Fundamental Physical Constants


Data are mainly copied from Fundamental Constants in Physics published by the Chemistry Department of the Free University of Berlin
Exponent (base 10) of decimal numbers: e n = 10^n .
Units are separated by spaces, positive numbers denote powers, all units to the right of the slash are in the denominator (negative powers).

Planck constant h6.6260755e-34 J s h/(2 pi) = 1.05457266e-34 J s .
Boltzmann constant k_B1.380658e-23 J/K .
Elementary charge e1.60217733e-19 C .
Avogadro number N_A6.0221367e23 particles/mol
Speed of light c2.99792458e8 m/s
Permeability of vacuum mu_0mu_0 = 4 pi e-7 T2 m3/J 12.566370614e-7 T2 m3/J
Permittivity of vacuum epsilon_0epsilon_0 = 1/(mu_0 c^2) 8.854187817e-12 C2/J m
Fine structure constant 1/alpha137.0359895
Electron rest mass m_e9.1093897e-31 kg
Proton rest mass m_p1.6726231e-27 kg
Neutron rest mass m_n1.6749286e-27 kg
Bohr magneton mu_Bmu_B = eh/(4 pi m_e) 9.2740154e-24 J/T
Nuclear magneton mu_Nmu_N = eh/(4 pi m_p) 5.0507866e-27 J/T
Free electron g factor g_e2.002319304386
Free electron gyromagnetic ratio gamma_egamma_e = 2 pi g_e mu_B / h 1.7608592e11 1/s Tgamma_e/(2 pi) = 28.024944 GHz/T
Electron magnetic moment mu_emu_e = -(1/2) g_e mu_B -9.2847701e-24 J/T
Proton gyromagnetic ratio (H2O) gamma_p2.67515255e8 1/s T gamma_p/(2 pi) = 42.576375 MHz/T
Proton magnetic moment mu_p1.41060761e-26 J/T
Proton-electron ratios m_p/m_e = 1836.152701 mu_e/mu_p = 658.2106881gamma_e/gamma_p = 658.2275841 (protons in water)

Charge-to-mass ratio for electron e / m_e1.75880e11 C/kg
Atomic mass unit 1.66057e-27 kg
Bohr radius a_05.29177e-11 m
Electron radius r_e2.81792e-15 m
Gas constant RR = N_A k_B8.3143 m2 kg/s2 K mol
Molar volume V_mol22.41383 m3/kmol
Faraday constant FF = N_A e9.64846e4 C/mol
Proton g factor (Lande factor) g_H5.585
Gravitational constant G6.6732e-11 m3/kg s2
Acceleration due to gravity g9.80665 m/s2
Compton wavelength of the electron lambda_clambda_c = h / (m_e c)2.42631e-12 m

Further Useful Constants

Atomic energy unit Hartree 1 Hartree = e^2 /(4 pi epsilon_0 a_0)
1 Hartree = 2.625501e+06 J/mol (approx. 627.5 kcal/mol)

Useful Conversion Factors

NMR (Nuclear Magnetic Resonance)

EPR (Electron Paramagnetic Resonance, ESR)

Proton Larmor frequency nu_p = gamma_p/(2 pi) B nu_p = 42.5764 MHz/T (H2O)
Electron Larmor frequencynu_e = gamma_e/(2 pi) g/g_e Bnu_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 Units1 G = 0.1 mT1 T = 10 kG
1 mT = 10 G A[MHz] = 2.80249 (g/g_e) A[G]
A[MHz] = 28.0249 (g/g_e) A[mT]A[MHz] = 13.9962 g A[mT]
A[MHz] = 2.99792e4 A[1/cm] A[1/cm] = 0.333564e-4 A[MHz]
A[1/cm] = 4.66863e-4 g A[mT]

Eddy Lingeman, January 1996, ed@nikhef.nl