From: physics. nist. gov/constants Fundamental Physical Constants- Complete Listing Relative std UNIVERSAL speed of light in vacuum c,co299792458 ms-l (exact) 4xx10 NA 12.566370614..×10-7NA (exact) electric constant 1/uoc 8.854187817×10-12F (exact) characteristic impedance 376.73031346 Newtonian constant of gravitation G 6673(10)×10-1 3kg-1s-21.5×10 G/hc6.707(10)×10-39 (Gev/c2)-21.5×10-3 Planck constant h 662606876(52)×10-34Js 7.8×10=8 In ev s 413566727(16)×10-15eV 3.9×10° h/2 九 1.054571596(82)×10-34Js 7.8×10-8 6.58211889(26)×10-16eVs 39×10-8 12 Planck length h/mpc=(hG/33)/2Ip 16160(12)×10-35 7.5×10- Planck time lp/c=(nG/c5)/2 53906(40)×10 7.5×10 ELECTROMAGNETIC elementary charge 1.602176462(63) 3.9×10 e/h2.417989491(95)×1014AJ 3.9×10-8 magnetic flux quantum h/2e 206783363681)×10-15Wb 3.9×10-8 conductance quantum 2e2/h 7748091696(28)×10-5S inverse of conductance quantum G0 12906.403786(47) 3.7×10-9 osephson constant 2e/h 483597898(19)×109 Hz v-I von Klitzing constant h/e2= uoc/ 25812.807572(95) 3.7×10 Bohr magneton eh/2me 927400899(37)×10-26JT-1 4.0×10-8 ineV T 5788381749(43)×10-5 evT-l 73×10-9 B/h13.99624624(56)×109HzT-1 4.0×10 B/hc46.6864521(19) m 4.0×10-8 B/k0.6717131(12) KT 1.7×10 nuclear magneton eh/2mp 505078317(20)×10-27JT-1 4.0×10 ineV t 3152451238(24)×10-8eVT 7.6×10-9 八N/h7.62259396(31) MHZ T 4.0×10-8 N/hc2.54262366(10)×10-2m-1T- 4.0×10-8 /k3.6582638(64)×10 KT 1.7×10 ATOMIC AND NUCLEAR fine-structure constante2/eohc 729735253327)×10-3 3.7× inverse fine-structure constant 137.03599976(50) Journal of Physical and Chemical Reference Data, Vol. 28, No. 6, 1999 and Reviews of Modern Physics, Vol. 72, No. 2, 2000
From: physics.nist.gov/constants Fundamental Physical Constants — Complete Listing Relative std. Quantity Symbol Value Unit uncert. ur UNIVERSAL speed of light in vacuum c, c0 299 792 458 m s−1 (exact) magnetic constant µ0 4π × 10−7 N A−2 = 12.566 370614... × 10−7 N A−2 (exact) electric constant 1/µ0c2 ε0 8.854 187 817... × 10−12 F m−1 (exact) characteristic impedance of vacuum √µ0/0 = µ0c Z0 376.730 313 461... (exact) Newtonian constant of gravitation G 6.673(10) × 10−11 m3 kg−1 s−2 1.5 × 10−3 G/c 6.707(10) × 10−39 (GeV/c2)−2 1.5 × 10−3 Planck constant h 6.626 068 76(52)× 10−34 Js 7.8 × 10−8 in eV s 4.135 667 27(16)× 10−15 eV s 3.9 × 10−8 h/2π 1.054 571 596(82) × 10−34 Js 7.8 × 10−8 in eV s 6.582 118 89(26) × 10−16 eV s 3.9 × 10−8 Planck mass (c/G)1/2 mP 2.1767(16) × 10−8 kg 7.5 × 10−4 Planck length /mPc = (G/c3)1/2 lP 1.6160(12) × 10−35 m 7.5 × 10−4 Planck time lP/c = (G/c5)1/2 tP 5.3906(40) × 10−44 s 7.5 × 10−4 ELECTROMAGNETIC elementary charge e 1.602 176 462(63) × 10−19 C 3.9 × 10−8 e/h 2.417 989 491(95)× 1014 A J−1 3.9 × 10−8 magnetic flux quantum h/2e 80 2.067 833 636(81)× 10−15 Wb 3.9 × 10−8 conductance quantum 2e2 /h G0 7.748 091 696(28)× 10−5 S 3.7 × 10−9 inverse of conductance quantum G−1 0 12 906.403 786(47) 3.7 × 10−9 Josephson constanta 2e/h KJ 483 597.898(19)× 109 Hz V−1 3.9 × 10−8 von Klitzing constantb h/e2 = µ0c/2α RK 25 812.807 572(95) 3.7 × 10−9 Bohr magneton e/2me µB 927.400 899(37) × 10−26 J T−1 4.0 × 10−8 in eV T−1 5.788 381 749(43)× 10−5 eV T−1 7.3 × 10−9 µB/h 13.996 246 24(56)× 109 Hz T−1 4.0 × 10−8 µB/hc 46.686 4521(19) m−1 T−1 4.0 × 10−8 µB/k 0.671 7131(12) K T−1 1.7 × 10−6 nuclear magneton e/2mp µN 5.050 783 17(20) × 10−27 J T−1 4.0 × 10−8 in eV T−1 3.152 451 238(24) × 10−8 eV T−1 7.6 × 10−9 µN/h 7.622 593 96(31) MHz T−1 4.0 × 10−8 µN/hc 2.542 623 66(10) × 10−2 m−1 T−1 4.0 × 10−8 µN/k 3.658 2638(64)× 10−4 K T−1 1.7 × 10−6 ATOMIC AND NUCLEAR General fine-structure constant e2 /4π0c α 7.297 352533(27) × 10−3 3.7 × 10−9 inverse fine-structure constant α−1 137.035 999 76(50) 3.7 × 10−9 Page 1 Source: Peter J. Mohr and Barry N. Taylor, CODATA Recommended Values of the Fundamental Physical Constants: 1998, Journal of Physical and Chemical Reference Data, Vol. 28, No. 6, 1999 and Reviews of Modern Physics, Vol. 72, No. 2, 2000
From: physics. nist. gov/constants Fundamental Physical Constants- Complete listing Relative std ydberg constant a-mec/2h 10973731.568549(83) 7.6×10=12 3289841960368(25)×1015Hz 7.6×10- 2.17987190(17)×10 Roohc in ev 13.60569172(53) 3.9×10-8 Bohr radius a/4xR∞=4x∈0h2/me2ao 0.5291772083(19)×10-10m 3.7×10-9 Hartree energy e2/4TE0a0=2Roohc 435974381(34)×10-18J 78×10-8 In h/2me3.636947516(27)×10-4ev 27.2113834(1 quantum of circulation s-17.3×10-9 h/m 7273895032(53)×10-4m2s-17.3×10 Fermi coupling constant GF/(hc)31.166391)×10-5 86×10-6 weak mixing angled ow(on-shell scheme) sinew 0.2224(19) 87×10-3 electron mass 910938188(72)×10-31kg 79×10-8 in u, me= Ar(e)u(electron relative atomic mass times u) 54857991012)×10-4 2.1×10 energy equivalent 818710414(64)×10 7.9×10 n mev 0.510998902(21) Mev 4.0×10-8 electron -muon mass ratio ml/m14.8363210(15) 3.0×10-8 electron-tau mass ratio me/mx28755547)×10-4 1.6×10-4 electron-proton mass ratio me/mp5.446170232(12)×10-4 2.1×10 electron-neutron mass ratio 5438673462(12)×10-4 electron-deuteron mass ratio 27244371170(58)×10-4 2.1×10- electron to alpha particle mass ratio me/ml1.3709335611(29)×10-4 electron charge to mass quotient 1758820174(71)× Ckg 40×10-8 electron molar mass Name M(e),M5.485799110(12)×10-7 kg mol-12.1×10 Compton wavelength h/mec 2426310215(8)×10-12m 73×10-9 λC/2x=aao=a2/4xR NC 3861592642(28)×10 7.3×10-9 classical electron radius a ao 2817940285(31)×10-15m 1.1×10=8 Thomson cross section(8T/3)r2 0665245854(15)×10-28m 2.2×10 electron magnetic moment 928476362(37)×10-26JT-140×10-8 to bohr magneton ratio He/uB 11596521869(41) to nuclear magneton ratio /u -1838.2819660(39) 2.1×10 electron magnetic moment anomaly luel/uB-1 11596521869(41)×10-3 3.5×10-9 electron g-factor -2(1+ae) 2.0023193043737(82) 4.1×10-12 electron-muon letic moment ratio e/pp206766972063) 3.0×10-8 Page 2 Journal of Physical and Chemical Reference Data, Vol. 28, No. 6, 1999 and Reviews of Modern Physics, Vol. 72, No. 2, 2000
From: physics.nist.gov/constants Fundamental Physical Constants — Complete Listing Relative std. Quantity Symbol Value Unit uncert. ur Rydberg constant α2mec/2h R∞ 10 973 731.568 549(83) m−1 7.6 × 10−12 R∞c 3.289 841 960368(25) × 1015 Hz 7.6 × 10−12 R∞hc 2.179 871 90(17) × 10−18 J 7.8 × 10−8 R∞hc in eV 13.605 691 72(53) eV 3.9 × 10−8 Bohr radius α/4π R∞ = 4π02 /mee2 a0 0.529 177 2083(19)× 10−10 m 3.7 × 10−9 Hartree energy e2 /4πε0a0 = 2R∞hc = α2mec2 Eh 4.359 743 81(34)× 10−18 J 7.8 × 10−8 in eV 27.211 3834(11) eV 3.9 × 10−8 quantum of circulation h/2me 3.636 947 516(27)× 10−4 m2 s−1 7.3 × 10−9 h/me 7.273 895 032(53)× 10−4 m2 s−1 7.3 × 10−9 Electroweak Fermi coupling constantc GF/(c)3 1.166 39(1) × 10−5 GeV−2 8.6 × 10−6 weak mixing angled θW (on-shell scheme) sin2 θW = s2 W ≡ 1 − (mW/mZ)2 sin2 θW 0.2224(19) 8.7 × 10−3 Electron, e− electron mass me 9.109 381 88(72)× 10−31 kg 7.9 × 10−8 in u, me = Ar(e) u (electron relative atomic mass times u) 5.485 799 110(12)× 10−4 u 2.1 × 10−9 energy equivalent mec2 8.187 10414(64) × 10−14 J 7.9 × 10−8 in MeV 0.510 998 902(21) MeV 4.0 × 10−8 electron-muon mass ratio me/mµ 4.836 332 10(15) × 10−3 3.0 × 10−8 electron-tau mass ratio me/mτ 2.875 55(47) × 10−4 1.6 × 10−4 electron-proton mass ratio me/mp 5.446 170 232(12) × 10−4 2.1 × 10−9 electron-neutron mass ratio me/mn 5.438 673 462(12)× 10−4 2.2 × 10−9 electron-deuteron mass ratio me/md 2.724 437 1170(58) × 10−4 2.1 × 10−9 electron to alpha particle mass ratio me/mα 1.370 933 5611(29) × 10−4 2.1 × 10−9 electron charge to mass quotient −e/me −1.758 820 174(71) × 1011 C kg−1 4.0 × 10−8 electron molar mass NAme M(e), Me 5.485 799 110(12)× 10−7 kg mol−1 2.1 × 10−9 Compton wavelength h/mec λC 2.426 310 215(18) × 10−12 m 7.3 × 10−9 λC/2π = αa0 = α2 /4π R∞ C 386.159 2642(28)× 10−15 m 7.3 × 10−9 classical electron radius α2a0 re 2.817 940 285(31) × 10−15 m 1.1 × 10−8 Thomson cross section (8π/3)r 2 e σe 0.665 245 854(15)× 10−28 m2 2.2 × 10−8 electron magnetic moment µe −928.476 362(37)× 10−26 J T−1 4.0 × 10−8 to Bohr magneton ratio µe/µB −1.001 159 6521869(41) 4.1 × 10−12 to nuclear magneton ratio µe/µN −1 838.281 9660(39) 2.1 × 10−9 electron magnetic moment anomaly |µe|/µB − 1 ae 1.159 652 1869(41) × 10−3 3.5 × 10−9 electron g-factor −2(1 + ae) ge −2.002 319 3043737(82) 4.1 × 10−12 electron-muon magnetic moment ratio µe/µµ 206.766 9720(63) 3.0 × 10−8 Page 2 Source: Peter J. Mohr and Barry N. Taylor, CODATA Recommended Values of the Fundamental Physical Constants: 1998, Journal of Physical and Chemical Reference Data, Vol. 28, No. 6, 1999 and Reviews of Modern Physics, Vol. 72, No. 2, 2000
From: physics. nist. gov/constants Fundamental Physical Constants-Complete listing Relative std Quantity Value uncert. lr electron-proton magnetic moment ratio ue/u -658.2106875(66) 10×10=8 electron to shielded proton magnetic moment ratio 658.2275954(71) l×10 (H2O, sphere,25°C) electron-neutron magnetic moment ratio pe/an 96092050(23) 2.4×10- electron-deuteron magnetic moment ratio -2143.923498(23) 1.1×10-8 electron to shielded helion magnetic moment ratio /864.05825510) 1.2×10-8 (gas, sphere,25°C) electron gyromagnetic ratio 2lueI/h ye 1.760859794(71)×1011s-1T-140×10- 28024.9540(11) MHzT-140×10-8 Muon, u muon mass 188353109(16)×10-28kg 84×10-8 in u, mu= Ar(u)u(muon relative atomic mass times u) 0.1134 8(34) 3.0×10 energy equivalent 1.69283332(14)×10-11J in mev 105.6583568(52) Mev 4.9×10-8 muon-electron mass ratio m/me206.7682657(63) 30×10-8 muon -tau mass ratio 94572(97)×10-2 muon-proton mass ratio m1/mp0.1126095173(34) 3.0×10-8 muon-neutron mass ratio m/mn0.124545079(34) muon molar mass NAmu M(),M40.34289168(34)×10-3 kg mol-13.0×10-8 muon Compton wavelength h/ 1173444197(35)×10-15m 2.9×10-8 1.86759444455)×10-15m 2.9×10=8 muon magnetic moment μμ -449044813(22)×10-26JT-1 to bohr magneton ratio -4.84197085(15)×10-3 3.0×10-8 to nuclear magneton ratio Au/uN 889059770(27) 3.0×10-8 muon magnetic moment anomaly p∥(eh/2m1)-1 116591602(64)×10-3 5.5×10- muon g-factor-2(1+ au) gt 2.0023318320(13) 6.4×10-10 magnetic mo ratio μ 3.18334539(10) 3.2×10 au. T 316788(52)×10-27 1.6×10-4 inu, mt= Ar()u(tau relative atomic mass times u) 1.90774(31) 1.6×10-4 energy equivalent c 284715(46)×10-10 J 1.6×10 in me v 1777.05(29) Mev 1.6×10-4 Journal of Physical and Chemical Reference Data, Vol. 28, No. 6, 1999 and Reviews of Modern Physics, Vol. 72, No. 2, 2000
From: physics.nist.gov/constants Fundamental Physical Constants — Complete Listing Relative std. Quantity Symbol Value Unit uncert. ur electron-proton magnetic moment ratio µe/µp − 658.2106875(66) 1.0 × 10−8 electron to shielded proton magnetic moment ratio µe/µ0 p − 658.227 5954(71) 1.1 × 10−8 (H2O, sphere, 25 ◦C) electron-neutron magnetic moment ratio µe/µn 960.920 50(23) 2.4 × 10−7 electron-deuteron magnetic moment ratio µe/µd −2 143.923 498(23) 1.1 × 10−8 electron to shielded helione magnetic moment ratio µe/µ0 h 864.058 255(10) 1.2 × 10−8 (gas, sphere, 25 ◦C) electron gyromagnetic ratio 2|µe|/ γe 1.760 859 794(71) × 1011 s−1 T−1 4.0 × 10−8 γe/2π 28 024.9540(11) MHz T−1 4.0 × 10−8 Muon, µ− muon mass mµ 1.883 531 09(16)× 10−28 kg 8.4 × 10−8 in u, mµ = Ar(µ) u (muon relative atomic mass times u) 0.113 428 9168(34) u 3.0 × 10−8 energy equivalent mµc2 1.692 833 32(14) × 10−11 J 8.4 × 10−8 in MeV 105.658 3568(52) MeV 4.9 × 10−8 muon-electron mass ratio mµ/me 206.768 2657(63) 3.0 × 10−8 muon-tau mass ratio mµ/mτ 5.945 72(97) × 10−2 1.6 × 10−4 muon-proton mass ratio mµ/mp 0.112 609 5173(34) 3.0 × 10−8 muon-neutron mass ratio mµ/mn 0.112 454 5079(34) 3.0 × 10−8 muon molar mass NAmµ M(µ), Mµ 0.113 428 9168(34)× 10−3 kg mol−1 3.0 × 10−8 muon Compton wavelength h/mµc λC,µ 11.734 441 97(35) × 10−15 m 2.9 × 10−8 λC,µ/2π C,µ 1.867 594444(55) × 10−15 m 2.9 × 10−8 muon magnetic moment µµ −4.490 448 13(22) × 10−26 J T−1 4.9 × 10−8 to Bohr magneton ratio µµ/µB −4.841 97085(15) × 10−3 3.0 × 10−8 to nuclear magneton ratio µµ/µN −8.890 597 70(27) 3.0 × 10−8 muon magnetic moment anomaly |µµ|/(e/2mµ) − 1 aµ 1.165 916 02(64)× 10−3 5.5 × 10−7 muon g-factor −2(1 + aµ) gµ −2.002 331 8320(13) 6.4 × 10−10 muon-proton magnetic moment ratio µµ/µp −3.183 345 39(10) 3.2 × 10−8 Tau, τ − tau massf mτ 3.167 88(52) × 10−27 kg 1.6 × 10−4 in u, mτ = Ar(τ) u (tau relative atomic mass times u) 1.907 74(31) u 1.6 × 10−4 energy equivalent mτc2 2.847 15(46) × 10−10 J 1.6 × 10−4 in MeV 1 777.05(29) MeV 1.6 × 10−4 Page 3 Source: Peter J. Mohr and Barry N. Taylor, CODATA Recommended Values of the Fundamental Physical Constants: 1998, Journal of Physical and Chemical Reference Data, Vol. 28, No. 6, 1999 and Reviews of Modern Physics, Vol. 72, No. 2, 2000
From: physics. nist. gov/constants Fundamental Physical Constants-Complete Listing Relative std Quantity Symbol Value Unit uncert. Il tau-electron mass ratio n/me3477.60(57) 16×10-4 tau-muon mass ratio i/ 168188(27) 1.6×10 tau-proton mass ratio m/mp1.89396(31) 1.6×10 tau-neutron mass ratio m/mn189135(31) 1.6×10 tau molar mass NAm M(),M11.90774(31)×10-3 kg mol-11.6×10- tau Compton wavelength h/mc ic 069770(11)×10-15 1.6×10-4 0.l11042(18)×10 15 Proton, p proton mass 1.67262158(13)×10-27kg 79×10-8 Ar (p)u(pr relative atomic mass times u) 1.00727646688(13) 1.3×10-10 nergy equivalent mDC 1.50327731(12)×10-10J .9 in mev 938.271998(38) Mev 4.0×10-8 proton-electron mass ratio m1p/me1836.1526675(39) 2.1×10-9 proton-muon mass ratio mp/m8.88024408(27) 30×10-8 proton-tau mass ratio mp/m:0.527994(86) 16×10-4 proton-neutron mass ratio mp/mn0.99862347855(58) 58×10=10 proton charge to mass quotient 957883408(38)×107 C kg 4.0×10-8 proton molar mass NAmp M(p),M1.00727646688(13)×10-3 kg mol-11.3×10-10 proton Compton wavelength h/mpc A 1.321409847(10)×10-15m 7.6×10-9 0.2103089089(16)×10~15m 7.6×10-9 proton magnetic moment 1410606633(58×10-26JT-14.1×10-8 to bohr magneton ratio p/B1.521032203(15)×10-3 1.0×10-8 to nuclear magneton ratio 2.792847337029) 10×10-8 proton g-factor 2up/uN 5.585694675(57) 10×10-8 Toton-neutron magnetic moment ratio 1.45989805(34) 2.4×10-7 shielded proton magnetic moment 1.410570399(59)×10-26JT-1 4.2×10-8 (H2O, sphere, 25C to bohr magneton ratio p/μB 1.520993132(16)×10-3 1.1 to nuclear magneton rati Hm/N2.792775597(31) 1.1×10=8 proton magnetic shielding correction I-un/u 25687(15)×10-6 5.7×10-4 (H2O, sphere,25°C) proton gyromagnetic ratio 2pp/h 26752222(11)×108 4.l×10-8 /2r 42.5774825(18) MHzT-14.1×10 shielded proton gyromagnetic ratio 2un/h Yp 267515341(11)×108 S-I T 4.2×10-8 (H2O, sphere,25°C) y/2x425763888(18) MHzT-14.2×10-8 Journal of Physical and Chemical Reference Data, Vol. 28, No. 6, 1999 and Reviews of Modern Physics, Vol. 72, No. 2, 2000
From: physics.nist.gov/constants Fundamental Physical Constants — Complete Listing Relative std. Quantity Symbol Value Unit uncert. ur tau-electron mass ratio mτ/me 3 477.60(57) 1.6 × 10−4 tau-muon mass ratio mτ/mµ 16.8188(27) 1.6 × 10−4 tau-proton mass ratio mτ/mp 1.893 96(31) 1.6 × 10−4 tau-neutron mass ratio mτ/mn 1.891 35(31) 1.6 × 10−4 tau molar mass NAmτ M(τ), Mτ 1.907 74(31) × 10−3 kg mol−1 1.6 × 10−4 tau Compton wavelength h/mτc λC,τ 0.697 70(11) × 10−15 m 1.6 × 10−4 λC,τ/2π C,τ 0.111 042(18) × 10−15 m 1.6 × 10−4 Proton, p proton mass mp 1.672 621 58(13) × 10−27 kg 7.9 × 10−8 in u, mp = Ar(p) u (proton relative atomic mass times u) 1.007 276 466 88(13) u 1.3 × 10−10 energy equivalent mpc2 1.503 277 31(12)× 10−10 J 7.9 × 10−8 in MeV 938.271 998(38) MeV 4.0 × 10−8 proton-electron mass ratio mp/me 1 836.152 6675(39) 2.1 × 10−9 proton-muon mass ratio mp/mµ 8.880 244 08(27) 3.0 × 10−8 proton-tau mass ratio mp/mτ 0.527 994(86) 1.6 × 10−4 proton-neutron mass ratio mp/mn 0.998 623 478 55(58) 5.8 × 10−10 proton charge to mass quotient e/mp 9.578 834 08(38) × 107 C kg−1 4.0 × 10−8 proton molar mass NAmp M(p), Mp 1.007 276 466 88(13)× 10−3 kg mol−1 1.3 × 10−10 proton Compton wavelength h/mpc λC,p 1.321 409 847(10)× 10−15 m 7.6 × 10−9 λC,p/2π C,p 0.210 308 9089(16) × 10−15 m 7.6 × 10−9 proton magnetic moment µp 1.410 606 633(58) × 10−26 J T−1 4.1 × 10−8 to Bohr magneton ratio µp/µB 1.521 032 203(15) × 10−3 1.0 × 10−8 to nuclear magneton ratio µp/µN 2.792 847 337(29) 1.0 × 10−8 proton g-factor 2µp/µN gp 5.585 694 675(57) 1.0 × 10−8 proton-neutron magnetic moment ratio µp/µn −1.459 898 05(34) 2.4 × 10−7 shielded proton magnetic moment µ0 p 1.410 570 399(59) × 10−26 J T−1 4.2 × 10−8 (H2O, sphere, 25 ◦C) to Bohr magneton ratio µ0 p/µB 1.520 993 132(16) × 10−3 1.1 × 10−8 to nuclear magneton ratio µ0 p/µN 2.792 775 597(31) 1.1 × 10−8 proton magnetic shielding correction 1 − µ0 p/µp σ0 p 25.687(15) × 10−6 5.7 × 10−4 (H2O, sphere, 25 ◦C) proton gyromagnetic ratio 2µp/ γp 2.675 222 12(11) × 108 s−1 T−1 4.1 × 10−8 γp/2π 42.577 4825(18) MHz T−1 4.1 × 10−8 shielded proton gyromagnetic ratio 2µ0 p/ γ 0 p 2.675 153 41(11)× 108 s−1 T−1 4.2 × 10−8 (H2O, sphere, 25 ◦C) γ 0 p/2π 42.576 3888(18) MHz T−1 4.2 × 10−8 Neutron, n Page 4 Source: Peter J. Mohr and Barry N. Taylor, CODATA Recommended Values of the Fundamental Physical Constants: 1998, Journal of Physical and Chemical Reference Data, Vol. 28, No. 6, 1999 and Reviews of Modern Physics, Vol. 72, No. 2, 2000
From: physics. nist. gov/constants Fundamental Physical Constants-Complete listing Relative std Ouar Symbol Value Unit t uncert. Il neutron mass 167492716(13)×10-27 79×10=8 in u, mn= Ar(n)u(neutron relative atomic mass times u) 1.00866491578(55) 54×10-10 energy equivalent 50534946(12)×10-10J n mev 939565330(38) Mev 40×10-8 neutron-electron mass ratio 1838.6836550(40) 2.2×10 neutron-muon mass ratio 889248478(27) 3.0×10 neutron-tau mass ratio mn/m 0.528722(86) 16×10-4 neutron-proton mass ratio 1.00137841887(5 58×10-10 neutron molar mass Namn M(n),Mn1.00866491578(55)×10-3 kg mol-5.4×10 neutron Compton wavelength h/ mnc \C,n 1319590898(10)×10-15m 7.6×10-9 No 02100194142(16)×10-15m 7.6×10-9 neutron magnetic moment n -0.96623640(23)×10-26JT-124×10-7 to bohr magneton ratio /u 1.04187563(25)×10-3 2.4×10 to nuclear magneton ratio An/AN 1.91304272(45) 2.4×10 neutron g-factor 2un/uN 3.82608545(90) 24×10-7 neutron -electron moment ratio An/pe 1.04066882(25)×10-3 2.4×10-7 neutron-proton magnetic moment ratio 0.68497934(16) 2.4×10 neutron to shielded proton magnetic moment ratio pn/pp-0.68499694(16) 2.4×10 (H2O, sphere,25°C) neutron gyromagnetic ratio 2lunI/h 183247188(44)×108 2.4×10 29.1646958(70) MHzT-124×10- d deuteron mass 3.34358309(26)×10-27 79×10=8 in u, md= Ar(d)u(deuteron relative atomic mass times u) 2.01355321271(35) energy equivalent 3.00506262(24)×10-10J 7.9×10 n mev 1875.612762(75) Mev 4.0×10-8 deuteron-electron mass ratio md/m3670.4829550(78) 2.1×10-9 deuteron-proton mass rat m/mp1.99900750083(41) 2.0×10-10 deuteron molar mass Namd M(d),Ma2.01355321271(35)×10-3 kg mol-11.7×10-10 deuteron magnetic moment 18)×10-26JT-1 4.2×10 to bohr magneton ratio d/B0.4669754556(50)×10-3 to nuclear magneton ratio 1d/N0.574382284(94) 1.1×10 deuteron-electron magnetic moment ratio ud/ue 4664345537(50)×10-4 1.1×10-8 deuteron-proton magnetic moment ratIo 0.3070122083(45) 1.5×10 Journal of Physical and Chemical Reference Data, Vol. 28, No. 6, 1999 and Reviews of Modern Physics, Vol. 72, No. 2, 2000
From: physics.nist.gov/constants Fundamental Physical Constants — Complete Listing Relative std. Quantity Symbol Value Unit uncert. ur neutron mass mn 1.674 927 16(13) × 10−27 kg 7.9 × 10−8 in u, mn = Ar(n) u (neutron relative atomic mass times u) 1.008 664915 78(55) u 5.4 × 10−10 energy equivalent mnc2 1.505 349 46(12)× 10−10 J 7.9 × 10−8 in MeV 939.565 330(38) MeV 4.0 × 10−8 neutron-electron mass ratio mn/me 1 838.683 6550(40) 2.2 × 10−9 neutron-muon mass ratio mn/mµ 8.892 484 78(27) 3.0 × 10−8 neutron-tau mass ratio mn/mτ 0.528 722(86) 1.6 × 10−4 neutron-proton mass ratio mn/mp 1.001 378 418 87(58) 5.8 × 10−10 neutron molar mass NAmn M(n), Mn 1.008 664915 78(55) × 10−3 kg mol−1 5.4 × 10−10 neutron Compton wavelength h/mnc λC,n 1.319 590 898(10) × 10−15 m 7.6 × 10−9 λC,n/2π C,n 0.210 019 4142(16) × 10−15 m 7.6 × 10−9 neutron magnetic moment µn −0.966 236 40(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 04272(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 µn/µ0 p −0.684 996 94(16) 2.4 × 10−7 (H2O, sphere, 25 ◦C) neutron gyromagnetic ratio 2|µn|/ γn 1.832 471 88(44) × 108 s−1 T−1 2.4 × 10−7 γn/2π 29.164 6958(70) MHz T−1 2.4 × 10−7 Deuteron, d deuteron mass md 3.343 583 09(26)× 10−27 kg 7.9 × 10−8 in u, md = Ar(d) u (deuteron relative atomic mass times u) 2.013 553 21271(35) u 1.7 × 10−10 energy equivalent mdc2 3.005 062 62(24) × 10−10 J 7.9 × 10−8 in MeV 1 875.612 762(75) MeV 4.0 × 10−8 deuteron-electron mass ratio md/me 3 670.482 9550(78) 2.1 × 10−9 deuteron-proton mass ratio md/mp 1.999 007 50083(41) 2.0 × 10−10 deuteron molar mass NAmd M(d), Md 2.013 553 21271(35) × 10−3 kg mol−1 1.7 × 10−10 deuteron magnetic moment µd 0.433 073 457(18)× 10−26 J T−1 4.2 × 10−8 to Bohr magneton ratio µd/µB 0.466 975 4556(50)× 10−3 1.1 × 10−8 to nuclear magneton ratio µd/µN 0.857 438 2284(94) 1.1 × 10−8 deuteron-electron magnetic moment ratio µd/µe −4.664 345 537(50) × 10−4 1.1 × 10−8 deuteron-proton magnetic moment ratio µd/µp 0.307 012 2083(45) 1.5 × 10−8 Page 5 Source: Peter J. Mohr and Barry N. Taylor, CODATA Recommended Values of the Fundamental Physical Constants: 1998, Journal of Physical and Chemical Reference Data, Vol. 28, No. 6, 1999 and Reviews of Modern Physics, Vol. 72, No. 2, 2000
From: physics. nist. gov/constants Fundamental Physical Constants--Complete Listing Relative std Quant ntity Unit deuteron-neutron agnetic moment ratIo 0.44820652(11) 24×10-7 helion masse 5.0064l174039)×10 79×10-8 in u, mh= A()u(helion relative atomic mass times u) 3.01493223469(86) 2.8×10-10 energy equivalent 449953848(35)×10-10J 79×10-8 in me v 2808.39132(11 Mev .0×10 helion -electron m 5495.885238(12) 2.1×10-9 helion-proton mas mh/mp29931526585093) 3.1×10-10 elion molar mass NAmh M(h,M3.01493223469(86)×10-3kgmo-l2.8×10-10 shielded helion magnetic moment 1.074552967(45)×10-26JT14.2×10-8 (gas, sphere,25°C) to bohr magneton ratio uh/uI 1158671474(14)×10-3 .2×10-8 to nuclear magneton ratio 2.127497718(25) 1.2×10-8 shielded helion to proton magnetic moment ratIo 0.761766563(12) 1.5×10-8 (gas, sphere,25° shielded helion to shielded proton magnetic moment ratIo 0.7617861313(33 4.3×10-9 (gas/H2O, spheres, 25C) shielded helion gyromagnetic ratio jUhl/h h 2.037894764(85)×10 4.2×10 yh/2T 324341025(14) MHzT-14.2×10-8 Alpha particle, a alpha particle mass 6.64465598(52)×10-27kg 79×10=8 in u, ma= Ar(a)u(alpha particle relative atomic mass times u) 4.0015061747(10) 2.5×10-10 energy equivalent 597191897(47)×10-10J 79×10 in me v 3727.37904(15) Mev 4.0×10-8 alpha particle to electron mass ratio 7294299508(16) 2.1×10-9 alpha particle to proton mass ratio 28×10-10 alpha particle molar mass NAma M(a),Ma4.0015061747(10)×10 kgmo-12.5×10-10 PHYSICO-CHEMICAL Avogadro constant 602214199(47)×1023 79×10 omic mass constant 53873(13) 27 energy equivalent 149241778(12)×10-10J 7.9×10-8 013(7) Faraday constants NAe 964853415(39) mol-140×10-8 Page 6 lues of the fundame Journal of Physical and Chemical Reference Data, Vol. 28, No. 6, 1999 and Reviews of Modern Physics, Vol. 72, No. 2, 2000
From: physics.nist.gov/constants Fundamental Physical Constants — Complete Listing Relative std. Quantity Symbol Value Unit uncert. ur deuteron-neutron magnetic moment ratio µd/µn −0.448 206 52(11) 2.4 × 10−7 Helion, h helion masse mh 5.006 411 74(39)× 10−27 kg 7.9 × 10−8 in u, mh = Ar(h) u (helion relative atomic mass times u) 3.014 932 234 69(86) u 2.8 × 10−10 energy equivalent mhc2 4.499 538 48(35)× 10−10 J 7.9 × 10−8 in MeV 2 808.391 32(11) MeV 4.0 × 10−8 helion-electron mass ratio mh/me 5 495.885 238(12) 2.1 × 10−9 helion-proton mass ratio mh/mp 2.993 152 658 50(93) 3.1 × 10−10 helion molar mass NAmh M(h), Mh 3.014 932 234 69(86) × 10−3 kg mol−1 2.8 × 10−10 shielded helion magnetic moment µ0 h −1.074 552 967(45) × 10−26 J T−1 4.2 × 10−8 (gas, sphere, 25 ◦C) to Bohr magneton ratio µ0 h/µB −1.158 671 474(14)× 10−3 1.2 × 10−8 to nuclear magneton ratio µ0 h/µN −2.127 497 718(25) 1.2 × 10−8 shielded helion to proton magnetic moment ratio µ0 h/µp −0.761 766 563(12) 1.5 × 10−8 (gas, sphere, 25 ◦C) shielded helion to shielded proton magnetic moment ratio µ0 h/µ0 p −0.761 786 1313(33) 4.3 × 10−9 (gas/H2O, spheres, 25 ◦C) shielded helion gyromagnetic ratio 2|µ0 h|/ γ 0 h 2.037 894 764(85) × 108 s−1 T−1 4.2 × 10−8 (gas, sphere, 25 ◦C) γ 0 h/2π 32.434 1025(14) MHz T−1 4.2 × 10−8 Alpha particle, α alpha particle mass mα 6.644 655 98(52) × 10−27 kg 7.9 × 10−8 in u, mα = Ar(α) u (alpha particle relative atomic mass times u) 4.001 506 1747(10) u 2.5 × 10−10 energy equivalent mαc2 5.971 918 97(47)× 10−10 J 7.9 × 10−8 in MeV 3 727.379 04(15) MeV 4.0 × 10−8 alpha particle to electron mass ratio mα/me 7 294.299 508(16) 2.1 × 10−9 alpha particle to proton mass ratio mα/mp 3.972 599 6846(11) 2.8 × 10−10 alpha particle molar mass NAmα M(α), Mα 4.001 506 1747(10)× 10−3 kg mol−1 2.5 × 10−10 PHYSICO-CHEMICAL Avogadro constant NA, L 6.022 141 99(47) × 1023 mol−1 7.9 × 10−8 atomic mass constant mu = 1 12m(12C) = 1 u mu 1.660 538 73(13) × 10−27 kg 7.9 × 10−8 = 10−3 kg mol−1 /NA energy equivalent muc2 1.492 417 78(12) × 10−10 J 7.9 × 10−8 in MeV 931.494 013(37) MeV 4.0 × 10−8 Faraday constantg NAe F 96 485.3415(39) C mol−1 4.0 × 10−8 Page 6 Source: Peter J. Mohr and Barry N. Taylor, CODATA Recommended Values of the Fundamental Physical Constants: 1998, Journal of Physical and Chemical Reference Data, Vol. 28, No. 6, 1999 and Reviews of Modern Physics, Vol. 72, No. 2, 2000
From: physics. nist. gov/constants Fundamental Physical Constants-Complete listing Relative std molar planck constant NAh3990312689(30)×10-10Jsmo-17.6×10-9 NAhc0.11962656492(91) J m mol 7.6×10 molar gas constant 8.314472(15) Jmol-1K-11.7×10-6 Boltzmann constant R/NA k 1.3806503(24)×10-23JK-1 1.7×10 8.617342(15)×10 k/h2.0836644536)×1010HzK-1 1.7×10 k/hc69.50356(12) molar volume of ideal gas RT/p T=273.15K,p=101.325kPa 22413996(39)×10 mol-1 1.7×10 Loschmidt constant NA/Vm 268677747×1025 1.7×1 T=273.15K,p=100kPa 22710981(40)×10-3 m3mol-11.7×10-6 Sackur- Tetrode constant (absolute entropy constant)h +In((muktI/h2)3/kTi/pol T1=1K 100 kPa So/R 1.1517048(44) 3.8×10° p0=101.325kPa -1.1648678(44 3.7×10 Stefan-Boltzmann constant (x2/60)k4/hc2 5670400(40)×10-8 Wm-2K-47.0×10-6 7.8×10 first radiation constant for spectral radiance 2hc2 CIL 1. 191042722(93)x 10-16 Wm2 sr-1 7. x 10-8 second radiation constant hc/k 14387752(25)×10-2mK 1.7×10- Wien displacement law constant b=λmaxT=c2/4.965114231 28977686(51)×10-3 7×10 See the " Adopted values" table for the conventional value adopted internationally for realizing representations of the volt using the Joseph son effect b See the"Adopted values"table for the conventional value adopted internationally for realizing representations of the ohm using the quantum Hall effect. Value recommended by the Particle Data Group, Caso et al., Eur. Phys. J. C3(1-4),1-794(1998) d Based on the ratio of the masses of the w and Z bosons mw/mz recommended by the Particle Data Group( Caso et al, 1998). The value for sin-ow they recommend, which is based on a particular variant of the modified minimal subtraction(MS)scheme, is sin-0w (Mz)=0.231 24(24) e The helion, symbol h, is the nucleus of the He atom f This and all other values involving mr are based on the value of mrc2 in Mev recommended by the Particle Data Group, Caso et al., Eur. Phys J. C 3(1-4), 1-794(1998), but with a standard uncertainty of 0. 29 MeV rather than the quoted uncertainty of-0 26 Mev,+0. 29 Me. g The numerical value of F to be used in coulometric chemical measurements is 96485.3432(76)[7. x 10-8]when the relevant current is measured in terms of representations of the volt and ohm based on the Josephson and quantum Hall effects and the internationally adopted conventional values of the Josephson and von Klitzing constants KJ-go and RK-g0 given in the"Adopted values" table h The entropy of an ideal monoatomic gas of relative atomic mass Ar is given by S=So+,R In Ar-R In(p/po)+3R In(T/K) Page 7 Journal of Physical and Chemical Reference Data, Vol. 28, No. 6, 1999 and Reviews of Modern Physics, Vol. 72, No. 2, 2000
From: physics.nist.gov/constants Fundamental Physical Constants — Complete Listing Relative std. Quantity Symbol Value Unit uncert. ur molar Planck constant NAh 3.990 312 689(30) × 10−10 J s mol−1 7.6 × 10−9 NAhc 0.119 626 56492(91) J m mol−1 7.6 × 10−9 molar gas constant R 8.314 472(15) J mol−1 K−1 1.7 × 10−6 Boltzmann constant R/NA k 1.380 6503(24) × 10−23 J K−1 1.7 × 10−6 in eV K−1 8.617 342(15) × 10−5 eV K−1 1.7 × 10−6 k/h 2.083 6644(36) × 1010 Hz K−1 1.7 × 10−6 k/hc 69.503 56(12) m−1 K−1 1.7 × 10−6 molar volume of ideal gas RT/p T = 273.15 K, p = 101.325 kPa Vm 22.413 996(39) × 10−3 m3 mol−1 1.7 × 10−6 Loschmidt constant NA/Vm n0 2.686 7775(47) × 1025 m−3 1.7 × 10−6 T = 273.15 K, p = 100 kPa Vm 22.710 981(40) × 10−3 m3 mol−1 1.7 × 10−6 Sackur-Tetrode constant (absolute entropy constant)h 5 2 + ln[(2πmukT1/h2)3/2kT1/p0] T1 = 1 K, p0 = 100 kPa S0/R −1.151 7048(44) 3.8 × 10−6 T1 = 1 K, p0 = 101.325 kPa −1.164 8678(44) 3.7 × 10−6 Stefan-Boltzmann constant (π2/60)k4 /3c2 σ 5.670 400(40) × 10−8 W m−2 K−4 7.0 × 10−6 first radiation constant 2πhc2 c1 3.741 771 07(29)× 10−16 W m2 7.8 × 10−8 first radiation constant for spectral radiance 2hc2 c1L 1.191 042 722(93) × 10−16 W m2 sr−1 7.8 × 10−8 second radiation constant hc/k c2 1.438 7752(25) × 10−2 mK 1.7 × 10−6 Wien displacement law constant b = λmaxT = c2/4.965 114 231... b 2.897 7686(51) × 10−3 mK 1.7 × 10−6 a See the “Adopted values” table for the conventional value adopted internationally for realizing representations of the volt using the Josephson effect. b See the “Adopted values” table for the conventional value adopted internationally for realizing representations of the ohm using the quantum Hall effect. c Value recommended by the Particle Data Group, Caso et al., Eur. Phys. J. C 3(1-4), 1-794 (1998). d Based on the ratio of the masses of the W and Z bosons mW/mZ recommended by the Particle Data Group (Caso et al., 1998). The value for sin2θW they recommend, which is based on a particular variant of the modified minimal subtraction (MS) scheme, is sin2θˆ W(MZ) = 0.231 24(24). e The helion, symbol h, is the nucleus of the 3He atom. f This and all other values involving mτ are based on the value of mτ c2 in MeV recommended by the Particle Data Group, Caso et al., Eur. Phys. J. C 3(1-4), 1-794 (1998), but with a standard uncertainty of 0.29 MeV rather than the quoted uncertainty of −0.26 MeV, +0.29 MeV. g The numerical value of F to be used in coulometric chemical measurements is 96 485.3432(76) [7.9×10−8] when the relevant current is measured in terms of representations of the volt and ohm based on the Josephson and quantum Hall effects and the internationally adopted conventional values of the Josephson and von Klitzing constants KJ−90 and RK−90 given in the “Adopted values” table. h The entropy of an ideal monoatomic gas of relative atomic mass Ar is given by S = S0 + 3 2 R ln Ar − R ln(p/p0) + 5 2 R ln(T/K). Page 7 Source: Peter J. Mohr and Barry N. Taylor, CODATA Recommended Values of the Fundamental Physical Constants: 1998, Journal of Physical and Chemical Reference Data, Vol. 28, No. 6, 1999 and Reviews of Modern Physics, Vol. 72, No. 2, 2000
