Best Known Values for Physical Constants

There is an uncertainty in the last digit, typically of 1 to 7 parts.

speed of light, c 299 792 458 m/s (exact) gravitational constant, G 6.672 6 ⫻ 10^⫺11N ⭈ m²⭈kg^⫺2 Planck’s constant, h 6.626 068 76 ⫻ 10^⫺34J ⭈ s Boltzmann constant, k_B 1.380 650 3 ⫻ 10^⫺23J ⭈ K^⫺1 Stefan-Boltzmann constant, ␴ 5.670 400 ⫻ 10^⫺8W ⭈ m^⫺2⭈K^⫺4 Rydberg constant, R 10 973 731.568 549 m^⫺1 fine-structure constant, ␣ 1/137.035 989

Bohr radius, a₀ 5.291 772 083 ⫻ 10^⫺11m Avogadro’s number, N_A 6.022 141 99 ⫻ 10²³mol^⫺1 mass of neutron, m_n 1.674 927 16 ⫻ 10^⫺27kg

939.565 330 MeV/c² mass of proton, m_p 1.672 621 58 ⫻ 10^⫺27kg

938.271 998 MeV/c² mass of electron, m_e 9.109 381 88 ⫻ 10^⫺31kg

0.510 998 902 MeV/c² elementary charge, e 1.602 176 462 ⫻ 10^⫺19C permeability of vacuum, ␮₀ 4␲⫻10^⫺7N/A²(exact)

12.566 370 6 ⫻ 10^⫺7N/A² permittivity of vacuum, ⑀₀ 1/␮_0c²_C²/N ⭈ m²(exact)

8.854 187 817 ⫻ 10^⫺12C²/N ⭈ m² Coulomb constant, k 1/(4␲⑀₀) (exact)

8.987 551 78 ⫻ 10⁹N ⭈ m²/C² Bohr magneton, ␮_B 9.274 008 99 ⫻ 10^⫺24J/T

5.788 381 749 ⫻ 10^⫺5eV/T Nuclear magneton, ␮_n 5.050 783 17 ⫻ 10^⫺27J/T

3.152 451 238 ⫻ 10^⫺8eV/T Atomic mass unit, u 931.494 013 MeV/c²

1.660 538 73 ⫻ 10^⫺27kg Values based on 1998 CODATA recommended values.

Best Known Values for Physical Constants

APPENDIX A

1 u 931.494 013 MeV/c² 1.660 538 73
10^27kg

Percent Abundance,

Atomic Mass or Decay

Number Number Atomic Mode (if Half-Life

Z Element Symbol A Mass** (u) radioactive)^† (if radioactive)

0 (Neutron) n 1 1.008665 ^ 10.6 min

1 Hydrogen H 1 1.007825 99.985

Deuterium D 2 2.014102 0.015

Tritium T 3 3.016049 ^ 12.33 yr

2 Helium He 3 3.016029 0.00014

4 4.002603 ⬇100

3 Lithium Li 6 6.015122 7.5

7 7.016004 92.5

4 Beryllium Be 7 7.016929 EC,  53.3 days

8 8.005305 2 6.7
10^17s

9 9.012182 100

5 Boron B 10 10.012937 19.8

11 11.009306 80.2

6 Carbon C 11 11.011433 , EC 20.4 min

12 12.000000 98.89

13 13.003355 1.11

14 14.003242 ^ 5730 yr

7 Nitrogen N 13 13.005739  9.96 min

14 14.003074 99.63

15 15.000109 0.37

8 Oxygen O 15 15.003066 , EC 122 s

16 15.994915 99.76

18 17.999160 0.204

9 Fluorine F 19 18.998403 100

10 Neon Ne 20 19.992440 90.51

22 21.991386 9.22

11 Sodium Na 22 21.994437 , EC,  2.602 yr

23 22.989770 100

24 23.990964 ^,  15.0 h

12 Magnesium Mg 24 23.985042 78.99

13 Aluminum Al 27 26.981538 100

14 Silicon Si 28 27.976926 92.23 2.62 h

31 30.975363 ^, 

15 Phosphorus P 31 30.973761 100

32 31.973907 ^ 14.28 days

Percent Abundance,

Atomic Mass or Decay

Number Number Atomic Mode (if Half-Life

Z Element Symbol A Mass** (u) radioactive)^† (if radioactive)

16 Sulfur S 32 31.972071 95.0

35 34.969032 ^ 87.4 days

17 Chlorine Cl 35 34.968853 75.77

37 36.965903

18 Argon Ar 40 39.962383 99.60

19 Potassium K 39 38.963707 93.26

40 39.963999 ^, EC, ,  1.28
10⁹yr

20 Calcium Ca 40 39.962591 96.94

21 Scandium Sc 45 44.955910 100

22 Titanium Ti 48 47.947947 73.7

23 Vanadium V 51 50.943964 99.75

24 Chromium Cr 52 51.940512 83.79

25 Manganese Mn 55 54.938049 100

26 Iron Fe 56 55.934942 91.8

27 Cobalt Co 59 58.933200 100

60 59.933822 ^,  5.271 yr

28 Nickel Ni 58 57.935348 68.3

60 59.930790 26.1

64 63.927969 0.91

29 Copper Cu 63 62.929601 69.2

64 63.929766 ^,  12.7 h

65 64.927794 30.8

30 Zinc Zn 64 63.929146 48.6

66 65.926036 27.9

31 Gallium Ga 69 68.925581 60.1

32 Germanium Ge 72 71.922076 27.4

74 73.921178 36.5

33 Arsenic As 75 74.921597 100

34 Selenium Se 80 79.916522 49.8

35 Bromine Br 79 78.918338 50.69

36 Krypton Kr 84 83.911508 57.0

89 88.917563 ^ 3.2 min

37 Rubidium Rb 85 84.911792 72.17

38 Strontium Sr 86 85.909265 9.8

88 87.905617 82.6 28.8 yr

90 89.907738 ^

39 Yttrium Y 89 88.905849 100

40 Zirconium Zr 90 89.904702 51.5

41 Niobium Nb 93 92.906376 100

42 Molybdenum Mo 98 97.905407 24.1

43 Technetium Te 97 96.906364 2.6
10⁶yr

98 97.907215 ^,  4.2
10⁶yr

44 Ruthenium Ru 102 101.904349 31.6

45 Rhodium Rh 103 102.905504 100

46 Palladium Pd 106 105.903484 27.3

47 Silver Ag 107 106.905093 51.83

109 108.904756 48.17

48 Cadmium Cd 114 113.903359 28.7

49 Indium In 115 114.903879 95.7; ^ 5.1
10¹⁴yr

APPENDIX B A.3

50 Tin Sn 120 119.902199 32.4

51 Antimony Sb 121 120.903822 57.3

52 Tellurium Te 130 129.906223 34.5; ^ 2
10²¹yr

53 Iodine I 127 126.904468 100

131 130.906118 ^,  8.04 days

54 Xenon Xe 132 131.904155 26.9

136 135.907220 8.9

55 Cesium Cs 133 132.905447 100

56 Barium Ba 137 136.905822 11.2

138 137.905242 71.7

144 143.922845 ^ 11.9 s

57 Lanthanum La 139 138.906349 99.911

58 Cerium Ce 140 139.905435 88.5

59 Praseodymium Pr 141 140.907648 100

60 Neodymium Nd 142 141.907719 27.2

61 Promethium Pm 145 144.912743 EC, , ^ 17.7 yr

146 145.914708 5.53 yr

62 Samarium Sm 152 151.919729 26.6

63 Europium Eu 153 152.921227 52.1

64 Gadolinium Gd 158 157.924101 24.8

65 Terbium Tb 159 158.925343 100

66 Dysprosium Dy 164 163.929171 28.1

67 Holmium Ho 165 164.930319 100

68 Erbium Er 166 165.930290 33.4

69 Thulium Tm 169 168.934211 100

70 Ytterbium Yb 174 173.938858 31.6

71 Lutecium Lu 175 174.940768 97.39

72 Hafnium Hf 180 179.946549 35.2

73 Tantalum Ta 181 180.947996 99.988

74 Tungsten W 184 183.950932 30.7

(wolfram)

75 Rhenium Re 187 186.955750 62.60, ^ 4
10¹⁰yr

76 Osmium Os 191 190.960928 ^,  15.4 days

192 191.961479 41.0

77 Iridium Ir 191 190.960591 37.3

193 192.962923 62.7

78 Platinum Pt 195 194.964774 33.8

79 Gold Au 197 196.966551 100

80 Mercury Hg 202 201.970625 29.8

81 Thallium Tl 205 204.974412 70.5

82 Lead Pb 203 202.973375 ^ 51.9 h

204 203.973028 ^, 1.48 1.4
10¹⁷yr

206 205.974449 24.1

207 206.975880 22.1

208 207.976636 52.3 22.3 yr

210 209.984163 , ^,  36.1 min 211 210.988735 ^, 

212 211.991871 ^,  10.64 h

214 213.999798 ^,  26.8 min

Percent Abundance,

Atomic Mass or Decay

Number Number Atomic Mode (if Half-Life

Z Element Symbol A Mass** (u) radioactive)^† (if radioactive)

83 Bismuth Bi 209 208.980384 100

211 210.987258 , ^,  2.15 min

84 Polonium Po 207 206.981570  5.8 h

208 207.981222  2.9 yr

209 208.982404 ,  102 yr

210 209.982848 ,  138.38 days

214 213.995176  164 s

218 218.008966 3.11 min

85 Astatine At 210 209.987131  8.1 h

211 210.987470 EC,  7.21 h

86 Radon Rn 211 210.990575 ,  14.6 h

220 220.011368 ,  55.6 s

222 222.017570 ,  3.8235 days

87 Francium Fr 223 223.019731 , ^,  22.0 min

88 Radium Ra 223 223.018501  11.43 d

224 224.020186  3.66 d

225 225.023604 ^ 14.8 days

226 226.025402 ,  1.599
10³yr

228 228.031064 ^ 5.75 yr

89 Actinium Ac 227 227.027747 , ^,  21.773 yr

90 Thorium Th 228 228.028715 ,  1.91 yr

230 230.033128 ,  7.54
10⁴yr

232 232.038051 100, ,  1.40
10¹⁰yr

91 Protactinium Pa 231 231.035880 ,  3.25
10⁴yr

233 233.040242 ^ 27.0 days

92 Uranium U 231 231.036264 EC 4.2 days

232 232.037129 ,  68.9 yr

233 233.039628 ,  1.592
10⁵yr

234 234.040947 0.006, ,  2.45
10⁵yr 235 235.043924 0.72; ,  7.038
10⁸yr

236 236.045563 ,  2.342
10⁷yr

238 238.050785 99.275; ,  4.468
10⁹yr

239 239.054289 ^ 23.5 min

93 Neptunium Np 237 237.048168  2.14
10⁶yr

239 239.052933 ^,  2.36 days

94 Plutonium Pu 239 239.052158 ,  2.41
10⁴yr

242 242.058737  3.75
10⁵yr

244 244.064198  8.00
10⁷yr

95 Americium Am 241 241.056824  432.7 yr

243 243.061372 ,  7.37
10³yr

96 Curium Cm 243 243.0614 29.1 yr

244 244.0627 18.1 yr

245 245.0655 8.48
10³yr

246 246.0672 4.76
10³yr

247 247.070346  15.6
10⁶yr

248 248.072343  3.48
10⁵yr

97 Berkelium Bk 247 247.070298 ,  1.4
10³yr

248 248.073107  9 yr

249 249.0750 3.26
10²yr

APPENDIX B A.5

98 Californium Cf 249 249.074845 ␣ 351 yr

251 251.079579 ␣ 9.0 ⫻ 10²yr

99 Einsteinium Es 252 252.082945 ␣, ␤^⫹ 472 days

254 254.088019 ␣, ␤^⫺, ␥ 276 days

100 Fermium Fm 253 253.085173 EC, ␣, ␥ 3.0 days

257 257.095099 ␣ 100 days

101 Mendelevium Md 258 258.098572 ␣ 51.5 days

260 260.1037 27.8 days

102 Nobelium No 255 255.093258 ␣, ␤^⫹ 3.1 min

259 259.100932 EC, ␣ 58 min

103 Lawrencium Lr 260 260.105314 EC, ␣ 180 s

104 Rutherfordium Rf 261 261.108685 EC, ␣ 65 s

105 Dubnium Db 262 262.113763 EC, ␣ 34 s

106 Seaborgium Sg 266 266.121955 ␣ ~21 s

107 Bohrium Bh 262 262.123028 ␣ 102 ms

264 264.124746 ␣ 0.44 sec

108 Hassium Hs 269 269.134086 ␣ 9 s

277 16.5 min

109 Meitnerium Mt 266 266.137950 ␣ 0.8 ms

268 268.138809 ␣ 70 ms

110 Darmstadtium Ds 271 271.146081 ␣ 1.1 ms

111 Unununium‡ Uuu 272 272.1535 1.5 ⫻ 10^⫺3s

112 Ununbium‡ Uub 285 15.4 min

114 Ununquadium‡ Uuq 289 30.4 s

116 Ununhexium‡ Uuh 289 0.60 ⫻ 10^⫺3s

*Data are taken from Chart of the Nuclides, 12th ed., General Electric, 1977, from C. M. Lederer and V. S. Shirley, eds., Table of Isotopes, 7th ed., John Wiley & Sons, Inc., New York, 1979, and from G. Audi and H. Wapstra, “The 1993 Atomic Mass Evaluation,” Nuclear Physics A565, 1, 1993, the International Union of Pure and Applied Chemistry (IUPAC), and Nuclear Wallet Cards on the Web at http://www.nndc.

bnl.gov/wallet.

**The masses given are those for the neutral atom, including the Z electrons.

†The abbreviation EC stands for “electron capture.”

‡Elements 111, 112, 114, and 116 have not yet been named. The IUPAC provisional names are shown.