Appendixes Appendix I Physical Constants and Conversion Factors Numerical values for the constants are from B. N. Taylor, W. H. Parker, and D. N. Langenberg, Revs. Mod. Phys., 41, 375 (1969). Units are quoted in mksa (Systeme International) and in cgs. Physical Quantity Symbol Value Units (51) Units (cgs) I. Speed of light c 2.9979250 108 meters sec-I 10 10 cm sec-I 2. Electron charge e 1.6021918 10-19 C 10-20 emu 4.803250 10-10 esu 3. Planck's constant h 6.6261965 10-34 joule sec 10-27 erg sec n = h/27T 1.05459198 10-34 joule sec I 0-27 erg sec 4. Avogadro's number No 6.022169 1026 kmole-' 10 23 mole-I 5. Electron rest mass me 9.109559 10-31 kg 10-28 gm 0.5110041 MeV 6. Proton rest mass mp 1.672614 10-27 kg 10-24 gm 938.2592 MeV 7. Neutron rest mass mn 1.674920 10-27 kg 10-24 gm 939.5528 MeV 8. Faraday's constant F 9.648671 107 coul kmole-' 10 3 emu mole-I 2.892599 1014 esu mole-I 9. Gas constant R 8.31434 103 joule kmole-' K-' 10 7 erg mole-I K-I 10. Boltzmann's constant k 1.380623 10-23 joule K-I 10-16 erg K-' II. Gravitational constant G 6.6732 IO- llnewt meter2 kgm-2 10-8 dyne cm 2 gm-2 Clusters of Constants In many atomic and nuclear calculations the above constants appear in clusters, the evaluation of which can become tedious. We provide here a list of some of the more frequently encountered combinations. The serious student is urged to be­ come familiar with the clusters listed here so that he will recognize them when they occur in a problem and use them in preference to looking up the constants separately, followed by several multiplications or divisions. 649 650 Appendix I In these clusters the symbols in brackets apply for calculations in mksa units. For cgs the symbols in parentheses are correct if e is in esu. Physical Quantity Symbol Value Units (Sf) Units (cgs) 1. Fine-structure a = [tLt,c 2/41T] (eWtc) 7.297351 10-3 10-3 constant a-I 137.03602 2. Ratio of proton mass to mp/me 1836.109 electron mass 3. Electron charge-to- elm, 1.7588029 lO" coul kg- I 107 emu gm-I mass ratio 4. Rydberg's constant [tLt,c 2/41T F (mee4/41r1'1"C) 1.09737312 107 meter-I 105 cm-I 5. nc 1.9732891 lO-ll MeV cm 6. Bohr radius ao [tLt,c2/41T]-1 (n2/mee2) 5.2917716 10-ll meter 10-9 cm 7. Classical electron [tLt,c 2/41T] (e 2/ mec2) 2.817939 10-15 meter 10-13 cm radius 8. Compton wave- length of the h/mec 2.4263097 10-12 meter 10-10 em electron 9. Compton wave- length of the h/mpc 1.3214410 10-15 meter 10-13 em proton 10. Compton wave- length of the h/mnc 1.3196218 10-15 meter 10-13 em neutron II. Bohr magneton [c] (en/2m eC) 9.274097 10-24 jouleltesla 10-21 erg/gauss 12. Nuclear magneton [c) (eI1/2mpc) 5.050952 10-27 joule/tesla 10-24 erg/ gauss Conversion Factors 1 atomic mass unit (12C = 12) = 1.660531 x 10-27 kg = 1.660531 X 10-24 gm = 931.4812 MeV 1 hertz = 1 cycle seC 1 1 tesla = 104 gauss 1 eV = 1.6021918 x 10-19 joule = 1.6021918 x 10-12 erg 1 kg = 5.609538 X 1029 MeV 1 coulomb = 10-1 emu = c x 10-1 esu 1 volt = 108 emu = 108 c-1 esu 1/47TEo = J-toc 2/47T J-to/47T = 10-7 henry meter-1 300K = 410 eV 1 year = 7T X 107 sec 1 torr = 1 mm of Hg pressure The Greek Alphabet Lower-Case Letter Capital Letter Name of Letter a A alpha f3 B beta 'Y r gamma 0 ~ delta E E epsilon l; Z zeta 'Y/ H eta () 0 theta iota K K kappa A A lambda J.t M mu v N nu g - xi 0 0 omicron 7T IT pi p P rho as ~ sigma T T tau v Y upsilon cf> <I> phi X X chi 1/1 'I' psi w n omega 651 Appendix II Atomic Weights of the Elements Atomic Atomic Atomic Weight Atomic Weight Symbol Number (amu) Symbol Number (amu) Actinium Ac 89 Germanium Ge 32 72.5 9 Aluminum AI 13 26.9815" Gold Au 79 196.9665" Americium Am 95 Hafnium Hf 72 178.49 Antimony Sb 51 121.75 Helium He 2 4.00260b Argon Ar 18 39.94.b., Holmium Ho 67 164.9303" b Arsenic As 33 74.9216" Hydrogen H 1.0080 •c Astatine At 85 Indium In 49 114.82 Barium Ba 56 137.34 Iodine I 53 126.9045" Berkelium Bk 97 Iridium Ir 77 192.22 Beryllium Be 4 9.01218" Iron Fe 26 55.847 Bismuth Bi 83 208.9806" Krypton Kr 36 83.80 b Boron B 5 10.8F Lanthanium La 57 138.9055 Bromine Br 35 79.904 Lawrencium Lr 103 Cadmium Cd 48 112.40 Lead Pb 82 207.2' Calcium Ca 20 40.08 Lithium Li 3 6.941' Californium Cf 98 Lutetium Lu 71 174.97 Carbon C 6 12.011 b,c Magnesium Mg 12 24.305 Cerium Ce 58 140.12 Manganese Mn 25 54.9380" Cesium Cs 55 132.9055" Mendelevium Md 101 Chlorine CI 17 35.453 Mercury Hg 80 200.59 Chromium Cr 24 51.996 Molybdenum Mo 42 95.94 Cobalt Co 27 58.9332" Neodymium Nd 60 144.24 c Copper Cu 29 63.546 Neon Ne 10 20.179 Curium Cm 96 Neptunium Np 93 237.0482" Dysprosium Dy 66 162.50 Nickel Ni 28 58.71 Einsteinium Es 99 Niobium Nb 41 92.9064" Erbium Er 68 167.26 Nitrogen N 7 14.0067b Europium Eu 63 151.96 Nobelium No 102 Fermium Fm 100 Osmium Os 76 190.2 Fluorine F 9 18.9984" O_xygen 0 8 15.999/'c Francium Fr 87 Palladium Pd 46 106.4 Gadolinium Gd 64 157.25 Phosphorus P 15 30.9738" Gallium Ga 31 69.72 Platinum Pt 78 195.0. 652 Atomic Weights of the Elements 653 Atomic Atomic Atomic Weight Atomic Weight Symbol Number (({IIlIl) Symbol Number (amu) Plutonium Pu 94 Sulfur S 16 32.06c Polonium Po 84 Tantalum Ta 73 180.947/ Potassium K 19 39.102 Technetium Tc 43 98.9062d Praseodymium Pr 59 140.0977" Tellurium Te 52 127.60 Promethium Pm 61 Terbium Tb 65 158.9254" Protactinium Pa 91 231.0359- Thallium TI 81 204.3, Radium Ra 88 226.0254"·d Thorium Th 90 232.0381" Radon Rn 86 Thulium Tm 69 168.9342" Rhenium Re 75 186.2 Tin Sn 50 118.69 Rhodium Rh 45 102.9055" Titanium Ti 22 47.90 Rubidium Rb 37 85.4678 Tungsten W 74 183.85 Rutheium Ru 44 101.0, Uranium U 92 238.029b Samarium Sm 62 150.4 Vanadium V 23 50.941/ Scandium Sc 21 44.9559" Xenon Xe 54 131.30 Selenium Se 34 78.96 Ytterbium Yb 70 173.0. Silicon Si 14 28.086 c Yttrium Y 39 88.9059" Silver Ag 47 107.868 Zinc Zn 30 65.3, Sodium Na II 22.9898" Zirconium Zr 40 91.22 Strontium Sr 38 87.62 "Elements with no isotopes. These elements exist as one type of atom only. b Elements with one predominant isotope (around 99 to 100% one isotope). c Elements for which the variation in isotopic abundance in earth samples limits the precision of the atomic weight. d Most commonly available isotope (radioactive). » PERIODIC CHART OF THE ELEMENTS 1"0 "0 CD I ~ I ,, ~L :::l II __ :: ___ .-'L-__- ~ I! ;J c.. i1f-~""'-.-"1 -- METALS X 1. II ~ ~ lliIJ~1J[1 _J~ - ~ _ ___ ___ _ E. Ifl~ ~ 1 - ~ r~~ T_ti~ _ 1. ).11.11 Ik --':J .: ~ll 36 3J "-;- l As Se Sr i Kr g -,' - J~] ~ ~Jl-~ j ~~ ]l. fl~[;J~IJL "Il- ~-r : ' = c.w ,_rw. ........ __ 11• ..- _ I ""' !I """"" - _ _ ~ '! """' : ~ - .... ~_~. ~ ,J ~ - ~ L,T"':":'"JL.~ ~ r 40 41 42 43 44 45 46 47 48 49 50 . 61 ___62 63 64 37" lr - 38-ll - 39 --- l Rb , Sr Y I r:lmr!-~G(1Jlf II· -r- -- - , Te "; I Jl X. I Zr : Nb ":' : ,!!. !! J I· ~!~tT~:'~~~ ;=-_ ~ ~~ ~ ~ - --. II 55 II 56 72 73 75 8r n-;78 l lf "- 80 81 ';~- 82 83 84 se 11 1i7-71 'T- ~i- 7 -;r --ii I 11-74- 11 lB5'lr- c. II Ba Hf :1 Ta W II Ra Os Ir ' Pt Au r He TI . Pb Bi II Po At Rn I ~ tall II ..... ,. ...... ...... .... r..- ........ ~ 0.-. .... c.w I ........ "..... - 65 66 I 67 : 6B 69 Th Il & II ~ ~lJ;~ ~ ~ il ~ - -lr7 1 II 101 ~ ~~ ~ r7 Ir.----~:- 1 r Met ~ I ~ :...:.. c.ro.:!.. ~ I F~':' Appendix IV Table of Nuclear Properties We provide here a listing of a few of the properties of some of the more impor­ tant nuclides. We list Z (the atomic number), the chemical symbol for each element, and the mass number A. The mass excess is the amount of energy by which the mass of an atom exceeds an integer multiple of atomic mass units. In symbols (mass excess) = (atomic mass)c2 - 931.4812 A The numbers quoted here are from J.