Fundamental Constants

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.
Quantity Symbol Value
Atomic mass unit u [latex]\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}[/latex]
Avogadro’s number [latex]{N}_{\text{A}}[/latex] [latex]6.02214076\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{23}\phantom{\rule{0.2em}{0ex}}\text{reciprocal mole}\left({\text{mol}}^{–1}\right)[/latex]
Bohr magneton [latex]{\mu }_{\text{B}}=\frac{e\hslash }{2{m}_{e}}[/latex] [latex]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}[/latex]
Bohr radius [latex]{a}_{0}=\frac{{\hslash }^{2}}{{m}_{e}{e}^{2}{k}_{e}}[/latex] [latex]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}[/latex]
Boltzmann’s constant [latex]{k}_{\text{B}}=\frac{R}{{N}_{\text{A}}}[/latex] [latex]1.380649\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{–23}\phantom{\rule{0.2em}{0ex}}\text{joule per kelvin}\left(\text{J}\cdot {\text{K}}^{–1}\right)[/latex]
Compton wavelength [latex]{\lambda }_{\text{C}}=\frac{h}{{m}_{e}c}[/latex] [latex]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}[/latex]
Coulomb constant [latex]{k}_{e}=\frac{1}{4\pi {\text{ε}}_{0}}[/latex] [latex]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)[/latex]
Deuteron mass [latex]{m}_{d}[/latex] [latex]\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}[/latex]
Electron mass [latex]{m}_{e}[/latex] [latex]\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}[/latex]
Electron volt eV [latex]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}[/latex]
Elementary charge e [latex]1.602176634\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-19}\phantom{\rule{0.2em}{0ex}}\text{C}[/latex]
Gas constant R [latex]8.314 472\phantom{\rule{0.2em}{0ex}}\left(15\right)\phantom{\rule{0.2em}{0ex}}\text{J/mol}·\text{K}[/latex]
Gravitational constant G [latex]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}[/latex]
Neutron mass [latex]{m}_{n}[/latex] [latex]\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}[/latex]
Nuclear magneton [latex]{\mu }_{n}=\frac{e\hslash }{2{m}_{p}}[/latex] [latex]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}[/latex]
Permeability of free space [latex]{\mu }_{0}[/latex] [latex]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)[/latex]
Permittivity of free space [latex]{\text{ε}}_{0}=\frac{1}{{\mu }_{0}{c}^{2}}[/latex] [latex]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)[/latex]
Planck’s constant h
[latex]\hslash =\frac{h}{2\pi }[/latex]
[latex]\begin{array}{c}6.62607015\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-34}\phantom{\rule{0.2em}{0ex}}\text{kg}·{\text{m}}^{2}·{\text{s}}^{–1}\hfill \\ 1.05457182\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-34}\phantom{\rule{0.2em}{0ex}}\text{kg}·{\text{m}}^{2}·{\text{s}}^{–1}\hfill \end{array}[/latex]
Proton mass [latex]{m}_{p}[/latex] [latex]\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}[/latex]
Rydberg constant [latex]{R}_{\text{H}}[/latex] [latex]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}[/latex]
Speed of light in vacuum c [latex]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)[/latex]

Useful combinations of constants for calculations:

[latex]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}[/latex]

[latex]\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}[/latex]

[latex]{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}[/latex]

[latex]{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}[/latex]

License

Icon for the Creative Commons Attribution 4.0 International License

University Physics Volume 2 by cnxuniphysics is licensed under a Creative Commons Attribution 4.0 International License, except where otherwise noted.

Share This Book