Fundamental Physical Constants


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Fundamental Physical Constants

(without warranty)

Planck constant h
6.6260755·10-34 J·s
h / (2 .pi.) = 1.05457266·10-34 J·s
 
Boltzmann constant kB
1.380658·10-23 J/K        ( = 8.617385·10-5 eV/K )
 
Elementary charge e
1.60217733·10-19 C
 
Avogadro number NA
6.0221367·1023 particles/mol
 
Speed of light c
2.99792458·108 m/s
 
Permeability of vacuum .mu.0
.mu.0 = 4 .pi. ·10-7 T2·m3/J
12.566370614·10-7 T2·m3/J
 
Permittivity of vacuum .epsilon.0
.epsilon.0 = 1 / (.mu.0 c2)
8.854187817·10-12 C2/J·m
 
Fine structure constant .alpha.
1 / 137.0359895
 
Electron rest mass me
9.1093897·10-31 kg
 
Proton rest mass mp
1.6726231·10-27 kg
 
Neutron rest mass mn
1.6749286·10-27 kg
 
Bohr magneton .mu.B
.mu.B = e h / (4 .pi. me)
9.2740154·10-24 J/T
 
Nuclear magneton .mu.N
.mu.N = e h / (4 .pi. mp)
5.0507866·10-27 J/T
 
Free electron g factor ge
2.002319304386
 
Free electron gyromagnetic ratio .gamma.e
.gamma.e = 2 .pi. ge .mu.B / h
1.7608592·1011 1/s·T
.gamma.e / (2 .pi.) = 28.024944 GHz/T
 
Electron magnetic moment .mu.e
.mu.e = -(1/2) ge .mu.B
-9.2847701·10-24 J/T
 
Proton gyromagnetic ratio (H2O) .gamma.p
2.67515255·108 1/s·T
.gamma.p / (2 .pi.) = 42.576375 MHz/T
 
Proton magnetic moment .mu.p
1.41060761·10-26 J/T
 
Proton-electron ratios
mp / me = 1836.152701
.mu.e / .mu.p = 658.2106881
.gamma.e / .gamma.p = 658.2275841 (protons in water)
 
Charge-to-mass ratio for the electron e / me
1.75880·1011 C/kg
 
Atomic mass unit amu
1.66054·10-27 kg
 
Bohr radius a0
5.29177·10-11 m
 
Electron radius re
2.81792·10-15 m
 
Gas constant R
R = NA kB
8.31451 m2·kg/s2·K·mol
 
Molar volume Vmol
22.41383 m3/kmol
 
Faraday constant F
F = NA e
9.64846·104 C/mol
 
Proton g factor (Landé factor) gH
5.585
 
Gravitational constant G
(6.673 +- 0.010)·10-11 m3/kg·s2 (CODATA)
6.67390·10-11 m3/kg·s2 +- 0.0014 % (Jens Gundlach, Univ. of Washington; from: Der Tagesspiegel 2000-05-08)
(6.6873 +- 0.0094)·10-11 m3/kg·s2 (Schwarz et al., Science 282, 2230 (1998))
 
Acceleration due to gravity g
9.80665 m/s2
 
Compton wavelength of the electron .lambda.c
.lambda.c = h / (me c)
2.42631·10-12 m
 

Further Useful Constants

Atomic energy unit Hartree
1 Hartree = e2 / (4 .pi. .epsilon.0 a0)
1 Hartree = 2.625501·106 J/mol (approx. 627.5 kcal/mol)
 

Useful Conversion Factors

NMR (Nuclear Magnetic Resonance)

Proton Larmor frequency
.nu.p = .gamma.p / (2 .pi.) B
.nu.p = 42.5764 MHz/T (H2O)
 

EPR (Electron Paramagnetic Resonance, ESR)

(Note that the use of brackets [ ] in the following expressions is not in accordance with standards which require the use of a slash, e.g. A/MHz.)
Electron Larmor frequency
.nu.e = .gamma.e / (2 .pi.) (g / ge) B
.nu.e [GHz] = 13.9962 g B [T]
g = 0.07144775 .nu.e [GHz] / B [T]
g = 3.04199 .nu.e [GHz] / .nu.p [MHz]
B [T] = 0.0234872 .nu.p [MHz]
 
Conversion of Units
1 G = 0.1 mT
1 T = 10 kG
1 mT = 10 G
A [MHz] = 2.80249 (g / ge) A [G]
A [MHz] = 28.0249 (g / ge) A [mT]
A [MHz] = 13.9962 g A [mT]
A [MHz] = 2.99792·104 A [cm-1]
A [cm-1] = 0.333564·10-4 A [MHz]
A [cm-1] = 4.66863·10-4 g A [mT]
 



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