Fundamental Constants
| Quantity | Symbol | Value |
|---|---|---|
| Atomic mass unit | u | [latex]\begin{array}{c}1.660 538 782\,(83)\times {10}^{-27}\,\text{kg}\hfill \\ 931.494 028\,(23)\,\text{MeV/}{c}^{2}\hfill \end{array}[/latex] |
| Avogadro’s number | [latex]{N}_{\text{A}}[/latex] | [latex]6.022 141 79\,(30)\times {10}^{23}\,\text{particles/mol}[/latex] |
| Bohr magneton | [latex]{\mu }_{\text{B}}=\frac{e\hslash }{2{m}_{e}}[/latex] | [latex]9.274 009 15\,(23)\times {10}^{-24}\,\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\,(36)\times {10}^{-11}\,\text{m}[/latex] |
| Boltzmann’s constant | [latex]{k}_{\text{B}}=\frac{R}{{N}_{\text{A}}}[/latex] | [latex]1.380 650 4\,(24)\times {10}^{-23}\,\text{J/K}[/latex] |
| Compton wavelength | [latex]{\lambda }_{\text{C}}=\frac{h}{{m}_{e}c}[/latex] | [latex]2.426 310 217 5\,(33)\times {10}^{-12}\,\text{m}[/latex] |
| Coulomb constant | [latex]{k}_{e}=\frac{1}{4\pi {\text{ε}}_{0}}[/latex] | [latex]8.987 551 788...\times {10}^{9}\,\text{N}\cdot {\text{m}}^{2}{\text{/C}}^{2}(\text{exact})[/latex] |
| Deuteron mass | [latex]{m}_{d}[/latex] | [latex]\begin{array}{c}3.343 583 20\,(17)\times {10}^{-27}\,\text{kg}\hfill \\ 2.013 553 212 724(78)\,\text{u}\hfill \\ 1875.612 859\,\text{MeV/}{c}^{2}\hfill \end{array}[/latex] |
| Electron mass | [latex]{m}_{e}[/latex] | [latex]\begin{array}{c}9.109 382 15\,(45)\times {10}^{-31}\,\text{kg}\hfill \\ 5.485 799 094 3(23)\times {10}^{-4}\,\text{u}\hfill \\ 0.510 998 910\,(13)\,\text{MeV/}{c}^{2}\hfill \end{array}[/latex] |
| Electron volt | eV | [latex]1.602 176 487\,(40)\times {10}^{-19}\,\text{J}[/latex] |
| Elementary charge | e | [latex]1.602 176 487\,(40)\times {10}^{-19}\,\text{C}[/latex] |
| Gas constant | R | [latex]8.314 472\,(15)\,\text{J/mol}\cdot \text{K}[/latex] |
| Gravitational constant | G | [latex]6.674 28\,(67)\times {10}^{-11}\,\text{N}\cdot {\text{m}}^{2}{\text{/kg}}^{2}[/latex] |
| Neutron mass | [latex]{m}_{n}[/latex] | [latex]\begin{array}{c}1.674 927 211\,(84)\times {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}[/latex] |
| Nuclear magneton | [latex]{\mu }_{n}=\frac{e\hslash }{2{m}_{p}}[/latex] | [latex]5.050 783 24\,(13)\times {10}^{-27}\,\text{J/T}[/latex] |
| Permeability of free space | [latex]{\mu }_{0}[/latex] | [latex]4\pi \times {10}^{-7}\,\text{T}\cdot \text{m/A}(\text{exact})[/latex] |
| Permittivity of free space | [latex]{\text{ε}}_{0}=\frac{1}{{\mu }_{0}{c}^{2}}[/latex] | [latex]8.854 187 817...\times {10}^{-12}\,{\text{C}}^{2}\text{/}\text{N}\cdot {\text{m}}^{2}(\text{exact})[/latex] |
| Planck’s constant | h
[latex]\hslash =\frac{h}{2\pi }[/latex] |
[latex]\begin{array}{c}6.626 068 96\,(33)\times {10}^{-34}\,\text{J}\cdot \text{s}\hfill \\ 1.054 571 628\,(53)\times {10}^{-34}\,\text{J}\cdot \text{s}\hfill \end{array}[/latex] |
| Proton mass | [latex]{m}_{p}[/latex] | [latex]\begin{array}{c}1.672 621 637\,(83)\times {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}[/latex] |
| Rydberg constant | [latex]{R}_{\text{H}}[/latex] | [latex]1.097 373 156 852 7\,(73)\times {10}^{7}\,{\text{m}}^{-1}[/latex] |
| Speed of light in vacuum | c | [latex]2.997 924 58\times {10}^{8}\,\text{m/s}\,(\text{exact})[/latex] |
Useful combinations of constants for calculations:
[latex]hc=12,400\,\text{eV}\cdot Å=1240\,\text{eV}\cdot \text{nm}=1240\,\text{MeV}\cdot \text{fm}[/latex]
[latex]\hslash c=1973\,\text{eV}\cdot Å=197.3\,\text{eV}\cdot \text{nm}=197.3\,\text{MeV}\cdot \text{fm}[/latex]
[latex]{k}_{e}{e}^{2}=14.40\,\text{eV}\cdot Å=1.440\,\text{eV}\cdot \text{nm}=1.440\,\text{MeV}\cdot \text{fm}[/latex]
[latex]{k}_{\text{B}}T=0.02585\,\text{eV at}\,T=300\,\text{K}[/latex]