ConstantID

Atomic and nuclear constants

Masses, magnetic moments, radii and ratios for the electron, muon, tau, proton, neutron and light nuclei, plus α, R∞ and the Bohr radius.

Atomic & nuclear a0 Bohr radius 5.291 772 105 44(82) × 10−11 m Atomic & nuclear me Electron mass 9.109 383 7139(28) × 10−31 kg Atomic & nuclear α Fine-structure constant 7.297 352 5643(11) × 10−3 Atomic & nuclear Eh Hartree energy 4.359 744 722 2060(48) × 10−18 J Atomic & nuclear mn Neutron mass 1.674 927 500 56(85) × 10−27 kg Atomic & nuclear mp Proton mass 1.672 621 925 95(52) × 10−27 kg Atomic & nuclear R∞ Rydberg constant 10 973 731.568 157(12) m−1

General

SymbolQuantityValue (uncertainty)UnitRel. unc.
a0 Bohr radius 5.291 772 105 44(82) × 10−11 m 1.5 × 10−10
re Classical electron radius 2.817 940 3205(13) × 10−15 m 4.6 × 10−10
λC Compton wavelength 2.426 310 235 38(76) × 10−12 m 3.1 × 10−10
α Fine-structure constant 7.297 352 5643(11) × 10−3 1.5 × 10−10
Eh Hartree energy 4.359 744 722 2060(48) × 10−18 J 1.1 × 10−12
Eh Hartree energy in eV 27.211 386 245 981(30) eV 1.1 × 10−12
α−1 Inverse fine-structure constant 137.035 999 177(21) 1.5 × 10−10
πℏ/me Quantum of circulation 3.636 947 5467(11) × 10−4 m2 s−1 3.0 × 10−10
h/me Quantum of circulation times 2 7.273 895 0934(23) × 10−4 m2 s−1 3.2 × 10−10
λ¯C Reduced Compton wavelength 3.861 592 6744(12) × 10−13 m 3.1 × 10−10
R∞ Rydberg constant 10 973 731.568 157(12) m−1 1.1 × 10−12
R∞c Rydberg constant times c in Hz 3.289 841 960 2500(36) × 1015 Hz 1.1 × 10−12
R∞hc Rydberg constant times hc in eV 13.605 693 122 990(15) eV 1.1 × 10−12
R∞hc Rydberg constant times hc in J 2.179 872 361 1030(24) × 10−18 J 1.1 × 10−12
σdp Shielding difference of d and p in HD 1.987 70(10) × 10−8 5.0 × 10−5
σtp Shielding difference of t and p in HT 2.394 50(20) × 10−8 8.4 × 10−5
σe Thomson cross section 6.652 458 7051(62) × 10−29 m2 9.3 × 10−10

Electroweak

SymbolQuantityValue (uncertainty)UnitRel. unc.
GF/(ℏc)3 Fermi coupling constant 1.166 3787(6) × 10−5 GeV−2 5.1 × 10−7
sin2θW Weak mixing angle 0.223 05(23) 1.0 × 10−3
mW/mZ W to Z mass ratio 0.881 45(13) 1.5 × 10−4

Electron

SymbolQuantityValue (uncertainty)UnitRel. unc.
−e/me Electron charge to mass quotient −1.758 820 008 38(55) × 1011 C kg−1 3.1 × 10−10
μe/μd Electron-deuteron magnetic moment ratio −2143.923 4921(56) 2.6 × 10−9
me/md Electron-deuteron mass ratio 2.724 437 107 629(47) × 10−4 1.7 × 10−11
ge Electron g factor −2.002 319 304 360 92(36) 1.8 × 10−13
γe Electron gyromagnetic ratio 1.760 859 627 84(55) × 1011 s−1 T−1 3.1 × 10−10
γe/2π Electron gyromagnetic ratio in MHz/T 28 024.951 3861(87) MHz T−1 3.1 × 10−10
me/mh Electron-helion mass ratio 1.819 543 074 649(53) × 10−4 2.9 × 10−11
μe Electron magnetic moment −9.284 764 6917(29) × 10−24 J T−1 3.1 × 10−10
ae Electron magnetic moment anomaly 1.159 652 180 46(18) × 10−3 1.6 × 10−10
μe/μB Electron magnetic moment to Bohr magneton ratio −1.001 159 652 180 46(18) 1.8 × 10−13
μe/μN Electron magnetic moment to nuclear magneton ratio −1838.281 971 877(32) 1.7 × 10−11
me Electron mass 9.109 383 7139(28) × 10−31 kg 3.1 × 10−10
mec2 Electron mass energy equivalent 8.187 105 7880(26) × 10−14 J 3.2 × 10−10
mec2 Electron mass energy equivalent in MeV 0.510 998 950 69(16) MeV 3.1 × 10−10
me Electron mass in u 5.485 799 090 441(97) × 10−4 u 1.8 × 10−11
M(e) Electron molar mass 5.485 799 0962(17) × 10−7 kg mol−1 3.1 × 10−10
μe/μμ Electron-muon magnetic moment ratio 206.766 9881(46) 2.2 × 10−8
me/mμ Electron-muon mass ratio 4.836 331 70(11) × 10−3 2.3 × 10−8
μe/μn Electron-neutron magnetic moment ratio 960.920 48(23) 2.4 × 10−7
me/mn Electron-neutron mass ratio 5.438 673 4416(22) × 10−4 4.0 × 10−10
μe/μp Electron-proton magnetic moment ratio −658.210 687 89(19) 2.9 × 10−10
me/mp Electron-proton mass ratio 5.446 170 214 889(94) × 10−4 1.7 × 10−11
Ar(e) Electron relative atomic mass 5.485 799 090 441(97) × 10−4 1.8 × 10−11
me/mτ Electron-tau mass ratio 2.875 85(19) × 10−4 6.6 × 10−5
me/mα Electron to alpha particle mass ratio 1.370 933 554 733(32) × 10−4 2.3 × 10−11
μe/μh′ Electron to shielded helion magnetic moment ratio 864.058 239 86(70) 8.1 × 10−10
μe/μp′ Electron to shielded proton magnetic moment ratio −658.227 5856(27) 4.1 × 10−9
me/mt Electron-triton mass ratio 1.819 200 062 327(68) × 10−4 3.7 × 10−11

Muon

SymbolQuantityValue (uncertainty)UnitRel. unc.
λC,μ Muon Compton wavelength 1.173 444 110(26) × 10−14 m 2.2 × 10−8
mμ/me Muon-electron mass ratio 206.768 2827(46) 2.2 × 10−8
gμ Muon g factor −2.002 331 841 23(82) 4.1 × 10−10
μμ Muon magnetic moment −4.490 448 30(10) × 10−26 J T−1 2.2 × 10−8
aμ Muon magnetic moment anomaly 1.165 920 62(41) × 10−3 3.5 × 10−7
μμ/μB Muon magnetic moment to Bohr magneton ratio −4.841 970 48(11) × 10−3 2.3 × 10−8
μμ/μN Muon magnetic moment to nuclear magneton ratio −8.890 597 04(20) 2.2 × 10−8
mμ Muon mass 1.883 531 627(42) × 10−28 kg 2.2 × 10−8
mμc2 Muon mass energy equivalent 1.692 833 804(38) × 10−11 J 2.2 × 10−8
mμc2 Muon mass energy equivalent in MeV 105.658 3755(23) MeV 2.2 × 10−8
mμ Muon mass in u 0.113 428 9257(25) u 2.2 × 10−8
M(μ) Muon molar mass 1.134 289 258(25) × 10−4 kg mol−1 2.2 × 10−8
mμ/mn Muon-neutron mass ratio 0.112 454 5168(25) 2.2 × 10−8
μμ/μp Muon-proton magnetic moment ratio −3.183 345 146(71) 2.2 × 10−8
mμ/mp Muon-proton mass ratio 0.112 609 5262(25) 2.2 × 10−8
mμ/mτ Muon-tau mass ratio 5.946 35(40) × 10−2 6.7 × 10−5
λ¯C,μ Reduced muon Compton wavelength 1.867 594 306(42) × 10−15 m 2.2 × 10−8

Tau

SymbolQuantityValue (uncertainty)UnitRel. unc.
λ¯C,τ Reduced tau Compton wavelength 1.110 538(75) × 10−16 m 6.8 × 10−5
λC,τ Tau Compton wavelength 6.977 71(47) × 10−16 m 6.7 × 10−5
mτ/me Tau-electron mass ratio 3477.23(23) 6.6 × 10−5
mτc2 Tau energy equivalent 1776.86(12) MeV 6.8 × 10−5
mτ Tau mass 3.167 54(21) × 10−27 kg 6.6 × 10−5
mτc2 Tau mass energy equivalent 2.846 84(19) × 10−10 J 6.7 × 10−5
mτ Tau mass in u 1.907 54(13) u 6.8 × 10−5
M(τ) Tau molar mass 1.907 54(13) × 10−3 kg mol−1 6.8 × 10−5
mτ/mμ Tau-muon mass ratio 16.8170(11) 6.5 × 10−5
mτ/mn Tau-neutron mass ratio 1.891 15(13) 6.9 × 10−5
mτ/mp Tau-proton mass ratio 1.893 76(13) 6.9 × 10−5

Proton

SymbolQuantityValue (uncertainty)UnitRel. unc.
e/mp Proton charge to mass quotient 9.578 833 1430(30) × 107 C kg−1 3.1 × 10−10
λC,p Proton Compton wavelength 1.321 409 853 60(41) × 10−15 m 3.1 × 10−10
mp/me Proton-electron mass ratio 1836.152 673 426(32) 1.7 × 10−11
gp Proton g factor 5.585 694 6893(16) 2.9 × 10−10
γp Proton gyromagnetic ratio 2.675 221 8708(11) × 108 s−1 T−1 4.1 × 10−10
γp/2π Proton gyromagnetic ratio in MHz/T 42.577 478 461(18) MHz T−1 4.2 × 10−10
μp Proton magnetic moment 1.410 606 795 45(60) × 10−26 J T−1 4.3 × 10−10
μp/μB Proton magnetic moment to Bohr magneton ratio 1.521 032 202 30(45) × 10−3 3.0 × 10−10
μp/μN Proton magnetic moment to nuclear magneton ratio 2.792 847 344 63(82) 2.9 × 10−10
σp′ Proton magnetic shielding correction 2.567 15(41) × 10−5 1.6 × 10−4
mp Proton mass 1.672 621 925 95(52) × 10−27 kg 3.1 × 10−10
mpc2 Proton mass energy equivalent 1.503 277 618 02(47) × 10−10 J 3.1 × 10−10
mpc2 Proton mass energy equivalent in MeV 938.272 089 43(29) MeV 3.1 × 10−10
mp Proton mass in u 1.007 276 466 5789(83) u 8.2 × 10−12
M(p) Proton molar mass 1.007 276 467 64(31) × 10−3 kg mol−1 3.1 × 10−10
mp/mμ Proton-muon mass ratio 8.880 243 38(20) 2.3 × 10−8
μp/μn Proton-neutron magnetic moment ratio −1.459 898 02(34) 2.3 × 10−7
mp/mn Proton-neutron mass ratio 0.998 623 477 97(40) 4.0 × 10−10
Ar(p) Proton relative atomic mass 1.007 276 466 5789(83) 8.2 × 10−12
rp Proton rms charge radius 8.4075(64) × 10−16 m 7.6 × 10−4
mp/mτ Proton-tau mass ratio 0.528 051(36) 6.8 × 10−5
λ¯C,p Reduced proton Compton wavelength 2.103 089 100 51(66) × 10−16 m 3.1 × 10−10
γp′ Shielded proton gyromagnetic ratio 2.675 153 194(11) × 108 s−1 T−1 4.1 × 10−9
γp′/2π Shielded proton gyromagnetic ratio in MHz/T 42.576 385 43(17) MHz T−1 4.0 × 10−9
μp′ Shielded proton magnetic moment 1.410 570 5830(58) × 10−26 J T−1 4.1 × 10−9
μp′/μB Shielded proton magnetic moment to Bohr magneton ratio 1.520 993 1551(62) × 10−3 4.1 × 10−9
μp′/μN Shielded proton magnetic moment to nuclear magneton ratio 2.792 775 648(11) 3.9 × 10−9

Neutron

SymbolQuantityValue (uncertainty)UnitRel. unc.
λC,n Neutron Compton wavelength 1.319 590 903 82(67) × 10−15 m 5.1 × 10−10
μn/μe Neutron-electron magnetic moment ratio 1.040 668 84(24) × 10−3 2.3 × 10−7
mn/me Neutron-electron mass ratio 1838.683 662 00(74) 4.0 × 10−10
gn Neutron g factor −3.826 085 52(90) 2.4 × 10−7
γn Neutron gyromagnetic ratio 1.832 471 74(43) × 108 s−1 T−1 2.3 × 10−7
γn/2π Neutron gyromagnetic ratio in MHz/T 29.164 6935(69) MHz T−1 2.4 × 10−7
μn Neutron magnetic moment −9.662 3653(23) × 10−27 J T−1 2.4 × 10−7
μn/μB Neutron magnetic moment to Bohr magneton ratio −1.041 875 65(25) × 10−3 2.4 × 10−7
μn/μN Neutron magnetic moment to nuclear magneton ratio −1.913 042 76(45) 2.4 × 10−7
mn Neutron mass 1.674 927 500 56(85) × 10−27 kg 5.1 × 10−10
mnc2 Neutron mass energy equivalent 1.505 349 765 14(76) × 10−10 J 5.0 × 10−10
mnc2 Neutron mass energy equivalent in MeV 939.565 421 94(48) MeV 5.1 × 10−10
mn Neutron mass in u 1.008 664 916 06(40) u 4.0 × 10−10
M(n) Neutron molar mass 1.008 664 917 12(51) × 10−3 kg mol−1 5.1 × 10−10
mn/mμ Neutron-muon mass ratio 8.892 484 08(20) 2.2 × 10−8
μn/μp Neutron-proton magnetic moment ratio −0.684 979 35(16) 2.3 × 10−7
mn−mp Neutron-proton mass difference 2.305 574 61(67) × 10−30 kg 2.9 × 10−7
(mn−mp)c2 Neutron-proton mass difference energy equivalent 2.072 147 12(60) × 10−13 J 2.9 × 10−7
(mn−mp)c2 Neutron-proton mass difference energy equivalent in MeV 1.293 332 51(38) MeV 2.9 × 10−7
mn−mp Neutron-proton mass difference in u 1.388 449 48(40) × 10−3 u 2.9 × 10−7
mn/mp Neutron-proton mass ratio 1.001 378 419 46(40) 4.0 × 10−10
Ar(n) Neutron relative atomic mass 1.008 664 916 06(40) 4.0 × 10−10
mn/mτ Neutron-tau mass ratio 0.528 779(36) 6.8 × 10−5
μn/μp′ Neutron to shielded proton magnetic moment ratio −0.684 996 94(16) 2.3 × 10−7
λ¯C,n Reduced neutron Compton wavelength 2.100 194 1520(11) × 10−16 m 5.2 × 10−10

Deuteron

SymbolQuantityValue (uncertainty)UnitRel. unc.
μd/μe Deuteron-electron magnetic moment ratio −4.664 345 550(12) × 10−4 2.6 × 10−9
md/me Deuteron-electron mass ratio 3670.482 967 655(63) 1.7 × 10−11
gd Deuteron g factor 0.857 438 2335(22) 2.6 × 10−9
μd Deuteron magnetic moment 4.330 735 087(11) × 10−27 J T−1 2.5 × 10−9
μd/μB Deuteron magnetic moment to Bohr magneton ratio 4.669 754 568(12) × 10−4 2.6 × 10−9
μd/μN Deuteron magnetic moment to nuclear magneton ratio 0.857 438 2335(22) 2.6 × 10−9
md Deuteron mass 3.343 583 7768(10) × 10−27 kg 3.0 × 10−10
mdc2 Deuteron mass energy equivalent 3.005 063 234 91(94) × 10−10 J 3.1 × 10−10
mdc2 Deuteron mass energy equivalent in MeV 1875.612 945 00(58) MeV 3.1 × 10−10
md Deuteron mass in u 2.013 553 212 544(15) u 7.4 × 10−12
M(d) Deuteron molar mass 2.013 553 214 66(63) × 10−3 kg mol−1 3.1 × 10−10
μd/μn Deuteron-neutron magnetic moment ratio −0.448 206 52(11) 2.5 × 10−7
μd/μp Deuteron-proton magnetic moment ratio 0.307 012 209 30(79) 2.6 × 10−9
md/mp Deuteron-proton mass ratio 1.999 007 501 2699(84) 4.2 × 10−12
Ar(d) Deuteron relative atomic mass 2.013 553 212 544(15) 7.4 × 10−12
rd Deuteron rms charge radius 2.127 78(27) × 10−15 m 1.3 × 10−4

Triton

SymbolQuantityValue (uncertainty)UnitRel. unc.
mt/me Triton-electron mass ratio 5496.921 535 51(21) 3.8 × 10−11
gt Triton g factor 5.957 924 930(12) 2.0 × 10−9
μt Triton magnetic moment 1.504 609 5178(30) × 10−26 J T−1 2.0 × 10−9
μt/μB Triton magnetic moment to Bohr magneton ratio 1.622 393 6648(32) × 10−3 2.0 × 10−9
μt/μN Triton magnetic moment to nuclear magneton ratio 2.978 962 4650(59) 2.0 × 10−9
mt Triton mass 5.007 356 7512(16) × 10−27 kg 3.2 × 10−10
mtc2 Triton mass energy equivalent 4.500 387 8119(14) × 10−10 J 3.1 × 10−10
mtc2 Triton mass energy equivalent in MeV 2808.921 136 68(88) MeV 3.1 × 10−10
mt Triton mass in u 3.015 500 715 97(10) u 3.3 × 10−11
M(t) Triton molar mass 3.015 500 719 13(94) × 10−3 kg mol−1 3.1 × 10−10
mt/mp Triton-proton mass ratio 2.993 717 034 03(10) 3.3 × 10−11
Ar(t) Triton relative atomic mass 3.015 500 715 97(10) 3.3 × 10−11
μt/μp Triton to proton magnetic moment ratio 1.066 639 9189(21) 2.0 × 10−9

Helion

SymbolQuantityValue (uncertainty)UnitRel. unc.
mh/me Helion-electron mass ratio 5495.885 279 84(16) 2.9 × 10−11
gh Helion g factor −4.255 250 6995(34) 8.0 × 10−10
μh Helion magnetic moment −1.074 617 551 98(93) × 10−26 J T−1 8.7 × 10−10
μh/μB Helion magnetic moment to Bohr magneton ratio −1.158 740 980 83(94) × 10−3 8.1 × 10−10
μh/μN Helion magnetic moment to nuclear magneton ratio −2.127 625 3498(17) 8.0 × 10−10
mh Helion mass 5.006 412 7862(16) × 10−27 kg 3.2 × 10−10
mhc2 Helion mass energy equivalent 4.499 539 4185(14) × 10−10 J 3.1 × 10−10
mhc2 Helion mass energy equivalent in MeV 2808.391 611 12(88) MeV 3.1 × 10−10
mh Helion mass in u 3.014 932 246 932(74) u 2.5 × 10−11
M(h) Helion molar mass 3.014 932 250 10(94) × 10−3 kg mol−1 3.1 × 10−10
mh/mp Helion-proton mass ratio 2.993 152 671 552(70) 2.3 × 10−11
Ar(h) Helion relative atomic mass 3.014 932 246 932(74) 2.5 × 10−11
σh′ Helion shielding shift 5.996 7029(23) × 10−5 3.8 × 10−7
γh′ Shielded helion gyromagnetic ratio 2.037 894 6078(18) × 108 s−1 T−1 8.8 × 10−10
γh′/2π Shielded helion gyromagnetic ratio in MHz/T 32.434 100 033(28) MHz T−1 8.6 × 10−10
μh′ Shielded helion magnetic moment −1.074 553 110 35(93) × 10−26 J T−1 8.7 × 10−10
μh′/μB Shielded helion magnetic moment to Bohr magneton ratio −1.158 671 494 57(94) × 10−3 8.1 × 10−10
μh′/μN Shielded helion magnetic moment to nuclear magneton ratio −2.127 497 7624(17) 8.0 × 10−10
μh′/μp Shielded helion to proton magnetic moment ratio −0.761 766 577 21(66) 8.7 × 10−10
μh′/μp′ Shielded helion to shielded proton magnetic moment ratio −0.761 786 1334(31) 4.1 × 10−9

Alpha particle

SymbolQuantityValue (uncertainty)UnitRel. unc.
mα/me Alpha particle-electron mass ratio 7294.299 541 71(17) 2.3 × 10−11
mα Alpha particle mass 6.644 657 3450(21) × 10−27 kg 3.2 × 10−10
mαc2 Alpha particle mass energy equivalent 5.971 920 1997(19) × 10−10 J 3.2 × 10−10
mαc2 Alpha particle mass energy equivalent in MeV 3727.379 4118(12) MeV 3.2 × 10−10
mα Alpha particle mass in u 4.001 506 179 129(62) u 1.5 × 10−11
M(α) Alpha particle molar mass 4.001 506 1833(12) × 10−3 kg mol−1 3.0 × 10−10
mα/mp Alpha particle-proton mass ratio 3.972 599 690 252(70) 1.8 × 10−11
Ar(α) Alpha particle relative atomic mass 4.001 506 179 129(62) 1.5 × 10−11
rα Alpha particle rms charge radius 1.6785(21) × 10−15 m 1.3 × 10−3