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
Bohr radius
5.291 772 105 44(82) × 10−11
m
Atomic & nuclear
Electron mass
9.109 383 7139(28) × 10−31
kg
Atomic & nuclear
Fine-structure constant
7.297 352 5643(11) × 10−3
Atomic & nuclear
Hartree energy
4.359 744 722 2060(48) × 10−18
J
Atomic & nuclear
Neutron mass
1.674 927 500 56(85) × 10−27
kg
Atomic & nuclear
Proton mass
1.672 621 925 95(52) × 10−27
kg
Atomic & nuclear
Rydberg constant
10 973 731.568 157(12)
m−1
General
| Symbol | Quantity | Value (uncertainty) | Unit | Rel. unc. |
|---|---|---|---|---|
| Bohr radius | 5.291 772 105 44(82) × 10−11 | m | 1.5 × 10−10 | |
| Classical electron radius | 2.817 940 3205(13) × 10−15 | m | 4.6 × 10−10 | |
| Compton wavelength | 2.426 310 235 38(76) × 10−12 | m | 3.1 × 10−10 | |
| Fine-structure constant | 7.297 352 5643(11) × 10−3 | 1.5 × 10−10 | ||
| Hartree energy | 4.359 744 722 2060(48) × 10−18 | J | 1.1 × 10−12 | |
| Hartree energy in eV | 27.211 386 245 981(30) | eV | 1.1 × 10−12 | |
| Inverse fine-structure constant | 137.035 999 177(21) | 1.5 × 10−10 | ||
| Quantum of circulation | 3.636 947 5467(11) × 10−4 | m2 s−1 | 3.0 × 10−10 | |
| Quantum of circulation times 2 | 7.273 895 0934(23) × 10−4 | m2 s−1 | 3.2 × 10−10 | |
| Reduced Compton wavelength | 3.861 592 6744(12) × 10−13 | m | 3.1 × 10−10 | |
| Rydberg constant | 10 973 731.568 157(12) | m−1 | 1.1 × 10−12 | |
| Rydberg constant times c in Hz | 3.289 841 960 2500(36) × 1015 | Hz | 1.1 × 10−12 | |
| Rydberg constant times hc in eV | 13.605 693 122 990(15) | eV | 1.1 × 10−12 | |
| Rydberg constant times hc in J | 2.179 872 361 1030(24) × 10−18 | J | 1.1 × 10−12 | |
| Shielding difference of d and p in HD | 1.987 70(10) × 10−8 | 5.0 × 10−5 | ||
| Shielding difference of t and p in HT | 2.394 50(20) × 10−8 | 8.4 × 10−5 | ||
| Thomson cross section | 6.652 458 7051(62) × 10−29 | m2 | 9.3 × 10−10 |
Electroweak
| Symbol | Quantity | Value (uncertainty) | Unit | Rel. unc. |
|---|---|---|---|---|
| Fermi coupling constant | 1.166 3787(6) × 10−5 | GeV−2 | 5.1 × 10−7 | |
| Weak mixing angle | 0.223 05(23) | 1.0 × 10−3 | ||
| W to Z mass ratio | 0.881 45(13) | 1.5 × 10−4 |
Electron
| Symbol | Quantity | Value (uncertainty) | Unit | Rel. unc. |
|---|---|---|---|---|
| Electron charge to mass quotient | −1.758 820 008 38(55) × 1011 | C kg−1 | 3.1 × 10−10 | |
| Electron-deuteron magnetic moment ratio | −2143.923 4921(56) | 2.6 × 10−9 | ||
| Electron-deuteron mass ratio | 2.724 437 107 629(47) × 10−4 | 1.7 × 10−11 | ||
| Electron g factor | −2.002 319 304 360 92(36) | 1.8 × 10−13 | ||
| Electron gyromagnetic ratio | 1.760 859 627 84(55) × 1011 | s−1 T−1 | 3.1 × 10−10 | |
| Electron gyromagnetic ratio in MHz/T | 28 024.951 3861(87) | MHz T−1 | 3.1 × 10−10 | |
| Electron-helion mass ratio | 1.819 543 074 649(53) × 10−4 | 2.9 × 10−11 | ||
| Electron magnetic moment | −9.284 764 6917(29) × 10−24 | J T−1 | 3.1 × 10−10 | |
| Electron magnetic moment anomaly | 1.159 652 180 46(18) × 10−3 | 1.6 × 10−10 | ||
| Electron magnetic moment to Bohr magneton ratio | −1.001 159 652 180 46(18) | 1.8 × 10−13 | ||
| Electron magnetic moment to nuclear magneton ratio | −1838.281 971 877(32) | 1.7 × 10−11 | ||
| Electron mass | 9.109 383 7139(28) × 10−31 | kg | 3.1 × 10−10 | |
| Electron mass energy equivalent | 8.187 105 7880(26) × 10−14 | J | 3.2 × 10−10 | |
| Electron mass energy equivalent in MeV | 0.510 998 950 69(16) | MeV | 3.1 × 10−10 | |
| Electron mass in u | 5.485 799 090 441(97) × 10−4 | u | 1.8 × 10−11 | |
| Electron molar mass | 5.485 799 0962(17) × 10−7 | kg mol−1 | 3.1 × 10−10 | |
| Electron-muon magnetic moment ratio | 206.766 9881(46) | 2.2 × 10−8 | ||
| Electron-muon mass ratio | 4.836 331 70(11) × 10−3 | 2.3 × 10−8 | ||
| Electron-neutron magnetic moment ratio | 960.920 48(23) | 2.4 × 10−7 | ||
| Electron-neutron mass ratio | 5.438 673 4416(22) × 10−4 | 4.0 × 10−10 | ||
| Electron-proton magnetic moment ratio | −658.210 687 89(19) | 2.9 × 10−10 | ||
| Electron-proton mass ratio | 5.446 170 214 889(94) × 10−4 | 1.7 × 10−11 | ||
| Electron relative atomic mass | 5.485 799 090 441(97) × 10−4 | 1.8 × 10−11 | ||
| Electron-tau mass ratio | 2.875 85(19) × 10−4 | 6.6 × 10−5 | ||
| Electron to alpha particle mass ratio | 1.370 933 554 733(32) × 10−4 | 2.3 × 10−11 | ||
| Electron to shielded helion magnetic moment ratio | 864.058 239 86(70) | 8.1 × 10−10 | ||
| Electron to shielded proton magnetic moment ratio | −658.227 5856(27) | 4.1 × 10−9 | ||
| Electron-triton mass ratio | 1.819 200 062 327(68) × 10−4 | 3.7 × 10−11 |
Muon
| Symbol | Quantity | Value (uncertainty) | Unit | Rel. unc. |
|---|---|---|---|---|
| Muon Compton wavelength | 1.173 444 110(26) × 10−14 | m | 2.2 × 10−8 | |
| Muon-electron mass ratio | 206.768 2827(46) | 2.2 × 10−8 | ||
| Muon g factor | −2.002 331 841 23(82) | 4.1 × 10−10 | ||
| Muon magnetic moment | −4.490 448 30(10) × 10−26 | J T−1 | 2.2 × 10−8 | |
| Muon magnetic moment anomaly | 1.165 920 62(41) × 10−3 | 3.5 × 10−7 | ||
| Muon magnetic moment to Bohr magneton ratio | −4.841 970 48(11) × 10−3 | 2.3 × 10−8 | ||
| Muon magnetic moment to nuclear magneton ratio | −8.890 597 04(20) | 2.2 × 10−8 | ||
| Muon mass | 1.883 531 627(42) × 10−28 | kg | 2.2 × 10−8 | |
| Muon mass energy equivalent | 1.692 833 804(38) × 10−11 | J | 2.2 × 10−8 | |
| Muon mass energy equivalent in MeV | 105.658 3755(23) | MeV | 2.2 × 10−8 | |
| Muon mass in u | 0.113 428 9257(25) | u | 2.2 × 10−8 | |
| Muon molar mass | 1.134 289 258(25) × 10−4 | kg mol−1 | 2.2 × 10−8 | |
| Muon-neutron mass ratio | 0.112 454 5168(25) | 2.2 × 10−8 | ||
| Muon-proton magnetic moment ratio | −3.183 345 146(71) | 2.2 × 10−8 | ||
| Muon-proton mass ratio | 0.112 609 5262(25) | 2.2 × 10−8 | ||
| Muon-tau mass ratio | 5.946 35(40) × 10−2 | 6.7 × 10−5 | ||
| Reduced muon Compton wavelength | 1.867 594 306(42) × 10−15 | m | 2.2 × 10−8 |
Tau
| Symbol | Quantity | Value (uncertainty) | Unit | Rel. unc. |
|---|---|---|---|---|
| Reduced tau Compton wavelength | 1.110 538(75) × 10−16 | m | 6.8 × 10−5 | |
| Tau Compton wavelength | 6.977 71(47) × 10−16 | m | 6.7 × 10−5 | |
| Tau-electron mass ratio | 3477.23(23) | 6.6 × 10−5 | ||
| Tau energy equivalent | 1776.86(12) | MeV | 6.8 × 10−5 | |
| Tau mass | 3.167 54(21) × 10−27 | kg | 6.6 × 10−5 | |
| Tau mass energy equivalent | 2.846 84(19) × 10−10 | J | 6.7 × 10−5 | |
| Tau mass in u | 1.907 54(13) | u | 6.8 × 10−5 | |
| Tau molar mass | 1.907 54(13) × 10−3 | kg mol−1 | 6.8 × 10−5 | |
| Tau-muon mass ratio | 16.8170(11) | 6.5 × 10−5 | ||
| Tau-neutron mass ratio | 1.891 15(13) | 6.9 × 10−5 | ||
| Tau-proton mass ratio | 1.893 76(13) | 6.9 × 10−5 |
Proton
| Symbol | Quantity | Value (uncertainty) | Unit | Rel. unc. |
|---|---|---|---|---|
| Proton charge to mass quotient | 9.578 833 1430(30) × 107 | C kg−1 | 3.1 × 10−10 | |
| Proton Compton wavelength | 1.321 409 853 60(41) × 10−15 | m | 3.1 × 10−10 | |
| Proton-electron mass ratio | 1836.152 673 426(32) | 1.7 × 10−11 | ||
| Proton g factor | 5.585 694 6893(16) | 2.9 × 10−10 | ||
| Proton gyromagnetic ratio | 2.675 221 8708(11) × 108 | s−1 T−1 | 4.1 × 10−10 | |
| Proton gyromagnetic ratio in MHz/T | 42.577 478 461(18) | MHz T−1 | 4.2 × 10−10 | |
| Proton magnetic moment | 1.410 606 795 45(60) × 10−26 | J T−1 | 4.3 × 10−10 | |
| Proton magnetic moment to Bohr magneton ratio | 1.521 032 202 30(45) × 10−3 | 3.0 × 10−10 | ||
| Proton magnetic moment to nuclear magneton ratio | 2.792 847 344 63(82) | 2.9 × 10−10 | ||
| Proton magnetic shielding correction | 2.567 15(41) × 10−5 | 1.6 × 10−4 | ||
| Proton mass | 1.672 621 925 95(52) × 10−27 | kg | 3.1 × 10−10 | |
| Proton mass energy equivalent | 1.503 277 618 02(47) × 10−10 | J | 3.1 × 10−10 | |
| Proton mass energy equivalent in MeV | 938.272 089 43(29) | MeV | 3.1 × 10−10 | |
| Proton mass in u | 1.007 276 466 5789(83) | u | 8.2 × 10−12 | |
| Proton molar mass | 1.007 276 467 64(31) × 10−3 | kg mol−1 | 3.1 × 10−10 | |
| Proton-muon mass ratio | 8.880 243 38(20) | 2.3 × 10−8 | ||
| Proton-neutron magnetic moment ratio | −1.459 898 02(34) | 2.3 × 10−7 | ||
| Proton-neutron mass ratio | 0.998 623 477 97(40) | 4.0 × 10−10 | ||
| Proton relative atomic mass | 1.007 276 466 5789(83) | 8.2 × 10−12 | ||
| Proton rms charge radius | 8.4075(64) × 10−16 | m | 7.6 × 10−4 | |
| Proton-tau mass ratio | 0.528 051(36) | 6.8 × 10−5 | ||
| Reduced proton Compton wavelength | 2.103 089 100 51(66) × 10−16 | m | 3.1 × 10−10 | |
| Shielded proton gyromagnetic ratio | 2.675 153 194(11) × 108 | s−1 T−1 | 4.1 × 10−9 | |
| Shielded proton gyromagnetic ratio in MHz/T | 42.576 385 43(17) | MHz T−1 | 4.0 × 10−9 | |
| Shielded proton magnetic moment | 1.410 570 5830(58) × 10−26 | J T−1 | 4.1 × 10−9 | |
| Shielded proton magnetic moment to Bohr magneton ratio | 1.520 993 1551(62) × 10−3 | 4.1 × 10−9 | ||
| Shielded proton magnetic moment to nuclear magneton ratio | 2.792 775 648(11) | 3.9 × 10−9 |
Neutron
| Symbol | Quantity | Value (uncertainty) | Unit | Rel. unc. |
|---|---|---|---|---|
| Neutron Compton wavelength | 1.319 590 903 82(67) × 10−15 | m | 5.1 × 10−10 | |
| Neutron-electron magnetic moment ratio | 1.040 668 84(24) × 10−3 | 2.3 × 10−7 | ||
| Neutron-electron mass ratio | 1838.683 662 00(74) | 4.0 × 10−10 | ||
| Neutron g factor | −3.826 085 52(90) | 2.4 × 10−7 | ||
| Neutron gyromagnetic ratio | 1.832 471 74(43) × 108 | s−1 T−1 | 2.3 × 10−7 | |
| Neutron gyromagnetic ratio in MHz/T | 29.164 6935(69) | MHz T−1 | 2.4 × 10−7 | |
| Neutron magnetic moment | −9.662 3653(23) × 10−27 | J T−1 | 2.4 × 10−7 | |
| Neutron magnetic moment to Bohr magneton ratio | −1.041 875 65(25) × 10−3 | 2.4 × 10−7 | ||
| Neutron magnetic moment to nuclear magneton ratio | −1.913 042 76(45) | 2.4 × 10−7 | ||
| Neutron mass | 1.674 927 500 56(85) × 10−27 | kg | 5.1 × 10−10 | |
| Neutron mass energy equivalent | 1.505 349 765 14(76) × 10−10 | J | 5.0 × 10−10 | |
| Neutron mass energy equivalent in MeV | 939.565 421 94(48) | MeV | 5.1 × 10−10 | |
| Neutron mass in u | 1.008 664 916 06(40) | u | 4.0 × 10−10 | |
| Neutron molar mass | 1.008 664 917 12(51) × 10−3 | kg mol−1 | 5.1 × 10−10 | |
| Neutron-muon mass ratio | 8.892 484 08(20) | 2.2 × 10−8 | ||
| Neutron-proton magnetic moment ratio | −0.684 979 35(16) | 2.3 × 10−7 | ||
| Neutron-proton mass difference | 2.305 574 61(67) × 10−30 | kg | 2.9 × 10−7 | |
| Neutron-proton mass difference energy equivalent | 2.072 147 12(60) × 10−13 | J | 2.9 × 10−7 | |
| Neutron-proton mass difference energy equivalent in MeV | 1.293 332 51(38) | MeV | 2.9 × 10−7 | |
| Neutron-proton mass difference in u | 1.388 449 48(40) × 10−3 | u | 2.9 × 10−7 | |
| Neutron-proton mass ratio | 1.001 378 419 46(40) | 4.0 × 10−10 | ||
| Neutron relative atomic mass | 1.008 664 916 06(40) | 4.0 × 10−10 | ||
| Neutron-tau mass ratio | 0.528 779(36) | 6.8 × 10−5 | ||
| Neutron to shielded proton magnetic moment ratio | −0.684 996 94(16) | 2.3 × 10−7 | ||
| Reduced neutron Compton wavelength | 2.100 194 1520(11) × 10−16 | m | 5.2 × 10−10 |
Deuteron
| Symbol | Quantity | Value (uncertainty) | Unit | Rel. unc. |
|---|---|---|---|---|
| Deuteron-electron magnetic moment ratio | −4.664 345 550(12) × 10−4 | 2.6 × 10−9 | ||
| Deuteron-electron mass ratio | 3670.482 967 655(63) | 1.7 × 10−11 | ||
| Deuteron g factor | 0.857 438 2335(22) | 2.6 × 10−9 | ||
| Deuteron magnetic moment | 4.330 735 087(11) × 10−27 | J T−1 | 2.5 × 10−9 | |
| Deuteron magnetic moment to Bohr magneton ratio | 4.669 754 568(12) × 10−4 | 2.6 × 10−9 | ||
| Deuteron magnetic moment to nuclear magneton ratio | 0.857 438 2335(22) | 2.6 × 10−9 | ||
| Deuteron mass | 3.343 583 7768(10) × 10−27 | kg | 3.0 × 10−10 | |
| Deuteron mass energy equivalent | 3.005 063 234 91(94) × 10−10 | J | 3.1 × 10−10 | |
| Deuteron mass energy equivalent in MeV | 1875.612 945 00(58) | MeV | 3.1 × 10−10 | |
| Deuteron mass in u | 2.013 553 212 544(15) | u | 7.4 × 10−12 | |
| Deuteron molar mass | 2.013 553 214 66(63) × 10−3 | kg mol−1 | 3.1 × 10−10 | |
| Deuteron-neutron magnetic moment ratio | −0.448 206 52(11) | 2.5 × 10−7 | ||
| Deuteron-proton magnetic moment ratio | 0.307 012 209 30(79) | 2.6 × 10−9 | ||
| Deuteron-proton mass ratio | 1.999 007 501 2699(84) | 4.2 × 10−12 | ||
| Deuteron relative atomic mass | 2.013 553 212 544(15) | 7.4 × 10−12 | ||
| Deuteron rms charge radius | 2.127 78(27) × 10−15 | m | 1.3 × 10−4 |
Triton
| Symbol | Quantity | Value (uncertainty) | Unit | Rel. unc. |
|---|---|---|---|---|
| Triton-electron mass ratio | 5496.921 535 51(21) | 3.8 × 10−11 | ||
| Triton g factor | 5.957 924 930(12) | 2.0 × 10−9 | ||
| Triton magnetic moment | 1.504 609 5178(30) × 10−26 | J T−1 | 2.0 × 10−9 | |
| Triton magnetic moment to Bohr magneton ratio | 1.622 393 6648(32) × 10−3 | 2.0 × 10−9 | ||
| Triton magnetic moment to nuclear magneton ratio | 2.978 962 4650(59) | 2.0 × 10−9 | ||
| Triton mass | 5.007 356 7512(16) × 10−27 | kg | 3.2 × 10−10 | |
| Triton mass energy equivalent | 4.500 387 8119(14) × 10−10 | J | 3.1 × 10−10 | |
| Triton mass energy equivalent in MeV | 2808.921 136 68(88) | MeV | 3.1 × 10−10 | |
| Triton mass in u | 3.015 500 715 97(10) | u | 3.3 × 10−11 | |
| Triton molar mass | 3.015 500 719 13(94) × 10−3 | kg mol−1 | 3.1 × 10−10 | |
| Triton-proton mass ratio | 2.993 717 034 03(10) | 3.3 × 10−11 | ||
| Triton relative atomic mass | 3.015 500 715 97(10) | 3.3 × 10−11 | ||
| Triton to proton magnetic moment ratio | 1.066 639 9189(21) | 2.0 × 10−9 |
Helion
| Symbol | Quantity | Value (uncertainty) | Unit | Rel. unc. |
|---|---|---|---|---|
| Helion-electron mass ratio | 5495.885 279 84(16) | 2.9 × 10−11 | ||
| Helion g factor | −4.255 250 6995(34) | 8.0 × 10−10 | ||
| Helion magnetic moment | −1.074 617 551 98(93) × 10−26 | J T−1 | 8.7 × 10−10 | |
| Helion magnetic moment to Bohr magneton ratio | −1.158 740 980 83(94) × 10−3 | 8.1 × 10−10 | ||
| Helion magnetic moment to nuclear magneton ratio | −2.127 625 3498(17) | 8.0 × 10−10 | ||
| Helion mass | 5.006 412 7862(16) × 10−27 | kg | 3.2 × 10−10 | |
| Helion mass energy equivalent | 4.499 539 4185(14) × 10−10 | J | 3.1 × 10−10 | |
| Helion mass energy equivalent in MeV | 2808.391 611 12(88) | MeV | 3.1 × 10−10 | |
| Helion mass in u | 3.014 932 246 932(74) | u | 2.5 × 10−11 | |
| Helion molar mass | 3.014 932 250 10(94) × 10−3 | kg mol−1 | 3.1 × 10−10 | |
| Helion-proton mass ratio | 2.993 152 671 552(70) | 2.3 × 10−11 | ||
| Helion relative atomic mass | 3.014 932 246 932(74) | 2.5 × 10−11 | ||
| Helion shielding shift | 5.996 7029(23) × 10−5 | 3.8 × 10−7 | ||
| Shielded helion gyromagnetic ratio | 2.037 894 6078(18) × 108 | s−1 T−1 | 8.8 × 10−10 | |
| Shielded helion gyromagnetic ratio in MHz/T | 32.434 100 033(28) | MHz T−1 | 8.6 × 10−10 | |
| Shielded helion magnetic moment | −1.074 553 110 35(93) × 10−26 | J T−1 | 8.7 × 10−10 | |
| Shielded helion magnetic moment to Bohr magneton ratio | −1.158 671 494 57(94) × 10−3 | 8.1 × 10−10 | ||
| Shielded helion magnetic moment to nuclear magneton ratio | −2.127 497 7624(17) | 8.0 × 10−10 | ||
| Shielded helion to proton magnetic moment ratio | −0.761 766 577 21(66) | 8.7 × 10−10 | ||
| Shielded helion to shielded proton magnetic moment ratio | −0.761 786 1334(31) | 4.1 × 10−9 |
Alpha particle
| Symbol | Quantity | Value (uncertainty) | Unit | Rel. unc. |
|---|---|---|---|---|
| Alpha particle-electron mass ratio | 7294.299 541 71(17) | 2.3 × 10−11 | ||
| Alpha particle mass | 6.644 657 3450(21) × 10−27 | kg | 3.2 × 10−10 | |
| Alpha particle mass energy equivalent | 5.971 920 1997(19) × 10−10 | J | 3.2 × 10−10 | |
| Alpha particle mass energy equivalent in MeV | 3727.379 4118(12) | MeV | 3.2 × 10−10 | |
| Alpha particle mass in u | 4.001 506 179 129(62) | u | 1.5 × 10−11 | |
| Alpha particle molar mass | 4.001 506 1833(12) × 10−3 | kg mol−1 | 3.0 × 10−10 | |
| Alpha particle-proton mass ratio | 3.972 599 690 252(70) | 1.8 × 10−11 | ||
| Alpha particle relative atomic mass | 4.001 506 179 129(62) | 1.5 × 10−11 | ||
| Alpha particle rms charge radius | 1.6785(21) × 10−15 | m | 1.3 × 10−3 |