Fundamental Physical Constants Extensive Listing Relative std. Quantity Symbol Value Unit uncert. u r

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1 UNIVERSAL speed of light in vacuum c, c m s 1 exact magnetic constant µ 0 4π 10 7 N A 2 = N A 2 exact electric constant 1/µ 0 c 2 ɛ F m 1 exact characteristic impedance of vacuum µ 0 c Z Ω exact Newtonian constant of gravitation G (31) m 3 kg 1 s G/ hc (31) (GeV/c 2 ) Planck constant h (81) J s (25) ev s h/2π h (13) J s (40) ev s hc (12) MeV fm Planck mass ( hc/g) 1/2 m P (51) 10 8 kg energy equivalent m P c (29) GeV Planck temperature ( hc 5 /G) 1/2 /k T P (33) K Planck length h/m P c = ( hg/c 3 ) 1/2 l P (38) m Planck time l P /c = ( hg/c 5 ) 1/2 t P (13) s ELECTROMAGNETIC elementary charge e (98) C e/h (15) A J magnetic flux quantum h/2e Φ (13) Wb conductance quantum 2e 2 /h G (18) 10 5 S inverse of conductance quantum G (29) Ω Josephson constant 1 2e/h K J (30) 10 9 Hz V von Klitzing constant 2 h/e 2 = µ 0 c/2α R K (59) Ω Bohr magneton e h/2m e µ B (57) J T (26) 10 5 ev T µ B /h (86) 10 9 Hz T µ B /hc (29) m 1 T µ B /k (39) K T nuclear magneton e h/2m p µ N (31) J T (15) 10 8 ev T µ N /h (47) MHz T µ N /hc (16) 10 2 m 1 T µ N /k (21) 10 4 K T ATOMIC AND NUCLEAR General fine-structure constant e 2 /4πɛ 0 hc α (17) inverse fine-structure constant α (31) Rydberg constant α 2 m e c/2h R (65) m R c (19) Hz R hc (27) J (84) ev Bohr radius α/4πr = 4πɛ 0 h 2 /m e e 2 a (12) m Hartree energy e 2 /4πɛ 0 a 0 = 2R hc = α 2 m e c 2 E h (54) J (17) ev quantum of circulation h/2m e (17) 10 4 m 2 s Page 1

2 h/m e (33) 10 4 m 2 s Electroweak Fermi coupling constant 3 G F /( hc) (6) 10 5 GeV weak mixing angle 4 θ W (on-shell scheme) sin 2 θ W = s 2 W 1 (m W/m Z ) 2 sin 2 θ W (21) Electron, e electron mass m e (11) kg (16) 10 4 u energy equivalent m e c (10) J (31) MeV electron-muon mass ratio m e /m µ (11) electron-tau mass ratio m e /m τ (26) electron-proton mass ratio m e /m p (52) electron-neutron mass ratio m e /m n (27) electron-deuteron mass ratio m e /m d (96) electron-triton mass ratio m e /m t (84) electron-helion mass ratio m e /m h (88) electron to alpha particle mass ratio m e /m α (45) electron charge to mass quotient e/m e (11) C kg electron molar mass N A m e M(e), M e (16) 10 7 kg mol Compton wavelength h/m e c λ C (11) m λ C /2π = αa 0 = α 2 /4πR λ C (18) m classical electron radius α 2 a 0 r e (19) m Thomson cross section (8π/3)re 2 σ e (91) m electron magnetic moment µ e (57) J T to Bohr magneton ratio µ e /µ B (26) to nuclear magneton ratio µ e /µ N (17) electron magnetic moment anomaly µ e /µ B 1 a e (26) electron g-factor 2(1 + a e ) g e (52) electron-muon magnetic moment ratio µ e /µ µ (46) electron-proton magnetic moment ratio µ e /µ p (20) electron to shielded proton magnetic moment ratio (H 2 O, sphere, 25 C) µ e /µ p (72) electron-neutron magnetic moment ratio µ e /µ n (23) electron-deuteron magnetic moment ratio µ e /µ d (12) electron to shielded helion magnetic moment ratio (gas, sphere, 25 C) µ e /µ h (10) electron gyromagnetic ratio 2 µ e / h γ e (11) s 1 T γ e /2π (17) MHz T Muon, µ muon mass m µ (48) kg (25) u energy equivalent m µ c (43) J (24) MeV muon-electron mass ratio m µ /m e (46) muon-tau mass ratio m µ /m τ (54) muon-proton mass ratio m µ /m p (25) Page 2

3 muon-neutron mass ratio m µ /m n (25) muon molar mass N A m µ M(µ), M µ (25) 10 3 kg mol muon Compton wavelength h/m µ c λ C,µ (26) m λ C,µ /2π λ C,µ (42) m muon magnetic moment µ µ (10) J T to Bohr magneton ratio µ µ /µ B (11) to nuclear magneton ratio µ µ /µ N (20) muon magnetic moment anomaly µ µ /(e h/2m µ ) 1 a µ (63) muon g-factor 2(1 + a µ ) g µ (13) muon-proton magnetic moment ratio µ µ /µ p (71) Tau, τ tau mass 5 m τ (29) kg (17) u energy equivalent m τ c (26) J (16) MeV tau-electron mass ratio m τ /m e (31) tau-muon mass ratio m τ /m µ (15) tau-proton mass ratio m τ /m p (17) tau-neutron mass ratio m τ /m n (17) tau molar mass N A m τ M(τ), M τ (17) 10 3 kg mol tau Compton wavelength h/m τ c λ C,τ (63) m λ C,τ /2π λ C,τ (10) m Proton, p proton mass m p (21) kg (91) u energy equivalent m p c (18) J (58) MeV proton-electron mass ratio m p /m e (17) proton-muon mass ratio m p /m µ (20) proton-tau mass ratio m p /m τ (48) proton-neutron mass ratio m p /m n (51) proton charge to mass quotient e/m p (59) 10 7 C kg proton molar mass N A m p M(p), M p (91) 10 3 kg mol proton Compton wavelength h/m p c λ C,p (61) m λ C,p /2π λ C,p (97) m proton rms charge radius r p (61) m proton magnetic moment µ p (97) J T to Bohr magneton ratio µ p /µ B (46) to nuclear magneton ratio µ p /µ N (85) proton g-factor 2µ p /µ N g p (17) proton-neutron magnetic moment ratio µ p /µ n (34) shielded proton magnetic moment µ p (18) J T (H 2 O, sphere, 25 C) to Bohr magneton ratio µ p/µ B (17) to nuclear magneton ratio µ p/µ N (30) proton magnetic shielding correction 1 µ p/µ p (H 2 O, sphere, 25 C) σ p (11) Page 3

4 proton gyromagnetic ratio 2µ p / h γ p (18) 10 8 s 1 T γ p /2π (29) MHz T shielded proton gyromagnetic ratio 2µ p/ h (H 2 O, sphere, 25 C) γ p (33) 10 8 s 1 T γ p/2π (53) MHz T Neutron, n neutron mass m n (21) kg (49) u energy equivalent m n c (19) J (58) MeV neutron-electron mass ratio m n /m e (90) neutron-muon mass ratio m n /m µ (20) neutron-tau mass ratio m n /m τ (48) neutron-proton mass ratio m n /m p (51) neutron-proton mass difference m n m p (85) kg (51) u energy equivalent (m n m p )c (76) J (48) MeV neutron molar mass N A m n M(n), M n (49) 10 3 kg mol neutron Compton wavelength h/m n c λ C,n (88) m λ C,n /2π λ C,n (14) m neutron magnetic moment µ n (23) J T to Bohr magneton ratio µ n /µ B (25) to nuclear magneton ratio µ n /µ N (45) neutron g-factor 2µ n /µ N g n (90) neutron-electron magnetic moment ratio µ n /µ e (25) neutron-proton magnetic moment ratio µ n /µ p (16) neutron to shielded proton magnetic moment ratio (H 2 O, sphere, 25 C) µ n /µ p (16) neutron gyromagnetic ratio 2 µ n / h γ n (43) 10 8 s 1 T γ n /2π (69) MHz T Deuteron, d deuteron mass m d (41) kg (40) u energy equivalent m d c (37) J (12) MeV deuteron-electron mass ratio m d /m e (13) deuteron-proton mass ratio m d /m p (19) deuteron molar mass N A m d M(d), M d (40) 10 3 kg mol deuteron rms charge radius r d (25) m deuteron magnetic moment µ d (36) J T to Bohr magneton ratio µ d /µ B (26) to nuclear magneton ratio µ d /µ N (48) deuteron g-factor µ d /µ N g d (48) deuteron-electron magnetic moment ratio µ d /µ e (26) deuteron-proton magnetic moment ratio µ d /µ p (15) deuteron-neutron magnetic moment ratio µ d /µ n (11) Triton, t Page 4

5 triton mass m t (62) kg (11) u energy equivalent m t c (55) J (17) MeV triton-electron mass ratio m t /m e (26) triton-proton mass ratio m t /m p (22) triton molar mass N A m t M(t), M t (11) 10 3 kg mol triton magnetic moment µ t (12) J T to Bohr magneton ratio µ t /µ B (76) to nuclear magneton ratio µ t /µ N (14) triton g-factor 2µ t /µ N g t (28) Helion, h helion mass m h (62) kg (12) u energy equivalent m h c (55) J (17) MeV helion-electron mass ratio m h /m e (27) helion-proton mass ratio m h /m p (29) helion molar mass N A m h M(h), M h (12) 10 3 kg mol helion magnetic moment µ h (14) J T to Bohr magneton ratio µ h /µ B (14) to nuclear magneton ratio µ h /µ N (25) helion g-factor 2µ h /µ N g h (50) shielded helion magnetic moment µ h (14) J T (gas, sphere, 25 C) to Bohr magneton ratio µ h /µ B (14) to nuclear magneton ratio µ h /µ N (25) shielded helion to proton magnetic moment ratio (gas, sphere, 25 C) µ h /µ p (92) shielded helion to shielded proton magnetic moment ratio (gas/h 2 O, spheres, 25 C) µ h /µ p (33) shielded helion gyromagnetic ratio 2 µ h / h (gas, sphere, 25 C) γ h (27) 10 8 s 1 T γ h /2π (43) MHz T Alpha particle, α alpha particle mass m α (82) kg (63) u energy equivalent m α c (73) J (23) MeV alpha particle to electron mass ratio m α /m e (24) alpha particle to proton mass ratio m α /m p (36) alpha particle molar mass N A m α M(α), M α (63) 10 3 kg mol PHYSICOCHEMICAL Avogadro constant N A, L (74) mol atomic mass constant m u = 1 12 m(12 C) = 1 u m u (20) kg energy equivalent m u c (18) J (57) MeV Page 5

6 Faraday constant 6 N A e F (59) C mol molar Planck constant N A h (18) J s mol N A hc (54) J m mol molar gas constant R (48) J mol 1 K Boltzmann constant R/N A k (79) J K (50) 10 5 ev K k/h (12) Hz K k/hc (40) m 1 K molar volume of ideal gas RT/p T = K, p = 100 kpa V m (13) 10 3 m 3 mol Loschmidt constant N A /V m n (15) m molar volume of ideal gas RT/p T = K, p = kpa V m (13) 10 3 m 3 mol Loschmidt constant N A /V m n (15) m Sackur-Tetrode (absolute entropy) constant ln[(2πm ukt 1 /h 2 ) 3/2 kt 1 /p 0 ] T 1 = 1 K, p 0 = 100 kpa S 0 /R (14) T 1 = 1 K, p 0 = kpa (14) Stefan-Boltzmann constant (π 2 /60)k 4 / h 3 c 2 σ (13) 10 8 W m 2 K first radiation constant 2πhc 2 c (46) W m first radiation constant for spectral radiance 2hc 2 c 1L (15) W m 2 sr second radiation constant hc/k c (83) 10 2 m K Wien displacement law constants b = λ max T = c 2 / b (17) 10 3 m K b = ν max /T = c/c 2 b (34) Hz K See the Adopted values table for the conventional value adopted internationally for realizing representations of the volt using the Josephson effect. 2 See the Adopted values table for the conventional value adopted internationally for realizing representations of the ohm using the quantum Hall effect. 3 Value recommended by the Particle Data Group (Olive et al., 2014). 4 Based on the ratio of the masses of the W and Z bosons m W/m Z recommended by the Particle Data Group (Olive et al., 2014). The value for sin 2 θ W they recommend, which is based on a particular variant of the modified minimal subtraction (MS) scheme, is sin 2 ˆθW(M Z) = (5). 5 This and all other values involving m τ are based on the value of m τc 2 in MeV recommended by the Particle Data Group (Olive et al., 2014). 6 The numerical value of F to be used in coulometric chemical measurements is (12) [ ] 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 K J 90 and R K 90 given in the Adopted values table. 7 The entropy of an ideal monoatomic gas of relative atomic mass A r is given by S = S R ln 2 Ar R ln(p/p0) + 5 R ln(t/k). 2 Page 6

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Fundamental Physical Constants Extensive Listing Relative std. Quantity Symbol Value Unit uncert. u r

Fundamental Physical Constants Extensive Listing Relative std. Quantity Symbol Value Unit uncert. u r UNIVERSAL speed of light in vacuum c, c 0 299 792 458 m s 1 exact magnetic constant µ 0 4π 10 7 N A 2 = 12.566 370 614... 10 7 N A 2 exact electric constant 1/µ 0 c 2 ɛ 0 8.854 187 817... 10 12 F m 1 exact