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Fundamental Physical Constants

    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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