Constant List

CODATA RECOMMENDED VALUES OF THE FUNDAMENTAL PHYSICAL CONSTANTS: 2002 NIST SP 961 (Dec/2005) Values from: P. J. Mohr and B. N. Taylor, Rev. Mod. Phys. 77, 1 (2005). A more extensive listing of constants is available in the above references and on the NIST Physics Laboratory Web site physics.nist.gov/constants. The number in parenthesis is the one-standard-deviation uncertainty in the last two digits of the given value. Quantity

Symbol

speed of light in vacuum magnetic constant

c, c0 µ0

electric constant 1/µ0 c2 Newtonian constant of gravitation Planck constant in eV s h/2π in eV s elementary charge magnetic flux quantum h/2e Josephson constant 2e/h von Klitzing constant h/e2 = µ0 c/2α Bohr magneton e¯ h/2me in eV T−1 nuclear magneton e¯ h/2mp in eV T−1 fine-structure constant e2/4π0 h ¯c inverse fine-structure constant Rydberg constant α2 me c/2h

0 G h

energy equivalent in eV Bohr radius α/4πR∞ = 4π0 h ¯ 2/me e2 Hartree energy e2/4π0 a0 = 2R∞ hc = α2 me c2 in eV electron mass in u energy equivalent in MeV electron-muon mass ratio electron-proton mass ratio electron charge to mass quotient Compton wavelength h/me c λC /2π = αa0 = α2/4πR∞ classical electron radius α2 a0 Thomson cross section (8π/3)re2 electron magnetic moment to Bohr magneton ratio to nuclear magneton ratio electron magnetic moment anomaly |µe |/µB − 1 electron g-factor −2(1 + ae ) electron-proton magnetic moment ratio muon mass in u energy equivalent in MeV muon-electron mass ratio muon magnetic moment to Bohr magneton ratio to nuclear magneton ratio muon magnetic moment anomaly |µµ |/(e¯ h/2mµ ) − 1

Numerical value

m e c2 me /mµ me /mp −e/me λC λC re σe µe µe /µB µe /µN ae ge µe /µp mµ m µ c2 mµ /me µµ µµ /µB µµ /µN

299 792 458 (exact) 4π × 10−7 (exact) = 12.566 370 614... × 10−7 8.854 187 817... × 10−12 6.6742(10) × 10−11 6.626 0693(11) × 10−34 4.135 667 43(35) × 10−15 1.054 571 68(18) × 10−34 6.582 119 15(56) × 10−16 1.602 176 53(14) × 10−19 2.067 833 72(18) × 10−15 483 597.879(41) × 109 25 812.807 449(86) 927.400 949(80) × 10−26 5.788 381 804(39) × 10−5 5.050 783 43(43) × 10−27 3.152 451 259(21) × 10−8 7.297 352 568(24) × 10−3 137.035 999 11(46) 10 973 731.568 525(73) 3.289 841 960 360(22) × 1015 13.605 6923(12) 0.529 177 2108(18) × 10−10 4.359 744 17(75) × 10−18 27.211 3845(23) 9.109 3826(16) × 10−31 5.485 799 0945(24) × 10−4 0.510 998 918(44) 4.836 331 67(13) × 10−3 5.446 170 2173(25) × 10−4 −1.758 820 12(15) × 1011 2.426 310 238(16) × 10−12 386.159 2678(26) × 10−15 2.817 940 325(28) × 10−15 0.665 245 873(13) × 10−28 −928.476 412(80) × 10−26 −1.001 159 652 1859(38) −1838.281 971 07(85) 1.159 652 1859(38) × 10−3 −2.002 319 304 3718(75) −658.210 6862(66) 0.113 428 9264(30) 105.658 3692(94) 206.768 2838(54) −4.490 447 99(40) × 10−26 −4.841 970 45(13) × 10−3 −8.890 596 98(23)

aµ

1.165 919 81(62) × 10−3

h ¯ e Φ0 KJ RK µB µN α α−1 R∞ R∞ c R∞ hc a0 Eh me

Unit

Quantity

m s−1 N A−2 N A−2 F m−1 m3 kg−1 s−2 Js eV s Js eV s C Wb Hz V−1 Ω J T−1 eV T−1 J T−1 eV T−1

m−1 Hz eV m J eV kg u MeV

C kg−1 m m m m2 J T−1

u MeV J T−1

muon g-factor −2(1 + aµ ) muon-proton magnetic moment ratio proton mass in u energy equivalent in MeV proton-electron mass ratio proton magnetic moment to nuclear magneton ratio proton magnetic shielding correction 1 − µ0p /µp (H2 O, sphere, 25 ◦ C) proton gyromagnetic ratio 2µp /¯ h shielded proton gyromagnetic ratio 2µ0p /¯ h (H2 O, sphere, 25 ◦ C) neutron mass in u energy equivalent in MeV neutron-proton mass ratio neutron magnetic moment to nuclear magneton ratio deuteron mass in u energy equivalent in MeV deuteron-proton mass ratio deuteron magnetic moment to nuclear magneton ratio helion (3 He nucleus) mass in u energy equivalent in MeV shielded helion magnetic moment (gas, sphere, 25 ◦ C) to Bohr magneton ratio to nuclear magneton ratio alpha particle mass in u energy equivalent in MeV Avogadro constant 1 atomic mass constant 12 m(12 C) = 1 u energy equivalent in MeV Faraday constant NA e molar gas constant Boltzmann constant R/NA in eV K−1 molar volume of ideal gas RT /p (T = 273.15 K, p = 101.325 kPa) Stefan-Boltzmann constant π2 k4/60¯ h 3 c2 first radiation constant 2πhc2 second radiation constant hc/k Wien displacement law constant b = λmax T = c2 /4.965 114 231... Cu x unit: λ(Cu Kα1 )/1 537.400 Mo x unit: λ(Mo Kα1 )/707.831

Symbol gµ µµ /µp mp

Numerical value

Unit

m p c2 mp /me µp µp /µN σp0

−2.002 331 8396(12) −3.183 345 118(89) 1.672 621 71(29) × 10−27 1.007 276 466 88(13) 938.272 029(80) 1836.152 672 61(85) 1.410 606 71(12) × 10−26 2.792 847 351(28) 25.689(15) × 10−6

γp γp /2π γp0

2.675 222 05(23) × 108 42.577 4813(37) 2.675 153 33(23) × 108

s−1 T−1 MHz T−1 s−1 T−1

γp0 /2π mn m n c2 mn /mp µn µn /µN md m d c2 md /mp µd µd /µN mh m h c2 µ0h

42.576 3875(37) 1.008 664 915 60(55) 939.565 360(81) 1.001 378 418 70(58) −0.966 236 45(24) × 10−26 −1.913 042 73(45) 2.013 553 212 70(35) 1875.612 82(16) 1.999 007 500 82(41) 0.433 073 482(38) × 10−26 0.857 438 2329(92) 3.014 932 2434(58) 2808.391 42(24) −1.074 553 024(93) × 10−26

MHz T−1 u MeV

µ0h /µB µ0h /µN mα m α c2 NA , L mu m u c2 F R k Vm

−1.158 671 474(14) × 10−3 −2.127 497 723(25) 4.001 506 179 149(56) 3727.379 17(32) 6.022 1415(10) × 1023 1.660 538 86(28) × 10−27 931.494 043(80) 96 485.3383(83) 8.314 472(15) 1.380 6505(24) × 10−23 8.617 343(15) × 10−5 22.413 996(39) × 10−3

u MeV mol−1 kg MeV C mol−1 J mol−1 K−1 J K−1 eV K−1 m3 mol−1

σ c1 c2

5.670 400(40) × 10−8 3.741 771 38(64) × 10−16 1.438 7752(25) × 10−2

W m−2 K−4 W m2 mK

b 2.897 7685(51) × 10−3 xu(Cu Kα1 ) 1.002 077 10(29) × 10−13 xu(Mo Kα1 ) 1.002 099 66(53) × 10−13

kg u MeV J T−1

J T−1 u MeV J T−1 u MeV J T−1

mK m m

Energy equivalents (1 (1 (1 (1 (1

m−1 )c m−1 )hc/k m−1 )hc m−1 )h/c Hz)/c

= = = = =

299 792 458 Hz 1.438 7752(25) × 10−2 K 1.239 841 91(11) × 10−6 eV 1.331 025 0506(89) × 10−15 u 3.335 640 951 . . . × 10−9 m−1

(1 (1 (1 (1 (1

Hz)h/k Hz)h K)k/hc K)k/h K)k

= = = = =

4.799 2374(84) × 10−11 K 4.135 667 43(35) × 10−15 eV 69.503 56(12) m−1 2.083 6644(36) × 1010 Hz 8.617 343(15) × 10−5 eV

(1 (1 (1 (1 (1

J) eV) eV)/hc eV)/h eV)/k

= = = = =

6.241 509 47(53) × 1018 eV 1.602 176 53(14) × 10−19 J 8.065 544 45(69) × 105 m−1 2.417 989 40(21) × 1014 Hz 1.160 4505(20) × 104 K

(1 (1 (1 (1 (1

eV)/c2 kg) u) u)c/h u)c2

= = = = =

1.073 544 171(92) × 10−9 u 6.022 1415(10) × 1026 u 1.660 538 86(28) × 10−27 kg 7.513 006 608(50) × 1014 m−1 931.494 043(80) × 106 eV