Fundamental Physical Constants—Complete ListingRelative std.Quantity Symbol Value Unit uncert.u rUNIVERSALspeed of light in vacuum c,c029*******m s−1(exact) magnetic constantµ04π×10−7N A−2=12.566370614...×10−7N A−2(exact) electric constant1/µ0c2ε08.854187817...×10−12F m−1(exact) characteristic impedanceof vacuum µ0/ 0=µ0c Z0376.730313461...Ω(exact) Newtonian constantof gravitation G6.673(10)×10−11m3kg−1s−21.5×10−3G/¯h c6.707(10)×10−39(GeV/c2)−21.5×10−3 Planck constant h6.62606876(52)×10−34J s7.8×10−8 in eV s4.13566727(16)×10−15eV s3.9×10−8 h/2π¯h1.054571596(82)×10−34J s7.8×10−8 in eV s6.58211889(26)×10−16eV s3.9×10−8Planck mass(¯h c/G)1/2m P2.1767(16)×10−8kg7.5×10−4 Planck length¯h/m P c=(¯h G/c3)1/2l P1.6160(12)×10−35m7.5×10−4 Planck time l P/c=(¯h G/c5)1/2t P5.3906(40)×10−44s7.5×10−4ELECTROMAGNETICelementary charge e1.602176462(63)×10−19C3.9×10−8e/h2.417989491(95)×1014A J−13.9×10−8magneticflux quantum h/2eΦ02.067833636(81)×10−15Wb3.9×10−8 conductance quantum2e2/h G07.748091696(28)×10−5S3.7×10−9 inverse of conductance quantum G−1012906.403786(47)Ω3.7×10−9 Josephson constant a2e/h K J483597.898(19)×109Hz V−13.9×10−8 von Klitzing constant bh/e2=µ0c/2αR K25812.807572(95)Ω3.7×10−9Bohr magneton e¯h/2m eµB927.400899(37)×10−26J T−14.0×10−8 in eV T−15.788381749(43)×10−5eV T−17.3×10−9µB/h13.99624624(56)×109Hz T−14.0×10−8µB/hc46.6864521(19)m−1T−14.0×10−8µB/k0.6717131(12)K T−11.7×10−6nuclear magneton e¯h/2m pµN5.05078317(20)×10−27J T−14.0×10−8 in eV T−13.152451238(24)×10−8eV T−17.6×10−9µN/h7.62259396(31)MHz T−14.0×10−8µN/hc2.54262366(10)×10−2m−1T−14.0×10−8µN/k3.6582638(64)×10−4K T−11.7×10−6ATOMIC AND NUCLEARGeneralfine-structure constant e2/4π 0¯h cα7.297352533(27)×10−33.7×10−9 inversefine-structure constantα−1137.03599976(50)3.7×10−9Fundamental Physical Constants—Complete ListingRelative std.Quantity Symbol Value Unit uncert.u r Rydberg constantα2m e c/2h R∞10973731.568549(83)m−17.6×10−12R∞c3.289841960368(25)×1015Hz7.6×10−12R∞hc2.17987190(17)×10−18J7.8×10−8 R∞hc in eV13.60569172(53)eV3.9×10−8Bohr radiusα/4πR∞=4π 0¯h2/m e e2a00.5291772083(19)×10−10m3.7×10−9 Hartree energy e2/4πε0a0=2R∞hc=α2m e c2E h4.35974381(34)×10−18J7.8×10−8 in eV27.2113834(11)eV3.9×10−8 quantum of circulation h/2m e3.636947516(27)×10−4m2s−17.3×10−9h/m e7.273895032(53)×10−4m2s−17.3×10−9ElectroweakFermi coupling constant c G F/(¯h c)31.16639(1)×10−5GeV−28.6×10−6 weak mixing angle dθW(on-shell scheme)≡1−(m W/m Z)2sin2θW0.2224(19)8.7×10−3 sin2θW=s2WElectron,e−electron mass m e9.10938188(72)×10−31kg7.9×10−8 in u,m e=A r(e)u(electronrelative atomic mass times u)5.485799110(12)×10−4u2.1×10−9 energy equivalent m e c28.18710414(64)×10−14J7.9×10−8 in MeV0.510998902(21)MeV4.0×10−8electron-muon mass ratio m e/mµ4.83633210(15)×10−33.0×10−8 electron-tau mass ratio m e/mτ2.87555(47)×10−41.6×10−4 electron-proton mass ratio m e/m p5.446170232(12)×10−42.1×10−9 electron-neutron mass ratio m e/m n5.438673462(12)×10−42.2×10−9 electron-deuteron mass ratio m e/m d2.7244371170(58)×10−42.1×10−9 electron to alpha particle mass ratio m e/mα1.3709335611(29)×10−42.1×10−9electron charge to mass quotient−e/m e−1.758820174(71)×1011C kg−14.0×10−8 electron molar mass N A m e M(e),M e5.485799110(12)×10−7kg mol−12.1×10−9 Compton wavelength h/m e cλC2.426310215(18)×10−12m7.3×10−9λC/2π=αa0=α2/4πR∞λC386.1592642(28)×10−15m7.3×10−9 classical electron radiusα2a0r e2.817940285(31)×10−15m1.1×10−8 Thomson cross section(8π/3)r2eσe0.665245854(15)×10−28m22.2×10−8electron magnetic momentµe−928.476362(37)×10−26J T−14.0×10−8 to Bohr magneton ratioµe/µB−1.0011596521869(41)4.1×10−12 to nuclear magneton ratioµe/µN−1838.2819660(39)2.1×10−9 electron magnetic momentanomaly|µe|/µB−1a e1.1596521869(41)×10−33.5×10−9 electron g-factor−2(1+a e)g e−2.0023193043737(82)4.1×10−12electron-muonmagnetic moment ratioµe/µµ206.7669720(63)3.0×10−8Fundamental Physical Constants—Complete ListingRelative std.Quantity Symbol Value Unit uncert.u r electron-protonmagnetic moment ratioµe/µp−658.2106875(66)1.0×10−8 electron to shielded protonmagnetic moment ratioµe/µ p−658.2275954(71)1.1×10−8 (H2O,sphere,25◦C)electron-neutronmagnetic moment ratioµe/µn960.92050(23)2.4×10−7 electron-deuteronmagnetic moment ratioµe/µd−2143.923498(23)1.1×10−8 electron to shielded helion emagnetic moment ratioµe/µh 864.058255(10)1.2×10−8(gas,sphere,25◦C)electron gyromagnetic ratio2|µe|/¯hγe1.760859794(71)×1011s−1T−14.0×10−8γe/2π28024.9540(11)MHz T−14.0×10−8Muon,µ−muon mass mµ1.88353109(16)×10−28kg8.4×10−8 in u,mµ=A r(µ)u(muonrelative atomic mass times u)0.1134289168(34)u3.0×10−8 energy equivalent mµc21.69283332(14)×10−11J8.4×10−8 in MeV105.6583568(52)MeV4.9×10−8 muon-electron mass ratio mµ/m e206.7682657(63)3.0×10−8 muon-tau mass ratio mµ/mτ5.94572(97)×10−21.6×10−4 muon-proton mass ratio mµ/m p0.1126095173(34)3.0×10−8 muon-neutron mass ratio mµ/m n0.1124545079(34)3.0×10−8 muon molar mass N A mµM(µ),Mµ0.1134289168(34)×10−3kg mol−13.0×10−8 muon Compton wavelength h/mµcλC,µ11.73444197(35)×10−15m2.9×10−8λC,µ/2πλC,µ1.867594444(55)×10−15m2.9×10−8 muon magnetic momentµµ−4.49044813(22)×10−26J T−14.9×10−8 to Bohr magneton ratioµµ/µB−4.84197085(15)×10−33.0×10−8 to nuclear magneton ratioµµ/µN−8.89059770(27)3.0×10−8 muon magnetic moment anomaly|µµ|/(e¯h/2mµ)−1aµ1.16591602(64)×10−35.5×10−7 muon g-factor−2(1+aµ)gµ−2.0023318320(13)6.4×10−10 muon-protonmagnetic moment ratioµµ/µp−3.18334539(10)3.2×10−8Tau,τ−tau mass f mτ3.16788(52)×10−27kg1.6×10−4 in u,mτ=A r(τ)u(taurelative atomic mass times u)1.90774(31)u1.6×10−4 energy equivalent mτc22.84715(46)×10−10J1.6×10−4 in MeV1777.05(29)MeV1.6×10−4Fundamental Physical Constants—Complete ListingRelative std.Quantity Symbol Value Unit uncert.u r tau-electron mass ratio mτ/m e3477.60(57)1.6×10−4 tau-muon mass ratio mτ/mµ16.8188(27)1.6×10−4 tau-proton mass ratio mτ/m p1.89396(31)1.6×10−4 tau-neutron mass ratio mτ/m n1.89135(31)1.6×10−4 tau molar mass N A mτM(τ),Mτ1.90774(31)×10−3kg mol−11.6×10−4tau Compton wavelength h/mτcλC,τ0.69770(11)×10−15m1.6×10−4λC,τ/2πλ,τ0.111042(18)×10−15m1.6×10−4Proton,pproton mass m p1.67262158(13)×10−27kg7.9×10−8 in u,m p=A r(p)u(protonrelative atomic mass times u)1.00727646688(13)u1.3×10−10 energy equivalent m p c21.50327731(12)×10−10J7.9×10−8 in MeV938.271998(38)MeV4.0×10−8 proton-electron mass ratio m p/m e1836.1526675(39)2.1×10−9 proton-muon mass ratio m p/mµ8.88024408(27)3.0×10−8 proton-tau mass ratio m p/mτ0.527994(86)1.6×10−4 proton-neutron mass ratio m p/m n0.99862347855(58)5.8×10−10 proton charge to mass quotient e/m p9.57883408(38)×107C kg−14.0×10−8 proton molar mass N A m p M(p),M p1.00727646688(13)×10−3kg mol−11.3×10−10proton Compton wavelength h/m p cλC,p1.321409847(10)×10−15m7.6×10−9λC,p/2πλC,p0.2103089089(16)×10−15m7.6×10−9 proton magnetic momentµp1.410606633(58)×10−26J T−14.1×10−8 to Bohr magneton ratioµp/µB1.521032203(15)×10−31.0×10−8 to nuclear magneton ratioµp/µN2.792847337(29)1.0×10−8 proton g-factor2µp/µN g p5.585694675(57)1.0×10−8 proton-neutronmagnetic moment ratioµp/µn−1.45989805(34)2.4×10−7 shielded proton magnetic momentµ p1.410570399(59)×10−26J T−14.2×10−8 (H2O,sphere,25◦C)to Bohr magneton ratioµ p/µB1.520993132(16)×10−31.1×10−8 to nuclear magneton ratioµ p/µN2.792775597(31)1.1×10−8 proton magnetic shieldingcorrection1−µ p/µpσ p25.687(15)×10−65.7×10−4 (H2O,sphere,25◦C)proton gyromagnetic ratio2µp/¯hγp2.67522212(11)×108s−1T−14.1×10−8γp/2π42.5774825(18)MHz T−14.1×10−8 shielded proton gyromagneticratio2µ p/¯hγ p2.67515341(11)×108s−1T−14.2×10−8 (H2O,sphere,25◦C)γ p/2π42.5763888(18)MHz T−14.2×10−8Neutron,nFundamental Physical Constants—Complete ListingRelative std.Quantity Symbol Value Unit uncert.u r neutron mass m n1.67492716(13)×10−27kg7.9×10−8 in u,m n=A r(n)u(neutronrelative atomic mass times u)1.00866491578(55)u5.4×10−10 energy equivalent m n c21.50534946(12)×10−10J7.9×10−8 in MeV939.565330(38)MeV4.0×10−8neutron-electron mass ratio m n/m e1838.6836550(40)2.2×10−9 neutron-muon mass ratio m n/mµ8.89248478(27)3.0×10−8 neutron-tau mass ratio m n/mτ0.528722(86)1.6×10−4 neutron-proton mass ratio m n/m p1.00137841887(58)5.8×10−10 neutron molar mass N A m n M(n),M n1.00866491578(55)×10−3kg mol−15.4×10−10neutron Compton wavelength h/m n cλC,n1.319590898(10)×10−15m7.6×10−9λC,n/2πλC,n0.2100194142(16)×10−15m7.6×10−9 neutron magnetic momentµn−0.96623640(23)×10−26J T−12.4×10−7 to Bohr magneton ratioµn/µB−1.04187563(25)×10−32.4×10−7to nuclear magneton ratioµn/µN−1.91304272(45)2.4×10−7neutron g-factor2µn/µN g n−3.82608545(90)2.4×10−7 neutron-electronmagnetic moment ratioµn/µe1.04066882(25)×10−32.4×10−7 neutron-protonmagnetic moment ratioµn/µp−0.68497934(16)2.4×10−7 neutron to shielded protonmagnetic moment ratioµn/µ p−0.68499694(16)2.4×10−7 (H2O,sphere,25◦C)neutron gyromagnetic ratio2|µn|/¯hγn1.83247188(44)×108s−1T−12.4×10−7γn/2π29.1646958(70)MHz T−12.4×10−7Deuteron,ddeuteron mass m d3.34358309(26)×10−27kg7.9×10−8 in u,m d=A r(d)u(deuteronrelative atomic mass times u)2.01355321271(35)u1.7×10−10 energy equivalent m d c23.00506262(24)×10−10J7.9×10−8 in MeV1875.612762(75)MeV4.0×10−8deuteron-electron mass ratio m d/m e3670.4829550(78)2.1×10−9 deuteron-proton mass ratio m d/m p1.99900750083(41)2.0×10−10 deuteron molar mass N A m d M(d),M d2.01355321271(35)×10−3kg mol−11.7×10−10 deuteron magnetic momentµd0.433073457(18)×10−26J T−14.2×10−8 to Bohr magneton ratioµd/µB0.4669754556(50)×10−31.1×10−8 to nuclear magneton ratioµd/µN0.8574382284(94)1.1×10−8 deuteron-electronmagnetic moment ratioµd/µe−4.664345537(50)×10−41.1×10−8 deuteron-protonmagnetic moment ratioµd/µp0.3070122083(45)1.5×10−8Fundamental Physical Constants—Complete ListingRelative std.Quantity Symbol Value Unit uncert.u r deuteron-neutronmagnetic moment ratioµd/µn−0.44820652(11)2.4×10−7Helion,hhelion mass e m h5.00641174(39)×10−27kg7.9×10−8 in u,m h=A r(h)u(helionrelative atomic mass times u)3.01493223469(86)u2.8×10−10 energy equivalent m h c24.49953848(35)×10−10J7.9×10−8 in MeV2808.39132(11)MeV4.0×10−8 helion-electron mass ratio m h/m e5495.885238(12)2.1×10−9 helion-proton mass ratio m h/m p2.99315265850(93)3.1×10−10 helion molar mass N A m h M(h),M h3.01493223469(86)×10−3kg mol−12.8×10−10shielded helion magnetic momentµh −1.074552967(45)×10−26J T−14.2×10−8(gas,sphere,25◦C)to Bohr magneton ratioµh /µB−1.158671474(14)×10−31.2×10−8to nuclear magneton ratioµh /µN−2.127497718(25)1.2×10−8shielded helion to protonmagnetic moment ratioµh /µp−0.761766563(12)1.5×10−8(gas,sphere,25◦C)shielded helion to shielded protonmagnetic moment ratioµh /µ p−0.7617861313(33)4.3×10−9(gas/H2O,spheres,25◦C) shielded helion gyromagneticratio2|µh |/¯hγ h2.037894764(85)×108s−1T−14.2×10−8(gas,sphere,25◦C)γh/2π32.4341025(14)MHz T−14.2×10−8Alpha particle,αalpha particle mass mα6.64465598(52)×10−27kg7.9×10−8 in u,mα=A r(α)u(alpha particlerelative atomic mass times u)4.0015061747(10)u2.5×10−10 energy equivalent mαc25.97191897(47)×10−10J7.9×10−8 in MeV3727.37904(15)MeV4.0×10−8 alpha particle to electron mass ratio mα/m e7294.299508(16)2.1×10−9 alpha particle to proton mass ratio mα/m p3.9725996846(11)2.8×10−10 alpha particle molar mass N A mαM(α),Mα4.0015061747(10)×10−3kg mol−12.5×10−10PHYSICO-CHEMICALAvogadro constant N A,L6.02214199(47)×1023mol−17.9×10−8 atomic mass constantm u=1m(12C)=1u m u1.66053873(13)×10−27kg7.9×10−8 =10−3kg mol−1/N Aenergy equivalent m u c21.49241778(12)×10−10J7.9×10−8 in MeV931.494013(37)MeV4.0×10−8 Faraday constant g N A e F96485.3415(39)C mol−14.0×10−8Fundamental Physical Constants—Complete ListingRelative std.Quantity Symbol Value Unit uncert.u r molar Planck constant N A h3.990312689(30)×10−10J s mol−17.6×10−9N A hc0.11962656492(91)J m mol−17.6×10−9 molar gas constant R8.314472(15)J mol−1K−11.7×10−6 Boltzmann constant R/N A k1.3806503(24)×10−23J K−11.7×10−6 in eV K−18.617342(15)×10−5eV K−11.7×10−6k/h2.0836644(36)×1010Hz K−11.7×10−6k/hc69.50356(12)m−1K−11.7×10−6 molar volume of ideal gas RT/pT=273.15K,p=101.325kPa V m22.413996(39)×10−3m3mol−11.7×10−6 Loschmidt constant N A/V m n02.6867775(47)×1025m−31.7×10−6 T=273.15K,p=100kPa V m22.710981(40)×10−3m3mol−11.7×10−6 Sackur-Tetrode constant(absolute entropy constant)h5 2+ln[(2πm u kT1/h2)3/2kT1/p0]T1=1K,p0=100kPa S0/R−1.1517048(44)3.8×10−6 T1=1K,p0=101.325kPa−1.1648678(44)3.7×10−6Stefan-Boltzmann constant(π2/60)k4/¯h3c2σ5.670400(40)×10−8W m−2K−47.0×10−6first radiation constant2πhc2c13.74177107(29)×10−16W m27.8×10−8first radiation constant for spectral radiance2hc2c1L1.191042722(93)×10−16W m2sr−17.8×10−8 second radiation constant hc/k c21.4387752(25)×10−2m K1.7×10−6Wien displacement law constantb=λmax T=c2/4.965114231...b2.8977686(51)×10−3m K1.7×10−6a 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.c 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 m W/m Z 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 sin2ˆθW(M Z)=0.23124(24).e The helion,symbol h,is the nucleus of the3He atom.f This and all other values involving mτare based on the value of mτc2in MeV recommended by the Particle Data Group,Caso et al.,Eur.Phys. J.C3(1-4),1-794(1998),but with a standard uncertainty of0.29MeV rather than the quoted uncertainty of−0.26MeV,+0.29MeV.g The numerical value of F to be used in coulometric chemical measurements is96485.3432(76)[7.9×10−8]when the relevant current is mea-sured 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 K J−90and R K−90given in the“Adopted values”table.h The entropy of an ideal monoatomic gas of relative atomic mass A r is given by S=S0+3R ln A r−R ln(p/p0)+5R ln(T/K).i The relative atomic mass A r(X)of particle X with mass m(X)is defined by A r(X)=m(X)/m u,where m u=m(12C)/12=M u/N A=1u is the atomic mass constant,N A is the Avogadro constant,and u is the atomic mass unit.Thus the mass of particle X in u is m(X)=A r(X)u and the molar mass of X is M(X)=A r(X)M u.j This is the value adopted internationally for realizing representations of the volt using the Josephson effect.k This is the value adopted internationally for realizing representations of the ohm using the quantum Hall effect.a This is the lattice parameter (unit cell edge length)of an ideal single crystal of naturally occurring Si free of impurities and imperfections,and is deduced from lattice spacing measurements on extremely pure and nearly perfect single crystals of Si by correcting for the effects of impurities.。