ABSTRACT
G/h¯c 6.708 37(80) × 10−39 (GeV/c2)−2 1.2 × 10−4 Planck constant h 6.626 069 57(29) × 10−34 J s 4.4 × 10−8
4.135 667 516(91) × 10−15 eV s 2.2 × 10−8 h/2π h¯ 1.054 571 726(47) × 10−34 J s 4.4 × 10−8
6.582 119 28(15) × 10−16 eV s 2.2 × 10−8 h¯c 197.326 9718(44) MeV fm 2.2 × 10−8
Planck mass (h¯c/G)1/2 mP 2.176 51(13) × 10−8 kg 6.0 × 10−5 energy equivalent mPc2 1.220 932(73) × 1019 GeV 6.0 × 10−5
Planck temperature (h¯c5/G)1/2/k TP 1.416 833(85) × 1032 K 6.0 × 10−5 Planck length h¯/mPc = (h¯G/c3)1/2 lP 1.616 199(97) × 10−35 m 6.0 × 10−5 Planck time lP/c = (h¯G/c5)1/2 tP 5.391 06(32) × 10−44 s 6.0 × 10−5
ELECTROMAGNETIC elementary charge e 1.602 176 565(35) × 10−19 C 2.2 × 10−8
e/h 2.417 989 348(53) × 1014 A J−1 2.2 × 10−8 magnetic flux quantum h/2e 0 2.067 833 758(46) × 10−15 Wb 2.2 × 10−8 conductance quantum 2e2/h G0 7.748 091 7346(25) × 10−5 S 3.2 × 10−10
inverse of conductance quantum G−10 12 906.403 7217(42) 3.2 × 10−10 Josephson constant1 2e/h KJ 483 597.870(11) × 109 Hz V−1 2.2 × 10−8 von Klitzing constant2 h/e2 = µ0c/2α RK 25 812.807 4434(84) 3.2 × 10−10 Bohr magneton eh¯/2me µB 927.400 968(20) × 10−26 J T−1 2.2 × 10−8
5.788 381 8066(38) × 10−5 eV T−1 6.5 × 10−10 µB/h 13.996 245 55(31) × 109 Hz T−1 2.2 × 10−8 µB/hc 46.686 4498(10) m−1 T−1 2.2 × 10−8 µB/k 0.671 713 88(61) K T−1 9.1 × 10−7
nuclear magneton eh¯/2mp µN 5.050 783 53(11) × 10−27 J T−1 2.2 × 10−8 3.152 451 2605(22) × 10−8 eV T−1 7.1 × 10−10
µN/h 7.622 593 57(17) MHz T−1 2.2 × 10−8 µN/hc 2.542 623 527(56) × 10−2 m−1 T−1 2.2 × 10−8 µN/k 3.658 2682(33) × 10−4 K T−1 9.1 × 10−7
U nits
Relative std. Quantity Symbol Numerical value Unit uncert. ur
ATOMIC AND NUCLEAR General
fine-structure constant e2/4pi0h¯c α 7.297 352 5698(24) × 10−3 3.2 × 10−10 inverse fine-structure constant α−1 137.035 999 074(44) 3.2 × 10−10
Rydberg constant α2mec/2h R∞ 10 973 731.568 539(55) m−1 5.0 × 10−12 R∞c 3.289 841 960 364(17) × 1015 Hz 5.0 × 10−12 R∞hc 2.179 872 171(96) × 10−18 J 4.4 × 10−8
13.605 692 53(30) eV 2.2 × 10−8 Bohr radius α/4piR∞ = 4pi0h¯2/mee2 a0 0.529 177 210 92(17) × 10−10 m 3.2 × 10−10 Hartree energy e2/4pi0a0 = 2R∞hc = α2mec2 Eh 4.359 744 34(19) × 10−18 J 4.4 × 10−8
27.211 385 05(60) eV 2.2 × 10−8 quantum of circulation h/2me 3.636 947 5520(24) × 10−4 m2 s−1 6.5 × 10−10
h/me 7.273 895 1040(47) × 10−4 m2 s−1 6.5 × 10−10 Electroweak
Fermi coupling constant3 GF/(h¯c)3 1.166 364(5) × 10−5 GeV−2 4.3 × 10−6 weak mixing angle4 θW (on-shell scheme) sin2 θW = s2W ≡ 1 − (mW/mZ)2 sin2 θW 0.2223(21) 9.5 × 10−3
Electron, e−
electron mass me 9.109 382 91(40) × 10−31 kg 4.4 × 10−8 5.485 799 0946(22) × 10−4 u 4.0 × 10−10
energy equivalent mec2 8.187 105 06(36) × 10−14 J 4.4 × 10−8 0.510 998 928(11) MeV 2.2 × 10−8
electron-muon mass ratio me/mµ 4.836 331 66(12) × 10−3 2.5 × 10−8 electron-tau mass ratio me/mτ 2.875 92(26) × 10−4 9.0 × 10−5 electron-proton mass ratio me/mp 5.446 170 2178(22) × 10−4 4.1 × 10−10 electron-neutron mass ratio me/mn 5.438 673 4461(32) × 10−4 5.8 × 10−10 electron-deuteron mass ratio me/md 2.724 437 1095(11) × 10−4 4.0 × 10−10 electron-triton mass ratio me/mt 1.819 200 0653(17) × 10−4 9.1 × 10−10 electron-helion mass ratio me/mh 1.819 543 0761(17) × 10−4 9.2 × 10−10 electron to alpha particle mass ratio me/mα 1.370 933 555 78(55) × 10−4 4.0 × 10−10 electron charge to mass quotient −e/me −1.758 820 088(39) × 1011 C kg−1 2.2 × 10−8 electron molar mass NAme M(e), Me 5.485 799 0946(22) × 10−7 kg mol−1 4.0 × 10−10 Compton wavelength h/mec λC 2.426 310 2389(16) × 10−12 m 6.5 × 10−10
λC/2pi = αa0 = α2/4piR∞ λC 386.159 268 00(25) × 10−15 m 6.5 × 10−10 classical electron radius α2a0 re 2.817 940 3267(27) × 10−15 m 9.7 × 10−10 Thomson cross section (8pi/3)r2e σe 0.665 245 8734(13) × 10−28 m2 1.9 × 10−9 electron magnetic moment µe −928.476 430(21) × 10−26 J T−1 2.2 × 10−8
to Bohr magneton ratio µe/µB −1.001 159 652 180 76(27) 2.6 × 10−13 to nuclear magneton ratio µe/µN −1838.281 970 90(75) 4.1 × 10−10
electron magnetic moment anomaly |µe|/µB − 1 ae 1.159 652 180 76(27) × 10−3 2.3 × 10−10
electron g-factor −2(1 + ae) ge −2.002 319 304 361 53(53) 2.6 × 10−13 electron-muon magnetic moment ratio µe/µµ 206.766 9896(52) 2.5 × 10−8 electron-proton magnetic moment ratio µe/µp −658.210 6848(54) 8.1 × 10−9 electron to shielded proton magnetic moment ratio (H2O, sphere, 25 ◦C) µe/µ�p −658.227 5971(72) 1.1 × 10−8
electron-neutron magnetic moment ratio µe/µn 960.920 50(23) 2.4 × 10−7 electron-deuteron magnetic moment ratio µe/µd −2143.923 498(18) 8.4 × 10−9 electron to shielded helion magnetic moment ratio (gas, sphere, 25 ◦C) µe/µ�h 864.058 257(10) 1.2 × 10−8
U ni ts
Relative std. Quantity Symbol Numerical value Unit uncert. ur
electron gyromagnetic ratio 2|µe|/h¯ γe 1.760 859 708(39) × 1011 s−1 T−1 2.2 × 10−8 γe/2pi 28 024.952 66(62) MHz T−1 2.2 × 10−8
Muon, µ− muon mass mµ 1.883 531 475(96) × 10−28 kg 5.1 × 10−8
0.113 428 9267(29) u 2.5 × 10−8 energy equivalent mµc2 1.692 833 667(86) × 10−11 J 5.1 × 10−8
105.658 3715(35) MeV 3.4 × 10−8 muon-electron mass ratio mµ/me 206.768 2843(52) 2.5 × 10−8 muon-tau mass ratio mµ/mτ 5.946 49(54) × 10−2 9.0 × 10−5 muon-proton mass ratio mµ/mp 0.112 609 5272(28) 2.5 × 10−8 muon-neutron mass ratio mµ/mn 0.112 454 5177(28) 2.5 × 10−8 muon molar mass NAmµ M(µ), Mµ 0.113 428 9267(29) × 10−3 kg mol−1 2.5 × 10−8 muon Compton wavelength h/mµc λC,µ 11.734 441 03(30) × 10−15 m 2.5 × 10−8
λC,µ/2pi λC,µ 1.867 594 294(47) × 10−15 m 2.5 × 10−8 muon magnetic moment µµ −4.490 448 07(15) × 10−26 J T−1 3.4 × 10−8
to Bohr magneton ratio µµ/µB −4.841 970 44(12) × 10−3 2.5 × 10−8 to nuclear magneton ratio µµ/µN −8.890 596 97(22) 2.5 × 10−8
muon magnetic moment anomaly |µµ|/(eh¯/2mµ) − 1 aµ 1.165 920 91(63) × 10−3 5.4 × 10−7
muon g-factor −2(1 + aµ) gµ −2.002 331 8418(13) 6.3 × 10−10 muon-proton magnetic moment ratio µµ/µp −3.183 345 107(84) 2.6 × 10−8
Tau, τ−
tau mass5 mτ 3.167 47(29) × 10−27 kg 9.0 × 10−5 1.907 49(17) u 9.0 × 10−5
energy equivalent mτc2 2.846 78(26) × 10−10 J 9.0 × 10−5 1776.82(16) MeV 9.0 × 10−5
tau-electron mass ratio mτ/me 3477.15(31) 9.0 × 10−5 tau-muon mass ratio mτ/mµ 16.8167(15) 9.0 × 10−5 tau-proton mass ratio mτ/mp 1.893 72(17) 9.0 × 10−5 tau-neutron mass ratio mτ/mn 1.891 11(17) 9.0 × 10−5 tau molar mass NAmτ M(τ), Mτ 1.907 49(17) × 10−3 kg mol−1 9.0 × 10−5 tau Compton wavelength h/mτc λC,τ 0.697 787(63) × 10−15 m 9.0 × 10−5
λC,τ/2pi λC,τ 0.111 056(10) × 10−15 m 9.0 × 10−5 Proton, p
proton mass mp 1.672 621 777(74) × 10−27 kg 4.4 × 10−8 1.007 276 466 812(90) u 8.9 × 10−11
energy equivalent mpc2 1.503 277 484(66) × 10−10 J 4.4 × 10−8 938.272 046(21) MeV 2.2 × 10−8
proton-electron mass ratio mp/me 1836.152 672 45(75) 4.1 × 10−10 proton-muon mass ratio mp/mµ 8.880 243 31(22) 2.5 × 10−8 proton-tau mass ratio mp/mτ 0.528 063(48) 9.0 × 10−5 proton-neutron mass ratio mp/mn 0.998 623 478 26(45) 4.5 × 10−10 proton charge to mass quotient e/mp 9.578 833 58(21) × 107 C kg−1 2.2 × 10−8 proton molar mass NAmp M(p), Mp 1.007 276 466 812(90) × 10−3 kg mol−1 8.9 × 10−11 proton Compton wavelength h/mpc λC,p 1.321 409 856 23(94) × 10−15 m 7.1 × 10−10
λC,p/2pi λC,p 0.210 308 910 47(15) × 10−15 m 7.1 × 10−10 proton rms charge radius rp 0.8775(51) × 10−15 m 5.9 × 10−3 proton magnetic moment µp 1.410 606 743(33) × 10−26 J T−1 2.4 × 10−8
to Bohr magneton ratio µp/µB 1.521 032 210(12) × 10−3 8.1 × 10−9 to nuclear magneton ratio µp/µN 2.792 847 356(23) 8.2 × 10−9
proton g-factor 2µp/µN gp 5.585 694 713(46) 8.2 × 10−9
U nits
Relative std. Quantity Symbol Numerical value Unit uncert. ur
proton-neutron magnetic moment ratio µp/µn −1.459 898 06(34) 2.4 × 10−7 shielded proton magnetic moment µ�p 1.410 570 499(35) × 10−26 J T−1 2.5 × 10−8 (H2O, sphere, 25 ◦C)
to Bohr magneton ratio µ�p/µB 1.520 993 128(17) × 10−3 1.1 × 10−8 to nuclear magneton ratio µ�p/µN 2.792 775 598(30) 1.1 × 10−8
proton magnetic shielding correction 1 − µ�p/µp (H2O, sphere, 25 ◦C) σ �p 25.694(14) × 10−6 5.3 × 10−4
proton gyromagnetic ratio 2µp/h¯ γp 2.675 222 005(63) × 108 s−1 T−1 2.4 × 10−8 γp/2pi 42.577 4806(10) MHz T−1 2.4 × 10−8
shielded proton gyromagnetic ratio 2µ�p/h¯ (H2O, sphere, 25
◦C) γ �p 2.675 153 268(66) × 108 s−1 T−1 2.5 × 10−8 γ �p/2pi 42.576 3866(10) MHz T
−1 2.5 × 10−8
Neutron, n neutron mass mn 1.674 927 351(74) × 10−27 kg 4.4 × 10−8
1.008 664 916 00(43) u 4.2 × 10−10 energy equivalent mnc2 1.505 349 631(66) × 10−10 J 4.4 × 10−8
939.565 379(21) MeV 2.2 × 10−8 neutron-electron mass ratio mn/me 1838.683 6605(11) 5.8 × 10−10 neutron-muon mass ratio mn/mµ 8.892 484 00(22) 2.5 × 10−8 neutron-tau mass ratio mn/mτ 0.528 790(48) 9.0 × 10−5 neutron-proton mass ratio mn/mp 1.001 378 419 17(45) 4.5 × 10−10 neutron-proton mass difference mn − mp 2.305 573 92(76) × 10−30 kg 3.3 × 10−7
0.001 388 449 19(45) u 3.3 × 10−7 energy equivalent (mn − mp)c2 2.072 146 50(68) × 10−13 J 3.3 × 10−7
1.293 332 17(42) MeV 3.3 × 10−7 neutron molar mass NAmn M(n), Mn 1.008 664 916 00(43) × 10−3 kg mol−1 4.2 × 10−10 neutron Compton wavelength h/mnc λC,n 1.319 590 9068(11) × 10−15 m 8.2 × 10−10
λC,n/2pi λC,n 0.210 019 415 68(17) × 10−15 m 8.2 × 10−10 neutron magnetic moment µn −0.966 236 47(23) × 10−26 J T−1 2.4 × 10−7
to Bohr magneton ratio µn/µB −1.041 875 63(25) × 10−3 2.4 × 10−7 to nuclear magneton ratio µn/µN −1.913 042 72(45) 2.4 × 10−7
neutron g-factor 2µn/µN gn −3.826 085 45(90) 2.4 × 10−7 neutron-electron magnetic moment ratio µn/µe 1.040 668 82(25) × 10−3 2.4 × 10−7 neutron-proton magnetic moment ratio µn/µp −0.684 979 34(16) 2.4 × 10−7 neutron to shielded proton magnetic moment ratio (H2O, sphere, 25 ◦C) µn/µ�p −0.684 996 94(16) 2.4 × 10−7
neutron gyromagnetic ratio 2|µn|/h¯ γn 1.832 471 79(43) × 108 s−1 T−1 2.4 × 10−7 γn/2pi 29.164 6943(69) MHz T−1 2.4 × 10−7
Deuteron, d deuteron mass md 3.343 583 48(15) × 10−27 kg 4.4 × 10−8
2.013 553 212 712(77) u 3.8 × 10−11 energy equivalent mdc2 3.005 062 97(13) × 10−10 J 4.4 × 10−8
1875.612 859(41) MeV 2.2 × 10−8 deuteron-electron mass ratio md/me 3670.482 9652(15) 4.0 × 10−10 deuteron-proton mass ratio md/mp 1.999 007 500 97(18) 9.2 × 10−11 deuteron molar mass NAmd M(d), Md 2.013 553 212 712(77) × 10−3 kg mol−1 3.8 × 10−11 deuteron rms charge radius rd 2.1424(21) × 10−15 m 9.8 × 10−4 deuteron magnetic moment µd 0.433 073 489(10) × 10−26 J T−1 2.4 × 10−8
to Bohr magneton ratio µd/µB 0.466 975 4556(39) × 10−3 8.4 × 10−9 to nuclear magneton ratio µd/µN 0.857 438 2308(72) 8.4 × 10−9
deuteron g-factor µd/µN gd 0.857 438 2308(72) 8.4 × 10−9 deuteron-electron magnetic moment ratio µd/µe −4.664 345 537(39) × 10−4 8.4 × 10−9 deuteron-proton magnetic moment ratio µd/µp 0.307 012 2070(24) 7.7 × 10−9 deuteron-neutron magnetic moment ratio µd/µn −0.448 206 52(11) 2.4 × 10−7
U ni ts
Relative std. Quantity Symbol Numerical value Unit uncert. ur
Triton, t triton mass mt 5.007 356 30(22) × 10−27 kg 4.4 × 10−8
3.015 500 7134(25) u 8.2 × 10−10 energy equivalent mtc2 4.500 387 41(20) × 10−10 J 4.4 × 10−8
2808.921 005(62) MeV 2.2 × 10−8 triton-electron mass ratio mt/me 5496.921 5267(50) 9.1 × 10−10 triton-proton mass ratio mt/mp 2.993 717 0308(25) 8.2 × 10−10 triton molar mass NAmt M(t), Mt 3.015 500 7134(25) × 10−3 kg mol−1 8.2 × 10−10 triton magnetic moment µt 1.504 609 447(38) × 10−26 J T−1 2.6 × 10−8
to Bohr magneton ratio µt/µB 1.622 393 657(21) × 10−3 1.3 × 10−8 to nuclear magneton ratio µt/µN 2.978 962 448(38) 1.3 × 10−8
triton g-factor 2µt/µN gt 5.957 924 896(76) 1.3 × 10−8 Helion, h
helion mass mh 5.006 412 34(22) × 10−27 kg 4.4 × 10−8 3.014 932 2468(25) u 8.3 × 10−10
energy equivalent mhc2 4.499 539 02(20) × 10−10 J 4.4 × 10−8 2808.391 482(62) MeV 2.2 × 10−8
helion-electron mass ratio mh/me 5495.885 2754(50) 9.2 × 10−10 helion-proton mass ratio mh/mp 2.993 152 6707(25) 8.2 × 10−10 helion molar mass NAmh M(h), Mh 3.014 932 2468(25) × 10−3 kg mol−1 8.3 × 10−10 helion magnetic moment µh −1.074 617 486(27) × 10−26 J T−1 2.5 × 10−8
to Bohr magneton ratio µh/µB −1.158 740 958(14) × 10−3 1.2 × 10−8 to nuclear magneton ratio µh/µN −2.127 625 306(25) 1.2 × 10−8
helion g-factor 2µh/µN gh −4.255 250 613(50) 1.2 × 10−8 shielded helion magnetic moment µ�h −1.074 553 044(27) × 10−26 J T−1 2.5 × 10−8 (gas, sphere, 25 ◦C)
to Bohr magneton ratio µ�h/µB −1.158 671 471(14) × 10−3 1.2 × 10−8 to nuclear magneton ratio µ�h/µN −2.127 497 718(25) 1.2 × 10−8
shielded helion to proton magnetic moment ratio (gas, sphere, 25 ◦C) µ�h/µp −0.761 766 558(11) 1.4 × 10−8
shielded helion to shielded proton magnetic moment ratio (gas/H2O, spheres, 25 ◦C) µ�h/µ
� p −0.761 786 1313(33) 4.3 × 10−9
shielded helion gyromagnetic ratio 2|µ�h|/h¯ (gas, sphere, 25 ◦C) γ �h 2.037 894 659(51) × 108 s−1 T−1 2.5 × 10−8
γ �h/2π 32.434 100 84(81) MHz T −1 2.5 × 10−8
Alpha particle, α alpha particle mass mα 6.644 656 75(29) × 10−27 kg 4.4 × 10−8
4.001 506 179 125(62) u 1.5 × 10−11 energy equivalent mαc2 5.971 919 67(26) × 10−10 J 4.4 × 10−8
3727.379 240(82) MeV 2.2 × 10−8 alpha particle to electron mass ratio mα/me 7294.299 5361(29) 4.0 × 10−10 alpha particle to proton mass ratio mα/mp 3.972 599 689 33(36) 9.0 × 10−11 alpha particle molar mass NAmα M(α), Mα 4.001 506 179 125(62) × 10−3 kg mol−1 1.5 × 10−11
PHYSICOCHEMICAL Avogadro constant NA, L 6.022 141 29(27) × 1023 mol−1 4.4 × 10−8 atomic mass constant mu = 112 m(12C) = 1 u mu 1.660 538 921(73) × 10−27 kg 4.4 × 10−8
energy equivalent muc2 1.492 417 954(66) × 10−10 J 4.4 × 10−8 931.494 061(21) MeV 2.2 × 10−8
Faraday constant6 NAe F 96 485.3365(21) C mol−1 2.2 × 10−8
U nits
Relative std. Quantity Symbol Numerical value Unit uncert. ur
molar Planck constant NAh 3.990 312 7176(28) × 10−10 J s mol−1 7.0 × 10−10 NAhc 0.119 626 565 779(84) J m mol−1 7.0 × 10−10
molar gas constant R 8.314 4621(75) J mol−1 K−1 9.1 × 10−7 Boltzmann constant R/NA k 1.380 6488(13) × 10−23 J K−1 9.1 × 10−7
8.617 3324(78) × 10−5 eV K−1 9.1 × 10−7 k/h 2.083 6618(19) × 1010 Hz K−1 9.1 × 10−7 k/hc 69.503 476(63) m−1 K−1 9.1 × 10−7
molar volume of ideal gas RT/p T = 273.15 K, p = 100 kPa Vm 22.710 953(21) × 10−3 m3 mol−1 9.1 × 10−7
Loschmidt constant NA/Vm n0 2.651 6462(24) × 1025 m−3 9.1 × 10−7 molar volume of ideal gas RT/p
T = 273.15 K, p = 101.325 kPa Vm 22.413 968(20) × 10−3 m3 mol−1 9.1 × 10−7 Loschmidt constant NA/Vm n0 2.686 7805(24) × 1025 m−3 9.1 × 10−7
Sackur-Tetrode (absolute entropy) constant7 5 2 + ln[(2pimukT1/h2)3/2kT1/p0]
T1 = 1 K, p0 = 100 kPa S0/R −1.151 7078(23) 2.0 × 10−6 T1 = 1 K, p0 = 101.325 kPa −1.164 8708(23) 1.9 × 10−6
Stefan-Boltzmann constant (pi2/60)k4/h¯3c2 σ 5.670 373(21) × 10−8 W m−2 K−4 3.6 × 10−6
first radiation constant 2pihc2 c1 3.741 771 53(17) × 10−16 W m2 4.4 × 10−8 first radiation constant for spectral radiance 2hc2c1L 1.191 042 869(53) × 10−16 W m2 sr−1 4.4 × 10−8 second radiation constant hc/k c2 1.438 7770(13) × 10−2 m K 9.1 × 10−7 Wien displacement law constants b = λmaxT = c2/4.965 114 231... b 2.897 7721(26) × 10−3 m K 9.1 × 10−7 b� = νmax/T = 2.821 439 372... c/c2 b� 5.878 9254(53) × 1010 Hz K−1 9.1 × 10−7
TABLE III: The variances, covariances, and correlation coefficients of the values of a selected group of constants based on the 2010 CODATA adjustment. The numbers in bold above the main diagonal are 1016 times the numerical values of the relative covariances; the numbers in bold on the main diagonal are 1016 times the numerical values of the relative variances; and the
numbers in italics below the main diagonal are the correlation coefficients.1
