Chapter 1 Fundamental Concepts The last half of the twentieth century was a time in which tremendous advances in science and technology revolutionized our entire way of life. Many new technolo- gies were invented and developed in this time period from basic laboratory research to widespread commercial application. Communication technology, genetic engi- neering, personal computers, medical diagnostics and therapy, bioengineering, and material sciences are just a few areas that were greatly affected. Nuclear science and engineering is another technology that has been transformed in 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 source of electrical power in many countries. Nuclear technology is widely used in medical imaging, diagnostics and therapy. Agriculture and many other industries make wide use of radioisotopes and other radiation sources. Finally, nuclear applications are found 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 interactions affect matter. In this book, we will describe sources of radiation, radiation inter- actions, and the results of such interactions. As the word "nuclear" suggests, we will address phenomena at a microscopic level, involving individual atoms and their constituent nuclei and electrons. The radiation we are concerned with is generally very penetrating and arises from physical processes at the atomic level. However, before we begin our exploration of the atomic world, it is necessary to introduce some basic fundamental atomic concepts, properties, nomenclature and units used to quantify the phenomena we will encounter. Such is the purpose of this introductory chapter. 1.1 Modern Units With only a few exceptions, units used in nuclear science and engineering are those defined by the SI system of metric units. This system is known as the "International System of Units" with the abbreviation SI taken from the French "Le Systeme International d'Unites." In this system, there are four categories of units: (1) base units of which there are seven, (2) derived units which are combinations of the base units, (3) supplementary units, and (4) temporary units which are in widespread Copyright 2002 by Marcel Dekker, Inc. All Rights Reserved.
Transcript
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
Copyright 2002 by Marcel Dekker, Inc. All Rights Reserved.
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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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
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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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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
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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.
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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
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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
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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.
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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.
