Fundamental Constants

Fundamental ConstantsNote: 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.
Quantity Symbol Value
Atomic mass unit u \begin{array}{c}1.660 538 782\phantom{\rule{0.2em}{0ex}}\left(83\right)\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-27}\phantom{\rule{0.2em}{0ex}}\text{kg}\hfill \\ 931.494 028\phantom{\rule{0.2em}{0ex}}\left(23\right)\phantom{\rule{0.2em}{0ex}}\text{MeV/}{c}^{2}\hfill \end{array}
Avogadro’s number {N}_{\text{A}} 6.022 141 79\phantom{\rule{0.2em}{0ex}}\left(30\right)\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{23}\phantom{\rule{0.2em}{0ex}}\text{particles/mol}
Bohr magneton {\mu }_{\text{B}}=\frac{e\hslash }{2{m}_{e}} 9.274 009 15\phantom{\rule{0.2em}{0ex}}\left(23\right)\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-24}\phantom{\rule{0.2em}{0ex}}\text{J/T}
Bohr radius {a}_{0}=\frac{{\hslash }^{2}}{{m}_{e}{e}^{2}{k}_{e}} 5.291 772 085 9\phantom{\rule{0.2em}{0ex}}\left(36\right)\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-11}\phantom{\rule{0.2em}{0ex}}\text{m}
Boltzmann’s constant {k}_{\text{B}}=\frac{R}{{N}_{\text{A}}} 1.380 650 4\phantom{\rule{0.2em}{0ex}}\left(24\right)\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-23}\phantom{\rule{0.2em}{0ex}}\text{J/K}
Compton wavelength {\lambda }_{\text{C}}=\frac{h}{{m}_{e}c} 2.426 310 217 5\phantom{\rule{0.2em}{0ex}}\left(33\right)\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-12}\phantom{\rule{0.2em}{0ex}}\text{m}
Coulomb constant {k}_{e}=\frac{1}{4\pi {\text{ε}}_{0}} 8.987 551 788...\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{9}\phantom{\rule{0.2em}{0ex}}\text{N}·{\text{m}}^{2}{\text{/C}}^{2}\left(\text{exact}\right)
Deuteron mass {m}_{d} \begin{array}{c}3.343 583 20\phantom{\rule{0.2em}{0ex}}\left(17\right)\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-27}\phantom{\rule{0.2em}{0ex}}\text{kg}\hfill \\ 2.013 553 212 724\left(78\right)\phantom{\rule{0.2em}{0ex}}\text{u}\hfill \\ 1875.612 859\phantom{\rule{0.2em}{0ex}}\text{MeV/}{c}^{2}\hfill \end{array}
Electron mass {m}_{e} \begin{array}{c}9.109 382 15\phantom{\rule{0.2em}{0ex}}\left(45\right)\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-31}\phantom{\rule{0.2em}{0ex}}\text{kg}\hfill \\ 5.485 799 094 3\left(23\right)\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-4}\phantom{\rule{0.2em}{0ex}}\text{u}\hfill \\ 0.510 998 910\phantom{\rule{0.2em}{0ex}}\left(13\right)\phantom{\rule{0.2em}{0ex}}\text{MeV/}{c}^{2}\hfill \end{array}
Electron volt eV 1.602 176 487\phantom{\rule{0.2em}{0ex}}\left(40\right)\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-19}\phantom{\rule{0.2em}{0ex}}\text{J}
Elementary charge e 1.602 176 487\phantom{\rule{0.2em}{0ex}}\left(40\right)\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-19}\phantom{\rule{0.2em}{0ex}}\text{C}
Gas constant R 8.314 472\phantom{\rule{0.2em}{0ex}}\left(15\right)\phantom{\rule{0.2em}{0ex}}\text{J/mol}·\text{K}
Gravitational constant G 6.674 28\phantom{\rule{0.2em}{0ex}}\left(67\right)\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-11}\phantom{\rule{0.2em}{0ex}}\text{N}·{\text{m}}^{2}{\text{/kg}}^{2}
Neutron mass {m}_{n} \begin{array}{c}1.674 927 211\phantom{\rule{0.2em}{0ex}}\left(84\right)\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-27}\phantom{\rule{0.2em}{0ex}}\text{kg}\hfill \\ 1.008 664 915 97\phantom{\rule{0.2em}{0ex}}\left(43\right)\phantom{\rule{0.2em}{0ex}}\text{u}\hfill \\ 939.565 346\phantom{\rule{0.2em}{0ex}}\left(23\right)\phantom{\rule{0.2em}{0ex}}\text{MeV/}{c}^{2}\hfill \end{array}
Nuclear magneton {\mu }_{n}=\frac{e\hslash }{2{m}_{p}} 5.050 783 24\phantom{\rule{0.2em}{0ex}}\left(13\right)\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-27}\phantom{\rule{0.2em}{0ex}}\text{J/T}
Permeability of free space {\mu }_{0} 4\pi \phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-7}\phantom{\rule{0.2em}{0ex}}\text{T}·\text{m/A}\left(\text{exact}\right)
Permittivity of free space {\text{ε}}_{0}=\frac{1}{{\mu }_{0}{c}^{2}} 8.854 187 817...\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-12}\phantom{\rule{0.2em}{0ex}}{\text{C}}^{2}\text{/}\text{N}·{\text{m}}^{2}\left(\text{exact}\right)
Planck’s constant h

\hslash =\frac{h}{2\pi }

 \begin{array}{c}6.626 068 96\phantom{\rule{0.2em}{0ex}}\left(33\right)\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-34}\phantom{\rule{0.2em}{0ex}}\text{J}·\text{s}\hfill \\ 1.054 571 628\phantom{\rule{0.2em}{0ex}}\left(53\right)\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-34}\phantom{\rule{0.2em}{0ex}}\text{J}·\text{s}\hfill \end{array}
Proton mass {m}_{p} \begin{array}{c}1.672 621 637\phantom{\rule{0.2em}{0ex}}\left(83\right)\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-27}\phantom{\rule{0.2em}{0ex}}\text{kg}\hfill \\ 1.007 276 466 77\phantom{\rule{0.2em}{0ex}}\left(10\right)\phantom{\rule{0.2em}{0ex}}\text{u}\hfill \\ 938.272 013\phantom{\rule{0.2em}{0ex}}\left(23\right)\phantom{\rule{0.2em}{0ex}}\text{MeV/}{c}^{2}\hfill \end{array}
Rydberg constant {R}_{\text{H}} 1.097 373 156 852 7\phantom{\rule{0.2em}{0ex}}\left(73\right)\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{7}\phantom{\rule{0.2em}{0ex}}{\text{m}}^{-1}
Speed of light in vacuum c 2.997 924 58\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{8}\phantom{\rule{0.2em}{0ex}}\text{m/s}\phantom{\rule{0.2em}{0ex}}\left(\text{exact}\right)

Useful combinations of constants for calculations:

hc=12,400\phantom{\rule{0.2em}{0ex}}\text{eV}·\text{Å}=1240\phantom{\rule{0.2em}{0ex}}\text{eV}·\text{nm}=1240\phantom{\rule{0.2em}{0ex}}\text{MeV}·\text{fm}

\hslash c=1973\phantom{\rule{0.2em}{0ex}}\text{eV}·\text{Å}=197.3\phantom{\rule{0.2em}{0ex}}\text{eV}·\text{nm}=197.3\phantom{\rule{0.2em}{0ex}}\text{MeV}·\text{fm}

{k}_{e}{e}^{2}=14.40\phantom{\rule{0.2em}{0ex}}\text{eV}·\text{Å}=1.440\phantom{\rule{0.2em}{0ex}}\text{eV}·\text{nm}=1.440\phantom{\rule{0.2em}{0ex}}\text{MeV}·\text{fm}

{k}_{\text{B}}T=0.02585\phantom{\rule{0.2em}{0ex}}\text{eV at}\phantom{\rule{0.2em}{0ex}}T=300\phantom{\rule{0.2em}{0ex}}\text{K}

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