2018 CODATA adjustment From: http://physics.nist.gov/constants Fundamental Physical Constants — Extensive Listing Relative std. Quantity Symbol Value Unit uncert. ur UNIVERSAL speed of light in vacuum c 299 792 458 m s−1 exact 2 −6 −2 −10 vacuum magnetic permeability 4pα¯h=e c µ0 1:256 637 062 12(19) × 10 NA 1:5 × 10 −7 −2 −10 µ0=(4p × 10 ) 1:000 000 000 55(15) NA 1:5 × 10 2 −12 −1 −10 vacuum electric permittivity 1/µ0c 0 8:854 187 8128(13) × 10 F m 1:5 × 10 −10 characteristic impedance of vacuum µ0c Z0 376:730 313 668(57) Ω 1:5 × 10 Newtonian constant of gravitation G 6:674 30(15) × 10−11 m3 kg−1 s−2 2:2 × 10−5 G=¯hc 6:708 83(15) × 10−39 (GeV=c2)−2 2:2 × 10−5 Planck constant∗ h 6:626 070 15 × 10−34 J Hz−1 exact 4:135 667 696 ::: × 10−15 eV Hz−1 exact ¯h 1:054 571 817 ::: × 10−34 J s exact 6:582 119 569 ::: × 10−16 eV s exact ¯hc 197:326 980 4 ::: MeV fm exact 1=2 −8 −5 Planck mass (¯hc=G) mP 2:176 434(24) × 10 kg 1:1 × 10 2 19 −5 energy equivalent mPc 1:220 890(14) × 10 GeV 1:1 × 10 5 1=2 32 −5 Planck temperature (¯hc =G) =k TP 1:416 784(16) × 10 K 1:1 × 10 3 1=2 −35 −5 Planck length ¯h=mPc = (¯hG=c ) lP 1:616 255(18) × 10 m 1:1 × 10 5 1=2 −44 −5 Planck time lP=c = (¯hG=c ) tP 5:391 247(60) × 10 s 1:1 × 10 ELECTROMAGNETIC elementary charge e 1:602 176 634 × 10−19 C exact e=¯h 1:519 267 447 ::: × 1015 AJ−1 exact −15 magnetic flux quantum 2p¯h=(2e) Φ0 2:067 833 848 ::: × 10 Wb exact 2 −5 conductance quantum 2e =2p¯h G0 7:748 091 729 ::: × 10 S exact −1 inverse of conductance quantum G0 12 906:403 72 ::: Ω exact 9 −1 Josephson constant 2e=h KJ 483 597:848 4 ::: × 10 Hz V exact 2 von Klitzing constant µ0c=2α = 2p¯h=e RK 25 812:807 45 ::: Ω exact −24 −1 −10 Bohr magneton e¯h=2me µB 9:274 010 0783(28) × 10 JT 3:0 × 10 5:788 381 8060(17) × 10−5 eV T−1 3:0 × 10−10 10 −1 −10 µB=h 1:399 624 493 61(42) × 10 Hz T 3:0 × 10 −1 −1 y −10 µB=hc 46:686 447 783(14) [m T ] 3:0 × 10 −1 −10 µB=k 0:671 713 815 63(20) KT 3:0 × 10 −27 −1 −10 nuclear magneton e¯h=2mp µN 5:050 783 7461(15) × 10 JT 3:1 × 10 3:152 451 258 44(96) × 10−8 eV T−1 3:1 × 10−10 −1 −10 µN=h 7:622 593 2291(23) MHz T 3:1 × 10 −2 −1 −1 y −10 µN=hc 2:542 623 413 53(78) × 10 [m T ] 3:1 × 10 −4 −1 −10 µN=k 3:658 267 7756(11) × 10 KT 3:1 × 10 ATOMIC AND NUCLEAR General 2 −3 −10 fine-structure constant e =4p0¯hc α 7:297 352 5693(11) × 10 1:5 × 10 inverse fine-structure constant α−1 137:035 999 084(21) 1:5 × 10−10 2 2 15 −12 Rydberg frequency α mec =2h = Eh=2h cR1 3:289 841 960 2508(64) × 10 Hz 1:9 × 10 −18 −12 energy equivalent hc R1 2:179 872 361 1035(42) × 10 J 1:9 × 10 13:605 693 122 994(26) eV 1:9 × 10−12 −1 y −12 Rydberg constant R1 10 973 731:568 160(21) [m ] 1:9 × 10 2 2 −11 −10 Bohr radius ¯h/αmec = 4p0¯h =mee a0 5:291 772 109 03(80) × 10 m 1:5 × 10 2 2 2 −18 −12 Hartree energy α mec = e =4p0a0 = 2hcR1 Eh 4:359 744 722 2071(85) × 10 J 1:9 × 10 27:211 386 245 988(53) eV 1:9 × 10−12 −4 2 −1 −10 quantum of circulation p¯h=me 3:636 947 5516(11) × 10 m s 3:0 × 10 Page 1 2018 CODATA adjustment From: http://physics.nist.gov/constants Fundamental Physical Constants — Extensive Listing Relative std. Quantity Symbol Value Unit uncert. ur −4 2 −1 −10 2p¯h=me 7:273 895 1032(22) × 10 m s 3:0 × 10 Electroweak z 3 −5 −2 −7 Fermi coupling constant GF=(¯hc) 1:166 3787(6) × 10 GeV 5:1 × 10 x weak mixing angle θW (on-shell scheme) 2 2 2 2 −3 sin θW = sW ≡ 1 − (mW=mZ) sin θW 0:222 90(30) 1:3 × 10 Electron, e− −31 −10 electron mass me 9:109 383 7015(28) × 10 kg 3:0 × 10 5:485 799 090 65(16) × 10−4 u 2:9 × 10−11 2 −14 −10 energy equivalent mec 8:187 105 7769(25) × 10 J 3:0 × 10 0:510 998 950 00(15) MeV 3:0 × 10−10 −3 −8 electron-muon mass ratio me=mm 4:836 331 69(11) × 10 2:2 × 10 −4 −5 electron-tau mass ratio me=mt 2:875 85(19) × 10 6:8 × 10 −4 −11 electron-proton mass ratio me=mp 5:446 170 214 87(33) × 10 6:0 × 10 −4 −10 electron-neutron mass ratio me=mn 5:438 673 4424(26) × 10 4:8 × 10 −4 −11 electron-deuteron mass ratio me=md 2:724 437 107 462(96) × 10 3:5 × 10 −4 −11 electron-triton mass ratio me=mt 1:819 200 062 251(90) × 10 5:0 × 10 −4 −11 electron-helion mass ratio me=mh 1:819 543 074 573(79) × 10 4:3 × 10 −4 −11 electron to alpha particle mass ratio me=ma 1:370 933 554 787(45) × 10 3:3 × 10 11 −1 −10 electron charge to mass quotient −e=me −1:758 820 010 76(53) × 10 C kg 3:0 × 10 −7 −1 −10 electron molar mass NAme M(e);Me 5:485 799 0888(17) × 10 kg mol 3:0 × 10 −13 −10 reduced Compton wavelength ¯h=mec = αa0 λC 3:861 592 6796(12) × 10 m 3:0 × 10 −12 y −10 Compton wavelength λC 2:426 310 238 67(73) × 10 [m] 3:0 × 10 2 −15 −10 classical electron radius α a0 re 2:817 940 3262(13) × 10 m 4:5 × 10 2 −29 2 −10 Thomson cross section (8p=3)re σe 6:652 458 7321(60) × 10 m 9:1 × 10 −24 −1 −10 electron magnetic moment µe −9:284 764 7043(28) × 10 JT 3:0 × 10 −13 to Bohr magneton ratio µe/µB −1:001 159 652 181 28(18) 1:7 × 10 −11 to nuclear magneton ratio µe/µN −1838:281 971 88(11) 6:0 × 10 electron magnetic moment −3 −10 anomaly jµej/µB − 1 ae 1:159 652 181 28(18) × 10 1:5 × 10 −13 electron g-factor −2(1 + ae) ge −2:002 319 304 362 56(35) 1:7 × 10 −8 electron-muon magnetic moment ratio µe/µm 206:766 9883(46) 2:2 × 10 −10 electron-proton magnetic moment ratio µe/µp −658:210 687 89(20) 3:0 × 10 electron to shielded proton magnetic ◦ 0 −8 moment ratio (H2O, sphere, 25 C) µe/µp −658:227 5971(72) 1:1 × 10 −7 electron-neutron magnetic moment ratio µe/µn 960:920 50(23) 2:4 × 10 −9 electron-deuteron magnetic moment ratio µe/µd −2143:923 4915(56) 2:6 × 10 electron to shielded helion magnetic ◦ 0 −8 moment ratio (gas, sphere, 25 C) µe/µh 864:058 257(10) 1:2 × 10 11 −1 −1 −10 electron gyromagnetic ratio 2jµej=¯h γe 1:760 859 630 23(53) × 10 s T 3:0 × 10 28 024:951 4242(85) MHz T−1 3:0 × 10−10 Muon, m− −28 −8 muon mass mm 1:883 531 627(42) × 10 kg 2:2 × 10 0:113 428 9259(25) u 2:2 × 10−8 2 −11 −8 energy equivalent mmc 1:692 833 804(38) × 10 J 2:2 × 10 105:658 3755(23) MeV 2:2 × 10−8 −8 muon-electron mass ratio mm=me 206:768 2830(46) 2:2 × 10 −2 −5 muon-tau mass ratio mm=mt 5:946 35(40) × 10 6:8 × 10 −8 muon-proton mass ratio mm=mp 0:112 609 5264(25) 2:2 × 10 Page 2 2018 CODATA adjustment From: http://physics.nist.gov/constants Fundamental Physical Constants — Extensive Listing Relative std. Quantity Symbol Value Unit uncert. ur −8 muon-neutron mass ratio mm=mn 0:112 454 5170(25) 2:2 × 10 −4 −1 −8 muon molar mass NAmm M(m);Mm 1:134 289 259(25) × 10 kg mol 2:2 × 10 −15 −8 reduced muon Compton wavelength ¯h=mmc λC;m 1:867 594 306(42) × 10 m 2:2 × 10 −14 y −8 muon Compton wavelength λC;m 1:173 444 110(26) × 10 [m] 2:2 × 10 −26 −1 −8 muon magnetic moment µm −4:490 448 30(10) × 10 JT 2:2 × 10 −3 −8 to Bohr magneton ratio µm/µB −4:841 970 47(11) × 10 2:2 × 10 −8 to nuclear magneton ratio µm/µN −8:890 597 03(20) 2:2 × 10 muon magnetic moment anomaly −3 −7 jµmj=(e¯h=2mm) − 1 am 1:165 920 89(63) × 10 5:4 × 10 −10 muon g-factor −2(1 + am) gm −2:002 331 8418(13) 6:3 × 10 −8 muon-proton magnetic moment ratio µm/µp −3:183 345 142(71) 2:2 × 10 Tau, t− { −27 −5 tau mass mt 3:167 54(21) × 10 kg 6:8 × 10 1:907 54(13) u 6:8 × 10−5 2 −10 −5 energy equivalent mtc 2:846 84(19) × 10 J 6:8 × 10 1776:86(12) MeV 6:8 × 10−5 −5 tau-electron mass ratio mt=me 3477:23(23) 6:8 × 10 −5 tau-muon mass ratio mt=mm 16:8170(11) 6:8 × 10 −5 tau-proton mass ratio mt=mp 1:893 76(13) 6:8 × 10 −5 tau-neutron mass ratio mt=mn 1:891 15(13) 6:8 × 10 −3 −1 −5 tau molar mass NAmt M(t);Mt 1:907 54(13) × 10 kg mol 6:8 × 10 −16 −5 reduced tau Compton wavelength ¯h=mtc λC;t 1:110 538(75) × 10 m 6:8 × 10 −16 y −5 tau Compton wavelength λC;t 6:977 71(47) × 10 [m] 6:8 × 10 Proton, p −27 −10 proton mass mp 1:672 621 923 69(51) × 10 kg 3:1 × 10 1:007 276 466 621(53) u 5:3 × 10−11 2 −10 −10 energy equivalent mpc 1:503 277 615 98(46) × 10 J 3:1 × 10 938:272 088 16(29) MeV 3:1 × 10−10 −11 proton-electron mass ratio mp=me 1836:152 673 43(11) 6:0 × 10 −8 proton-muon mass ratio mp=mm 8:880 243 37(20) 2:2 × 10 −5 proton-tau mass ratio mp=mt 0:528 051(36) 6:8 × 10 −10 proton-neutron mass ratio mp=mn 0:998 623 478 12(49) 4:9 × 10 7 −1 −10 proton charge to mass quotient e=mp 9:578 833 1560(29) × 10 C kg 3:1 × 10 −3 −1 −10 proton molar mass NAmp M(p), Mp 1:007 276 466 27(31) × 10 kg mol 3:1 × 10 −16 −10 reduced proton Compton wavelength ¯h=mpc λC;p 2:103 089 103 36(64) × 10 m 3:1 × 10 −15 y −10 proton Compton wavelength λC;p 1:321 409 855 39(40) × 10 [m] 3:1 × 10 −16 −3 proton rms charge radius rp 8:414(19) × 10 m 2:2 × 10 −26 −1 −10 proton magnetic moment µp 1:410 606 797 36(60) × 10 JT 4:2 × 10 −3 −10 to Bohr magneton ratio µp/µB 1:521 032 202 30(46) × 10 3:0 × 10 −10 to nuclear magneton ratio µp/µN 2:792 847 344 63(82) 2:9 × 10 −10 proton g-factor 2µp/µN gp 5:585 694 6893(16) 2:9 × 10 −7 proton-neutron magnetic moment ratio µp/µn −1:459 898 05(34) 2:4 × 10 0 −26 −1 −8 shielded proton magnetic moment µp 1:410 570 560(15) × 10 JT 1:1 × 10 ◦ (H2O, sphere, 25 C) 0 −3 −8 to Bohr magneton ratio µp/µB 1:520 993 128(17) × 10 1:1 × 10 0 −8 to nuclear magneton ratio µp/µN 2:792 775 599(30) 1:1 × 10 proton magnetic shielding correction 0 ◦ 0 −5 −4 1 − µp/µp (H2O, sphere, 25 C) σp 2:5689(11) × 10 4:2 × 10 Page 3 2018 CODATA adjustment From: http://physics.nist.gov/constants Fundamental Physical Constants — Extensive Listing Relative std.