C – Fundamental Constants

Samuel J. Ling; Jeff Sanny; William Moebs; Daryl Janzen

C – Fundamental Constants

Quantity	Symbol	Value
Atomic mass unit	$\mathrm{u}$	$1.660~538~782~(83)\times10^{-27}~\mathrm{kg}$ $931.494~028~(23)~\mathrm{MeV}/c^2$
Avogadro’s number	$N_A$	$6.022~141~79~(30)\times10^{23}~\mathrm{particles/mol}$
Bohr magneton	$\mu_{\mathrm{B}}=\frac{e\hbar}{2m_e}$	$9.274~009~15~(23)\times10^{-24}~\mathrm{J/T}$
Bohr radius	$a_0=\frac{\hbar^2}{m_ee^2k_e}$	$5.291~772~085~9~(36)\times10^{-11}~\mathrm{m}$
Boltzmann’s constant	$k_{\mathrm{B}}=\frac{R}{N_A}$	$1.380~650~4~(24)\times10^{-23}~\mathrm{J/K}$
Compton wavelength	$\lambda_{\mathrm{C}}=\frac{h}{m_ec}$	$2.426~310~217~5~(33)\times10^{-12}~\mathrm{m}$
Coulomb constant	$k_e=\frac{1}{4\pi\epsilon_0}$	$8.987~551~788\ldots\times10^9~\mathrm{N}\cdot\mathrm{m}^2/\mathrm{C}^2$
Deuteron mass	$m_d$	$3.343~583~20~(17)\times10^{-27}~\mathrm{kg}$ $2.103~553~212~724~(78)~\mathrm{u}$ $1875.612~859~\mathrm{MeV}/c^2$
Electron mass	$m_e$	$9.109~382~15~(45)\times10^{-31}~\mathrm{kg}$ $5.485~799~094~3~(23)\times10^{-4}~\mathrm{u}$ $0.510~998~910~(13)~\mathrm{MeV}/c^2$
Electron volt	$\mathrm{eV}$	$1.602~176~487~(40)\times10^{-19}~\mathrm{J}$
Elementary charge	$e$	$1.602~176~487~(40)\times10^{-19}~\mathrm{C}$
Gas constant	$R$	$8.314~472~(15)~\mathrm{J/mol}\cdot\mathrm{K}$
Gravitational constant	$G$	$6.674~28~(67)\times10^{-11}~\mathrm{N}\cdot\mathrm{m}^2/\mathrm{kg}^2$
Neutron mass	$m_n$	$1.674~927~211~(84)\times10^{-27}~\mathrm{kg}$ $1.008~664~915~97~(43)~\mathrm{u}$ $939.565~346~(23)~\mathrm{MeV}/c^2$
Nuclear magneton	$\mu_n=\frac{e\hbar}{2m_p}$	$5.050~783~24~(13)\times10^{-27}~\mathrm{J/T}$
Permeability of free space	$\mu_0$	$4\pi\times10^{-7}~\mathrm{T}\cdot\mathrm{m/A}$ (exact)
Permittivity of free space	$\epsilon_0=\frac{1}{\mu_0c^2}$	$8.854~187~817\ldots\times10^{-12}~\mathrm{C}^2/\mathrm{N}\cdot\mathrm{m}^2$ (exact)
Planck’s constant	$h$ $\hbar=\frac{h}{2\pi}$	$6.626~068~96~(33)\times10^{-34}~\mathrm{J}\cdot\mathrm{s}$ $1.054~571~628~(53)\times10^{-34}~\mathrm{J}\cdot\mathrm{s}$
Proton mass	$m_p$	$1.672~621~637~(83)\times10^{-27}~\mathrm{kg}$ $1.007~276~466~77~(10)~\mathrm{u}$ $938.272~013~(23)~\mathrm{MeV}/c^2$
Rydberg constant	$R_{\mathrm{H}}$	$1.097~373~156~852~7~(73)\times10^7~\mathrm{m}^{-1}$
Speed of light in vacuum	$c$	$2.997~924~58\times10^8~\mathrm{m/s}$ (exact)

Table C1 Fundamental Constants

Note: These constants are the values recommended in 2006 by CODATA, based on a least-squares adjustment of data from different measurements. The numbers in parentheses for the values represent the uncertainties of the last two digits.