(3.35xlO22) = 6.69xlO22 atoms/cm3.
The composition of a mixture such as concrete is often specified by the massfraction Wi of each constituent. If the mixture has a mass density p, the massdensity of the iih constituent is pi — Wip. The density Ni of the iih component isthus
PiNa wlPNa1 = ~A~ = ~A~' ( }
S\i S^-i
If the composition of a substance is specified by a chemical formula, such asXnYm, the molecular weight of the mixture is A = nAx + mAy and the massfraction of component X is
/- -,(1.6)t •nAx + mAy
Finally, as a general rule of thumb, it should be remembered that atom densitiesin solids and liquids are usually between 1021 and 1023 /cm~3. Gases at standardtemperature and pressure are typically less by a factor of 1000.
1.2.6 Size of an AtomFor a substance with an atom density of TV atoms/cm3, each atom has an associatedvolume of V = I/A7" cm3. If this volume is considered a cube, the cube width is F1/3.For 238U, the cubical size of an atom is thus I/A7"1/3 = 2.7 x 10~8 cm. Measurements
Copyright 2002 by Marcel Dekker, Inc. All Rights Reserved.
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of the size of atoms reveals a diffuse electron cloud about the nucleus. Althoughthere is no sharp edge to an atom, an effective radius can be defined such thatoutside this radius an electron is very unlikely to be found. Except for hydrogen,atoms have radii of about 2 to 2.5 x 10~8 cm. As Z increases, i.e., as more electronsand protons are added, the size of the electron cloud changes little, but simplybecomes more dense. Hydrogen, the lightest element, is also the smallest with aradius of about 0.5 x 10~8 cm.
1.2.7 Atomic and Isotopic AbundancesDuring the first few minutes after the big bang only the lightest elements (hydrogen,helium and lithium) were created. All the others were created inside stars eitherduring their normal aging process or during supernova explosions. In both processes,nuclei are combined or fused to form heavier nuclei. Our earth with all the naturallyoccurring elements was formed from debris of dead stars. The abundances of theelements for our solar system is a consequence of the history of stellar formationand death in our corner of the universe. Elemental abundances are listed in TableA. 3. For a given element, the different stable isotopes also have a natural relativeabundance unique to our solar system. These isotopic abundances are listed inTable A. 4.
1.2.8 Nuclear DimensionsSize of a NucleusIf each proton and neutron in the nucleus has the same volume, the volume of a nu-cleus should be proportional to A. This has been confirmed by many measurementsthat have explored the shape and size of nuclei. Nuclei, to a first approximation, arespherical or very slightly ellipsoidal with a somewhat diffuse surface, In particular,it is found that an effective spherical nuclear radius is
R = R0Al/3, with R0 ~ 1.25 x 1CT13 cm. (1.7)
The associated volume is
Vicious = ̂ - 7.25 X W~39A Cm3. (1.8)
Since the atomic radius of about 2 x 10~8 cm is 105 times greater than thenuclear radius, the nucleus occupies only about 10~15 of the volume of a atom. Ifan atom were to be scaled to the size of a large concert hall, then the nucleus wouldbe the size of a very small gnat!
Nuclear Density
Since the mass of a nucleon (neutron or proton) is much greater than the mass ofelectrons in an atom (mn = 1837 me), the mass density of a nucleus is
This is the density of the earth if it were compressed to a ball 200 m in diameter.
Copyright 2002 by Marcel Dekker, Inc. All Rights Reserved.
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Almost all atoms with Z > 10 have radii between 1 and 2e-8 cm.
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radius
1.3 Chart of the NuclidesThe number of known different atoms, each with a distinct combination of Z andA, is large, numbering over 3200 nuclides. Of these, 266 are stable (i.e., non-radioactive) and are found in nature. There are also 65 long-lived radioisotopesfound in nature. The remaining nuclides have been made by humans and are ra-dioactive with lifetimes much shorter than the age of the solar system. The lightestatom (A = 1) is ordinary hydrogen JH, while the mass of the heaviest is contin-ually increasing as heavier and heavier nuclides are produced in nuclear researchlaboratories. One of the heaviest (A = 269) is meitnerium logMt.
A very compact way to portray this panoply of atoms and some of their proper-ties is known as the Chart of the Nuclides. This chart is a two-dimensional matrix ofsquares (one for each known nuclide) arranged by atomic number Z (y-axis) versusneutron number N (x-axis). Each square contains information about the nuclide.The type and amount of information provided for each nuclide is limited only bythe physical size of the chart. Several versions of the chart are available on theinternet (see web addresses given in the next section and in Appendix A).
Perhaps, the most detailed Chart of the Nuclides is that provided by GeneralElectric Co. (GE). This chart (like many other information resources) is not avail-able on the web; rather, it can be purchased from GE ($15 for students) and is highlyrecommended as a basic data resource for any nuclear analysis. It is available asa 32" x55" chart or as a 64-page book. Information for ordering this chart can befound on the web at http://www.ssts.lmsg.lmco.com/nuclides/index.html.
1.3.1 Other Sources of Atomic/Nuclear InformationA vast amount of atomic and nuclear data is available on the world-wide web.However, it often takes considerable effort to find exactly what you need. The siteslisted below contain many links to data sources, and you should explore these tobecome familiar with them and what data can be obtained through them.
These two sites have links to the some of the major nuclear and atomic data repos-itories in the world.
These sites contain much information about nuclear technology and other relatedtopics. Many are home pages for various governmental agencies and some are sitesoffering useful links, software, reports, and other pertinent information.
http://physics.nist.gov/http:/ /www.nist .gov/http://www.energy.gov/http:/ /www.nrc.gov/http:/ /www.doe.gov/http://www.epa.gov/oar/http:/ /www.nrpb.org.uk/http://www-rsicc.ornl.gov/rsic.htmlhttp://www.iaea.org/worldatom/ht tp: / /www.nea. f r /
PROBLEMS
1. Both the hertz and the curie have dimensions of s"1. Explain the differencebetween these two units.
2. Explain the SI errors (if any) in and give the correct equivalent units for thefollowing units: (a) m-grams/pL, (b) megaohms/nm, (c) N-m/s/s, (d) gramcm/(s~1/mL). and (e) Bq/milli-Curie.
3. In vacuum, how far does light move in 1 ps?
4. In a medical test for a certain molecule, the concentration in the blood isreported as 123 mcg/dL. What is the concentration in proper SI notation?
5. How many neutrons and protons are there in each of the following riuclides:(a) 10B. (b) 24Na, (c) 59Co, (d) 208Pb. and (e) 235U?
6. What are the molecular weights of (a) H2 gas, (b) H2O, and (c) HDO?
7. What is the mass in kg of a molecule of uranyl sulfate UC^SCV/
8. Show by argument that the reciprocal of Avogadro's constant is the gramequivalent of 1 atomic mass unit.
9. How many atoms of 234U are there in 1 kg of natural uranium?
10. How many atoms of deuterium are there in 2 kg of water?
11. Estimate the number of atoms in a 3000 pound automobile. State any assump-tions you make.
12. Dry air at normal temperature and pressure has a mass density of 0.0012 g/cm3
with a mass fraction of oxygen of 0.23. WThat is the atom density (atom/cm3)of 180?
Copyright 2002 by Marcel Dekker, Inc. All Rights Reserved.
13. A reactor is fueled with 4 kg uranium enriched to 20 atom-percent in 235U.The remainder of the fuel is 238U. The fuel has a mass density of 19.2 g/cm3.(a) What is the mass of 235U in the reactor? (b) What are the atom densitiesof 235U and 238U in the fuel?
14. A sample of uranium is enriched to 3.2 atom-percent in 235U with the remainderbeing 238U. What is the enrichment of 235U in weight-percent?
15. A crystal of Nal has a density of 2.17 g/cm3. What is the atom density ofsodium in the crystal?
16. A concrete with a density of 2.35 g/cm3 has a hydrogen content of 0.0085weight fraction. What is the atom density of hydrogen in the concrete?
17. How much larger in diameter is a uranium atom compared to an iron atom?
18. By inspecting the chart of the nuclides, determine which element has the moststable isotopes?
19. Find an internet site where the isotopic abundances of mercury may be found.
20. The earth has a radius of about 6.35 x 106 m and a mass of 5.98 x 1024 kg.What would be the radius if the earth had the same mass density as matter ina nucleus?
Copyright 2002 by Marcel Dekker, Inc. All Rights Reserved.
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INTRODUCTION TO NUCLEAR ENGINEERING Example 1.1
Problem: What is the atomic weight of boron?
Solution: From Table A.4, we find that naturally occurringboron (chemical symbol B) consists of two stable isotopes 10Band 11B with isotopic abundances of 19.9 and 80.1 atom-percentrespectively. From Appendix B the atomic weight of 10B and 11Bare found to be 10.012937 and 11.009306, respectively. Thenfrom Eq. (1.2) we find:
γ10 0.199:= Isotopic abundance of 10B, Table A.4
γ11 0.801:= Isotopic abundance of 11B, Table A.4
A10 10.012937:= Atomic weight of isotope 10B, Appendix B.1
A11 11.009306:= Atomic weight of isotope 11B, Appendix B.1
AB γ10 A10⋅ γ11 A11⋅+:= Atomic weight of boron, B, calculated fromEq. (1.2)
AB 10.81103=
This value agrees with the tabulated value AB = 10.811 as listedin Tables A.2 and A.3!
This concludes the problem solution for Example Problem 1.1!
[Ex_1_1.xmcd]
INTRODUCTION TO NUCLEAR ENGINEERING Example 1.2
Problem: How many atoms of 10B are there in 5 grams of boron?
Solution: From Table A.3, the atomic weight of elemental boron(chemical symbol B) is AB = 10.811. The 5 gram sample of boronequal m/AB moles of boron, and since each mole contains Naatoms, the number of boron atoms is:
m 5.0:= grams, Mass of elemental boron
Na 6.022 1023⋅:= atoms/mole, Avogadro's number
AB 10.811:= g/mol, Atomic weight of boron, B
NBm Na⋅
AB:= atoms, Total number of atoms of B there
are in 5 grams of boron
NB 2.785 1023×=
From Table A.4, the isotopic abundance of 10B in elementalboron is found to be 19.9%. The number N10 of
10B atoms in thesample is, therefore:
γ10 0.199:= Isotopic abundance of 10B, TableA.4
N10 NB γ10⋅:= atoms, Number of atoms of 10B in sample
N10 5.542 1022×=
This concludes the problem solution for Example Problem 1.2!
[Ex_1_2.xmcd]
INTRODUCTION TO NUCLEAR ENGINEERING Example 1.3
Problem: Estimate the mass of an atom of 238U.
Solution: From equation (1.3) we find:
AU238 238:= g/mol, Mass number of 238U
Na 6.022 1023⋅:= atoms/mole, Avogadro's number
MassU238AU238
Na:= g/atom, Estimate of mass of a single atom
of 238U
MassU238 395.2175357024245 10 24−×=
From Appendix B.1,the mass of 238U is found to be 238.050782 u,which numerically equals its gram atomic weight A. Then amore precise value for the mass of an atom of 238U is,therefore:
AWU238 238.050782:= g/mol, Atomic weight of 238U
N2a 6.0221420 1023⋅:= atoms/mole, Avogadro's number
Mass2U238AWU238
N2a:= g/atom, Estimate of mass of a single atom
of 238U
Mass2U238 395.29254208884487 10 24−×=
Note that approximating the atomic weight with the mass numberproduces a negligible difference.
This concludes the problem solution for Example Problem 1.3!
[Ex_1_3.xmcd]
INTRODUCTION TO NUCLEAR ENGINEERING Example 1.4
Problem: What the hydrogen atom density in water?
Solution: First, the molecular weight of water is:
Na 6.0221420 1023⋅:= atoms/mole, Avogadro's number
NH2OρH2O Na⋅
AH2O:= molecules/cm3, Molecular density of H2O
NH2O 33.45634444444444 1021×=
Now the hydrogen atom density simply becomes the number ofhydrogen atoms per molecule times the molecular density of water.Stated in another fashion, for every molecule of water, there mustbe twice as many atoms of hydrogen! Therefore, the hydrogen atomdensity in water becomes:
NH 2 NH2O⋅:= atoms/cm3, Atom density of H inH2O
NH 6.691268888888888 1022×=
This concludes the problem solution for Example Problem 1.4!
[Ex_1_4.xmcd]
5 Aug 2006
ERRATA FOR
FUNDAMENTALS OF NUCLEARSCIENCE AND ENGINEERING
J. Kenneth Shultis and Richard E. FawMarcel Dekker, New York, 2002.
ISBN 0-8247-0834-2
NOTE: Many errors have been corrected in the second printing. Those discover after the second printing are indicatedby an *.
Location (Discoverer) As Is Change to
p. 4, Table 1.4, item 5 solidis solidus
p. 5, line 3 from bot. (Stewart) New URL: http://www.almaden.ibm.com/vis/stm/gallery.html
p. 8, Sec. 1.2.2, line 1 one neutral one-twelfth of a neutral
p. 8, Sec 1.2.2, line 3 one atom one-twelfth of an atom
p. 9, Ex. 1.1, line 3 (Vanmeter) abundance of 19.1 abundance of 19.9
p. 9, first line last paragraph ...by the mass of... ... by one-twelth the mass of ...
p. 11, Ex. 1.4, line 2 (McNutt) 2AH + 2AO 2AH + AO
p. 12, 3rd line (Stewart) Except for hydrogen...2.5×10−8 cm. Almost all atoms with Z > 10 haveradii between 1 and 2 × 10−8 cm.
*p. 12, last line 200 m in diameter 200 m in radius
p. 15, Problem 17 (Stewart) atom (twice) nulceus (twice)
p. 17, Last line of Example 2.1 3.12 × 10−9 3.13 × 10−10
*p. 27, 5th line of text recoil election recoil electron
*p. 44, Table 22, He line He 2 1 He 2 2
*p. 54, 2 lines above last para-graph (Stewart)
RH = μee4/(8εoh
2) RH = μee4/(8ε2och
3)
*p. 58, Fig. 3.8 caption mass density number density
*p. 111, Sec. 5.6.1, line 9 MeV. Tritium keV. Tritium
p. 126, last two lines (Bennion)√
Ex
√Ey (twice)
*p. 128, 2nd last caption line speeds. in the speeds in the
(cont.)
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nucleus
Location (Discoverer) As Is Change to
p. 136, seventh line (Holbert) average kinetic energy most probable kinetic energy
*p. 139, Eq. (6.33) n +23592U
10n + 235
92U
*p. 141, Eq. (6.37) 99m43Tc∗
β−−→6.01 h
99m43Tc∗
γ−→6.01 h
*p. 142, line 2 236U 235U
*p. 145, Table 6.4 Tw and Ew switch the heading labels Tw and Ew
p. 149, 6 lines from bottom(Holbert)
Eav = kT Eav = (3/2)kT
*p. 150, line 9 MPa Pa
p. 164, first line (Duteau) particles cm−2 particles cm−2s−1
p. 165, Eq. (7.8) (Duteau) remove the term ... μt
∫ ∞0
x p(x) dx = ...
*p. 169, line 4 losses loses
*p. 171, 6 lines above Eq. (7.23) source of that source that
*p. 174, lines 1 and 5 5 Ci 500 Ci
*p. 187, Ex. 7.5, last line 2.657 2.609
p. 197, Example 7.7 (Mentzer) 10−2.5839+1.3767x+.. = 0.00707 g/cm2 10−2.5814+1.3767x+.. = 0.00711 g/cm2
p. 197, line after above correction Rp(2 MeV) = 0.00707 cm. Rp(2 MeV) = 0.00711 cm.
*p. 198, lines 4 and 5 The ranges ... 7.18 Figs. 7.17 and 7.18 demonstrate theresidual energy after a fission frag-ment passes through a mass thick-ness ρR of different materials. Thex-axis intercept is the range of thefragment.
*p. 198, Caption of Figs. 7.17 &7.18, lines 3 & 4
distance x ... xρ distance R into various materials.Delete last sentence
*p. 200, Prob. 10, 2nd line tank is make tank is made
p. 222, Prob. 5 230 μs 230 ns
p. 229, Ex. 9.1, last 2 equations mGy/h μGy/h
*p. 248, 4th line of Section 9.6.2 an sudden accidental a sudden accidental
p. 250, Table 9.13, 2nd block to 0.1 mGy (100 mrad) to 1 mGy (100 mrad)
*p 254, Table 9.14, heading 3rdcol.
per ECC per annual ECC
p. 260, Prob. 2, 2nd line (Holbert) ... frequency of 0.941 ... ... frequency of 0.849 ...
*p. 268, Ex. 10.1, line 2 atom ratio NU/NC atom ratio NC/NU
*p. 268, Ex. 10.1, line 5 Appendix C.2 Appendix C.1 and Table 10.1
The world-wide web is a valuable but dynamic resource with new sites being created and old ones being shut down.Site web pages are also constantly being redesigned and addresses changed. Many of the web addresses on pages 13and 14 have changed.
Section 1.3, last line: The address for the chart of the nuclides is now http://www.chartofthenuclides.com .
Section 1.3.1: Everything past the first paragraph should be replaced with the following:
The following site, in particular, has a large number of links to the major nuclear and atomic data repositories inthe world.
http://www.nndc.bnl.gov/usndp/usndp-subject.html
The following sites offer large compilations of fundamental nuclear and atomic data as well as links to other datasites.
The sites below contain much information about nuclear technology and other related topics. Many are home pagesfor various governmental agencies and some are sites offering useful links, software, reports, and other pertinentinformation.
