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

    \[\begin{array}{c}1.660 538 782\,(83)\,×\,{10}^{-27}\,\text{kg}\hfill \\ 931.494 028\,(23)\,\text{MeV/}{c}^{2}\hfill \end{array}\]

Avogadro’s number

    \[{N}_{\text{A}}\]

    \[6.022 141 79\,(30)\,×\,{10}^{23}\,\text{particles/mol}\]

Bohr magneton

    \[{\mu }_{\text{B}}=\frac{e\hslash }{2{m}_{e}}\]

    \[9.274 009 15\,(23)\,×\,{10}^{-24}\,\text{J/T}\]

Bohr radius

    \[{a}_{0}=\frac{{\hslash }^{2}}{{m}_{e}{e}^{2}{k}_{e}}\]

    \[5.291 772 085 9\,(36)\,×\,{10}^{-11}\,\text{m}\]

Boltzmann’s constant

    \[{k}_{\text{B}}=\frac{R}{{N}_{\text{A}}}\]

    \[1.380 650 4\,(24)\,×\,{10}^{-23}\,\text{J/K}\]

Compton wavelength

    \[{\lambda }_{\text{C}}=\frac{h}{{m}_{e}c}\]

    \[2.426 310 217 5\,(33)\,×\,{10}^{-12}\,\text{m}\]

Coulomb constant

    \[{k}_{e}=\frac{1}{4\pi {\text{ε}}_{0}}\]

    \[8.987 551 788...\,×\,{10}^{9}\,\text{N}·{\text{m}}^{2}{\text{/C}}^{2}(\text{exact})\]

Deuteron mass

    \[{m}_{d}\]

    \[\begin{array}{c}3.343 583 20\,(17)\,×\,{10}^{-27}\,\text{kg}\hfill \\ 2.013 553 212 724(78)\,\text{u}\hfill \\ 1875.612 859\,\text{MeV/}{c}^{2}\hfill \end{array}\]

Electron mass

    \[{m}_{e}\]

    \[\begin{array}{c}9.109 382 15\,(45)\,×\,{10}^{-31}\,\text{kg}\hfill \\ 5.485 799 094 3(23)\,×\,{10}^{-4}\,\text{u}\hfill \\ 0.510 998 910\,(13)\,\text{MeV/}{c}^{2}\hfill \end{array}\]

Electron volt eV

    \[1.602 176 487\,(40)\,×\,{10}^{-19}\,\text{J}\]

Elementary charge e

    \[1.602 176 487\,(40)\,×\,{10}^{-19}\,\text{C}\]

Gas constant R

    \[8.314 472\,(15)\,\text{J/mol}·\text{K}\]

Gravitational constant G

    \[6.674 28\,(67)\,×\,{10}^{-11}\,\text{N}·{\text{m}}^{2}{\text{/kg}}^{2}\]

Neutron mass

    \[{m}_{n}\]

    \[\begin{array}{c}1.674 927 211\,(84)\,×\,{10}^{-27}\,\text{kg}\hfill \\ 1.008 664 915 97\,(43)\,\text{u}\hfill \\ 939.565 346\,(23)\,\text{MeV/}{c}^{2}\hfill \end{array}\]

Nuclear magneton

    \[{\mu }_{n}=\frac{e\hslash }{2{m}_{p}}\]

    \[5.050 783 24\,(13)\,×\,{10}^{-27}\,\text{J/T}\]

Permeability of free space

    \[{\mu }_{0}\]

    \[4\pi \,×\,{10}^{-7}\,\text{T}·\text{m/A}(\text{exact})\]

Permittivity of free space

    \[{\text{ε}}_{0}=\frac{1}{{\mu }_{0}{c}^{2}}\]

    \[8.854 187 817...\,×\,{10}^{-12}\,{\text{C}}^{2}\text{/}\text{N}·{\text{m}}^{2}(\text{exact})\]

Planck’s constant h

    \[\hslash =\frac{h}{2\pi }\]

    \[\begin{array}{c}6.626 068 96\,(33)\,×\,{10}^{-34}\,\text{J}·\text{s}\hfill \\ 1.054 571 628\,(53)\,×\,{10}^{-34}\,\text{J}·\text{s}\hfill \end{array}\]

Proton mass

    \[{m}_{p}\]

    \[\begin{array}{c}1.672 621 637\,(83)\,×\,{10}^{-27}\,\text{kg}\hfill \\ 1.007 276 466 77\,(10)\,\text{u}\hfill \\ 938.272 013\,(23)\,\text{MeV/}{c}^{2}\hfill \end{array}\]

Rydberg constant

    \[{R}_{\text{H}}\]

    \[1.097 373 156 852 7\,(73)\,×\,{10}^{7}\,{\text{m}}^{-1}\]

Speed of light in vacuum c

    \[2.997 924 58\,×\,{10}^{8}\,\text{m/s}\,(\text{exact})\]

Useful combinations of constants for calculations:

    \[hc=12,400\,\text{eV}·\text{Å}=1240\,\text{eV}·\text{nm}=1240\,\text{MeV}·\text{fm}\]

    \[\hslash c=1973\,\text{eV}·\text{Å}=197.3\,\text{eV}·\text{nm}=197.3\,\text{MeV}·\text{fm}\]

    \[{k}_{e}{e}^{2}=14.40\,\text{eV}·\text{Å}=1.440\,\text{eV}·\text{nm}=1.440\,\text{MeV}·\text{fm}\]

    \[{k}_{\text{B}}T=0.02585\,\text{eV at}\,T=300\,\text{K}\]

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