Introduction to Nuclear Engineering - Lamarsh - Ch2 - Atomic & Nuclear Physics

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<p>2 AtomicandNuclearPhysics ...,.. .. ... ,.,.. . ..... ... .,. ... .. ..,. . . .. .... . ... . ... .,.., ,... . .. .. ... ,.... .. ... ,.,.. . .. . .. .., .. . .. Z. T FUNDAMENTALPARTICLES .. ,.,.. . . .,.......... .......... ,.. ......... ,.. ... . .. ... . .., .. .. ...... ,.. . . .. .. .,,.... .. ,. , ,... . .. ., ,.... ... .,. ..,. . ,.. .. .... .. . ,.. .. ... . ,.. .... .. . . ,. .. ... ... .,. ......... . barons. .. ,.. . ..,. ... ... . .... .... .. .,.. . ,... .,. . . ... .. .., ... .. . .... .. . .,.,.... ... . ....,,... .. ..,.... .. . .,... .., ... 5 b Atomi c and Nucl earPhysics Photon e Photon Figure 2.1The annihilation of a negatron and positron with the release of two photons.Chap.2 . ......,... .. .. . ...... ,... ., .,.... . ..... ,.. .. . ., . ..... ., . .., . .,.. . ... .,.., 1 Electron.. . ... . ..... H = 9.10954X 10-31 .,3 .. .. . .., e = 1.60219 10-19 ... .. . . ,,.... .,., . .,.. .., -e,. . .,., . ,.. .., +e..., . .. . . .,.. .., .. . ,.. . .. .. .,.. ..negatrons .. ., . .... . . . .... .. ... . .. . .. ..positrons, . .., . ... .. . ,, ...... . ,.. . .. . .,.. . . .. ..,,. .. . .. ...., . ,... ,....,. ... . . .. .... . ,2.1.... ,.. . .... .. electron annihilation, .. . ,... .. .,,. . . annihilation radiation. Proton... ,. ... . . .... H_ = 1.67265 10</p> <p> ., .. .. . ,.. .., ,.. . ..,... .., . . . .. .. .,.. .., ... .. . .. . .. ,.. .. .,.. . ... .,.., 'A discussion of quark theory may be found in several of the particle physics references at the end of this chapter. 2 According to the theory of relativity,the mass of a paricle is a function of its speed relative to the observer. In giving the masses of the fundamentalparicles,it is necessary to specify that the particle is at rest with respect to the observer-hence, the ter rest mass. Adiscussionof units,theirsymbols,andabbreviations, together with tablesof conversion factors, are found in AppendixIat the end of this book.Tabulations of fundamentalconstantsand nuclear data are given in Appendix I. Sec.2. 2Atomi c and Nucl ear Structure7Neutron.. ..... ... . .,., ., ... . ..... ,...., mn= .. </p> <p> ., ... ., ... .. ... . . . .. ,. ., .... .. . .. .. .... ... .,.. ,. .. . ..... .,.. .., . .. ... .. ..... . ,.. .. ... . . ..., ... .... Photon . . ... . .. . ,.. . ... ... .... . ,.. .. .... . .... .... .. ,..... .. . ..., ..,... ., ., .... . ... .. .,,.... .. .... ,....,.. ... ...,. .... . . .. .,, .. ,. .... .. ..,. .... . . . photon. ... . . ,. .. . . .... .. . .., ... ... . . ..... . ., . .,..., . .,,. c = .X .. Neutri no... . ... ,. .. . . .... .. . . .., .. .,,.. . . .,.. .. .. . . .. .. ,,..... ., .... . electron neutrinos .. electron antineutrinos) . .,.. . . .. ,.. .. ... . ... .,..,.. ,.,... . ....,... . ... .. . . .. ., . .., ,. .. ....Z.Z ATOMIC AND NUCLEAR STRUCTURE . . . . ... ... ... . . .., ..,.. .. ... .. .... .. . .. ..... ... . ..... .... .... , . ..,, ..., .,.. .. .. .... . .,.,.. .. ...... . ...,.. . . .... . . . atomic number. .. .. . ,.. . .,. . .. . . ..,. .... . . .. . ... .. . . .. ..., .. .. ,....., ...., .. . .... .. .. . .,... ... ...... .. ., . .... ... ......, .,,. . ... . . ... . ... . ... . ... . .. . . .. ....... . . .... . .... .. . neutron number .. . . , N.. . ...nucleons-that . ,.. .. .... . . ..... ,... + N= A,.. A. . . atomic mass numbernucleon number. .. .... .,.... ... .. ... ,... ....,.. .. .... . . nuclides. ... .. . . , . ... .,.. .. .. .,. . .. . .. .... ... .. ..,., 8Atomi c and Nucl ear Physi csChap.2 .. ... .. = AZ)..... . .,.. .. .. .,,. (Z=.. . .., ,. .. .... </p> <p>. . . .,,. .. .. . ... .. . .. . ,. . . .... . . .. . deuteriumheavy hydrogen); </p> <p>. . . ... (Z = . .. ... .... ..... ,.. .. . .... .. . .,. ., Z . .... .. .. . ..., .. . . H,;. .. . . .. ... ... .. </p> <p>. ... .. ... . ... ...,.. . .. ........ ... Z . .. . .. A),. .... .. isotopes..,,..... ... . .. .,. </p> <p> (Z= =.. . .... .... radioactive) .,. </p> <p> .. </p> <p> (Z = = ... .. .,. .. . .. .... .. . . ... .. . .. . . ...., .., ... . ... ... ., . . .. . ,.. ..... .. .,.. ,.. .. . . ..... ... .. ...,....., .., .,,. ... . . ., . . . ., </p> <p> ..... . </p> <p> .... . .,.. .,. .. . ..... . ,.. . ,,.. .... .. ., ...... . ,.. . .. ,... .. ,..,.. ..... .. .. . ,... .,. . ,. . . ... .. a/o.Example 2.1 A glass of water is known to contain 6. 6 1 024 atoms of hydrogen. How many atoms of deuterium eH) are present? Solution.Accordingto Table .2 in AppendixII,theisotopicabundance of 2His 0. 01 5 a/o.The fraction of the hydrogen,which is 2H, is therefore1 .5 1 0-4The total number of2H atoms in the glass is then 1 . 5 1 0-4 6. 6 X1 024 =9. 9 1 020 [Ans. ] 2. 3ATOMIC AND MOLECULAR WEI GHT .. atomicweight.. .. . . .. . ..... ... .. .. . ..... ... </p> <p> .. . . .. . ... . .. .,.</p> <p> . .., ... ,.,. . .,..meZ). ..... ... .. . , AZ .. </p> <p>. ....... </p> <p>... . .. .,. AZ,M(AZ) ,. ,.. , A meZ) M(Z)=. X</p> <p> . m(.Sec.2. 3Atomi c andMol ecul arWei ght9 ..,,. .. .. .. ... ,., . .. ..., .. </p> <p>... ..,., . .. .. .. ... . .. .,. . . = .. . . . .. . .. ... .. . ... . .... ....,. .. .. .,.. .. . .. . .. . average .. .,.. ... ....Yi. . ., ..... . .. ,. .. .,.. .,. Mi, .. . .. .,.. .. . . . .. . ..... .. ... ..... ... </p> <p> .. . . . molecular weight. ... . ., . .... .. .,... .... ... .... .,,. ,.. ..... .. </p> <p> .. . ... .,. . . . .=Example 2.2 Using the data in the following table, compute the atomic weight of naturally occurring oxygen. IsotopeAbundance (a/o) 99. 759 0. 037 0. 2Solution.From Eq. (2. 2), it follows that Atomic weight 1 5. 99492 1 6. 9991 3 1 7.9991 6 M(O) =0. 01 [ye60)M(170) +y(I70)M(170) + yesO)MesO)] - 1 5.99938.[Ans ] ....,.... .. .. .. ... .,.. . .... .... ., ... ........... ., ... . gram atomicweight.. grammolecularweight. . .. . ..... ..... ...., . .... . ,... ,... ..... .,.. ..... ... ....... . .. . . mole. .... . ,.. .. .,.. .</p> <p> . ..,. ,.. ., . . ,.. . , .. . . .. .. .,. . . ... ..... .. . . . .. .. .,. . ,..... .. . ......... . . ..., ..... . . .... .,... .... ..... .... ..,,. .. . .,,.. .. ... .. .. .,..... .. . .... ..... ..... . .., . .. ..... .. </p> <p>T0 Atomi candNucl earPhysi csChap.2 .. . .... ... ...... . .. ,.. .. .. .. , ... ...... . .... .. Avogadro's law, .. . ......... . . . . . Avogadro's number. ... ... . . , NA .. . ,..NA =.... X</p> <p>.., .,. . .... ,...,. . ..... .., .. ....., .. . ,.. .</p> <p> ... . .... . , .. .... N A ..... .. . ..... .. . . </p> <p> = . = . </p> <p> , ... X .. .... . . .... .. . ..... . ......... ... . ...., .,.. ... . . atomic mass unit, ... ... ... . . .. . .. . ..... ... .. .. . ..., .. ,... ,.. ..., m </p> <p> . . ,., ,..,.,. ,.. ... = . X </p> <p>, = I /NA , = . X ,. . E. . . .. ... . ......, .. . ... . ...., ,... .. .,.. .. . ,... 40rdinarily a number of this type would be written as 6.0222045x However, in nuclear engineering problems, for reasons given in Chap. 3 (Example 3. 1 ), Avogadro's number should always be written as the numerical factor times1 024 Sec.2. 5Mass and Energy1 1Z.4 ATOMIC ANDNUCLEARRADI I.. .... ... ..... .. ... . .. . . . . ... . .. . , ... .., ...., .. . . . .... .. . . .. ., ,... .. .... .... ...... .. . ,.. , . ..., ... . . .... .. . ... . . .. ..,. .. ,.. ... .. ..., . . .,,..., . .... ......, .. 2 . . .. . ..... .. .... .. ...., .. .... .. .. . ..., . .., . . . . .. .... .. .. ... .. .... . . .. . . ... . ..., . ..., . .... ... ...,. ..... .. ... .... .. ...... . ... .... . .. . .. . ... ... ... . .,,.... . .... ..,.. . .,. .. . ... ,.. , . .., ... . = 1. 25fr A </p> <p>... . . . ... . .. A . . ... .... ... . .. . ... .. . .... .,. . ,,... .. ..... . ., ... . ... \. .... . ,,..A.... .. .... .. . . A / \.. . . ....... , .. .... . ..... .. ... ... ..,... .. ..,,.. .. .. . ...,. ,. ... .. ... . ... .., ... ., . .,... ... ,., .. .... .......,. ,.,.. ,,... Z.b MASS ANDENERGY .. ..., ....... . .,.., . .. .... .. .,, . ,.... .. .. .. . . ,... . ., ....... ,.. ,. .... ro... .. .....,, L,,,... . ,.. , ..... .... ... .. .. C . . .,,. ..., . ...... ,.. .. .. ..L = .X</p> <p> =. </p> <p>,. =. ,.. ..... ...... .... .,, .... . ... ....,.. .. 25.. ...... 12Atomi c and Nucl ear Physi csChap.2 .. ...,, .. . . .. . ... .,.., . . electron volt,. , . ... . . .. . ... . . .. .,,.. . ..... ..,. .. . ,... . ... . .. . ,... ..,. . .., , . ,.. ,.. .1 . = 1.60219 10-19 .. 1 . = 1. 60219 10-19 ,. . .,, ... ,.., ... . . . (106 . .. . .. (103 . Example 2.3 Calculate the rest-mass energy of the electron in MeV Solution.From Eq. (2.4), the rest-mass energy of the electron is mec2 -9. 1 095 1 0-28 (2.9979 1 01 0)2 -8. 1 871 1 0-7 ergs -8. 1 87 1 1 0-14 JOUle. Expressed in MeV this is 8. 1 87 1 1 0-14 joule- 1 . 6022 1 0-13 joule/MeV -0. 5 1 1 0 MeV. [Ans. ]Example 2.4 Compute the energy equivalent of the atomic mass unit. Solution.This can most easily be computed using the result of the previous example. Thus, since according to Section 2. 3,1amu- 1 . 6606 1 0-24g, it follows that 1 amu is equivalent to 1 . 6606 1 0-24 g/amu - 0. 5 1 1 0 MeV/electron -93 1 . 5 MeV.[Ans. ] 9. 1 095 1 0- g/electron ... . , . . .. . .... .... .... .. . . ..,. ... (2.5) .. Hg . . . .... .. v . . ., . ., (2.5),. .. .. H .. Hg .. v ,.. ... .. v .,,... c, H .... ... . .. total energy. ,. .. . . ..... .,, ,.. . .. .,, . ,.. , (2.6) Sec. 2. 5Mass and Energy13 .. m. .. ,.. . ., (2.5). .., . kinetic energyE . . .. .. . . .,, .. . ..... .,, ... . 2 1 moc 1 J1 v2jc2 (2.7) (2.8) .. .. . . . . . .,(2. 8) ...,.. . ,..(vjc)2 ..., . ... .. ... v&lt; c, . .. ..,... . . . . .. ..., .,...E . (2.9) ... . . ... ..... .,, . .... ......... .. ., (2.9) ..,.. ...., (2. 8) ., ... . .. .,, .,. . ., (2.9) . ... .,. .. . ..... .,, ... . ., (2. 9) . .. ,. (2. 1 0) . . ,.. .. ., (2.9) . ...., ... ..,... ,.,.. ,. v_ 0.2cE ::0. 02Erest(2. 1 1 ) .,...., 2.3,. ..... .,,.. . . 0.5 1 1. . ., (2. 1 1 ) , .. .. . ... ... ., (2. 8) ....... .. .. .,. ,. ... .. 0.02 0. 5 1 1. 0.01 0 . 1 0 . N .. ...,. .. .... ... .,.., ... .. .,. ,. ... ... . ....,.. ., (2. 8).. ., ... . . ..... ... . ... 1 ,000 . .. 0.02 . =20 . . ,. .... ., ... .. .,. . ...20 .. ,... . . . ... .,.., ,..... . .. .,,.... . ., (2.9). ... . ... .... . .. . ., (2. 9), . .., ..., ... . .. v = 1. 383 1 06J,(2. 1 2) .. v . . .. .. E . . .. .,,. ... .. . .,..,.. .. .,.(2. 8) .. (2.9) . .. .,,.. .. ... . .... ..., ., . .,,,,... ...... .. ,... ... . ..... .,, ... . ,,.. . 14Atomi c and Nucl ear Physi csChap.2 . kinetic energy . .,... ,..... ., .. . . ., ,. .. . . .,, . ,.. , ,. . .. ......, E = hv, . .. h. .... .... .. v . . ,..,. ..,. ... .... .. . ,.. .... .... ... ....,, .E . .,.. . . h. ,... .. 2. 6PARTICLE WAVELENGTHS ... ,. . . .. ... .. ,.. . ... ... .. .... ....,. .. ....,. .... .. . ,. ...., ..... p . hA =, . . |.. h. .,.. .... .... ,..... . ....p . ,.. , p = mv,.. .. m . . ..... ,. .. v . . ., ..... .,.p .... .. p= J.mg Eg.. E . . .. .,, ... .. .,... . .. . ., ... ,. ....,. .. h =. .mgL. ... ... . ... .... ... . ... .,.., ..., . .... ... .... ,.. . .., .,.... ... ....,. .X = .. .. A . . ... .. E . . .. .,,. ... . . . ... ... .....,. p, , ..., . ... ,.... . . ,., .. ... ,.. |= </p> <p>Etotal - Erest' c . Sec.2. 7 .. . Excited States and Radi ati on hc A = </p> <p>L,, L,1 5 (2.19) .. ...... ,.. . .... . . ,.. , ., (2.15),. .. , . .,... L}=c (2.20) . ... L. . .,,. ,. ... ., (2.20) . .. . ., (2.14), . .. . hc A- L(2.21) .., .... .... .. c . . .,,,. ... ,.. .., 1.240 10-6 A = L(2.22) .. A . . .. .. L . . . .,... (2.22). ..,... .. . . ,... . ....Z.1 EXCITEDSTATES AND RADIATION .. Z.. .. .. .. .. . .... .. . ... ... . ... .... .. . . ,., .. . . .. ... ....., .,. . ,... . ... . . . . .. (Z= 82),..... . . . ,... . ....K-electron. .. ,....., .. . . .. .. . . ionization, .. . .,.. ... . . .... .. . ionization energies. .. . ,... . . ... ... ,... .. . . ..,.. ...... .... .,, . . . . ... .. .. . ..., .. .. .. . . . ground state. ... . .. ,..... . .,, ... . ,.. .. .,,. .. . .. excited state.. energy level. .. ,.. .. .. . .... . ... .. ....,, , .. energy-level diagram, . . . .... . , 2.2.,,. .. .,.. .,, .. .,... .... . ... . . ... . .,, .. . . .. .. . .. . .. . .. ... ... . .. . .. ..,...., .,. ..... ... . . .,, .. . .. .., . .. ...., .... ,.. .. ... ... . .... .. . ,.. . . , Tb Atomi c andNuclearPhysi cs ..ss12.07 10.19 o Figure 2.2The energy levels of the hydrogen atom (not to scale). Chap.2 . .. .. .. .,, ,... .. . . .,.. . ... ..., ... . .,,. .. . . . . .. . 10. 1 9 . . ,2. 2) .,.. ,.. .. . ,.. .. .. .,,1 0. 1 9. . . . ., (2.22),.. ,.. ... . ....,./ = 1 .240X 1 0-6/ 1 0. 1 9=1 .21 7 1 0-7 . ..... ....,. . . . ... ,.. ..,. .,.. Example 2.5 A high-energy electron strikes a lead atom and ejects one of the K -electrons from the atom.Whatwavelength radiationisemittedwhenanouter electrondropsinto the vacancy? Solution.The ionization energy of the K -electron is 88 ke V, and so the atom minus this electron is actually in an excited state 88 ke V above the ground state. When the outer electron drops into theKposition,the resulting atom still lacks an electron, but now this is aouter, weaky bound electron. In its fnal state, therefore, the atom is excited by only 7. 38 eV, much less than its initial 88 keY Thus, the photon in this transition is emitted with an energy of slightly less than 88 keY. The corresponding wavelength is A - 1 . 240X1 0-6/8. 8 1 04 - 1 . 409 1 0-"m. [Ans. ]Such a photon is i n the x-ray region of the electromagnetic spectrum. This process, the ejection of an inner, tightly bound electron, followed by the transition of another electron, is one way in which x-rays are produced. .. .... . .. . . .. . ... .. ....,... ..., .. . .... . ...,. .. . . .. . . .. ..Sec.2. 7Exci ted StatesandRadi ati onT7. .. .. . ... . .., .. . . . .... .,, . ,.. .. .,. ., ,.. .. . .. ... . ... .. . ... ... . .... . , 2. 3</p> <p> .,...,.2.2 .. 2. 3 .... .. . .,.. . ... .. . .,. .. ... . ..., ,... ...... ..,. .. .... . .. ., . . 24 etc 22 20 18 16 14 I &gt;12 cc:U 10 8 6 4 2 Figure 2.3The energy levels of 0 carbon1 2. 18Atomi c and Nucl ear Physi csChap.2 ....,,. .. </p> <p>. .. . . ,.. ... . .. . .. . ... . .., .. .... . ... .., ... . .. . .., .. .. .. . ...... . ... .., .,. . ,., .. .. ..., .., . ,.. .. .. .,, ,... .. .. . .,.. .. .. .. ..... .,.,... . . .. .., . . .... . ...., ... ,. ... . .,.,... ,..., . . ..... .. ... ,... . . y-rays. .... . .. . .. .. .. . . ... .,, , ... .... . .. ,.. . ... .,,. .... . ... . .. .,,.. .... .. .. .. . . .. , . . .. .. .. .,, ,..... ... .... .. . .... .,,. . ... .... ... .,. .. .., .... . . .,.... ..... . ....,. . . . . . ,... . . ... .... . . , .. . .. ..... .... . ..,.. . , . ...... . .,. ,.... . . . ,.. ...... .... ... ,..., . .. .., . . Auger electrons. 2. 8NUCLEAR STABI LITY AND RADIOACTIVEDECAY ,. 2. 4 .... . ,. .... ... .. . .... .. .. ... .... . . ., .. .. ... .,. ,.... .. .. .. , 2.4 . .... .. . Segre chart. chart a/the nuclides. .. ,. ,. .. . . . .... ... ,.. . ... .. Z,. ... .. 20, .. . ... ,. ... . . , . ... .. .... . ....,. ..,. ... .. .. ... .... . ..... . ... ,. .., . .... ,. , .,....,. ,... . . .. . ,.., .., ,.. . . . , 2. 4 .. ., .. ......... .. ,.. ... .. ..,. ,.., . . ... ... ....</p>