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.

Useful combinations of constants for calculations:

hc=12,400~\mathrm{eV}\cdot{\AA}=1240~\mathrm{eV}\cdot\mathrm{nm}=1240~\mathrm{MeV}\cdot\mathrm{fm}

\hbar c=1973~\mathrm{eV}=197.3~\mathrm{eV}\cdot\mathrm{nm}=197.3~\mathrm{MeV}\cdot\mathrm{fm}

k_ee^2=14.40~\mathrm{eV}\cdot{\AA}=1.440~\mathrm{eV}\cdot\mathrm{nm}=1.440~\mathrm{MeV}\cdot\mathrm{fm}

k_{\mathrm{B}}T=0.02585~\mathrm{eV} at T=300~\mathrm{K}

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Introduction to Electricity, Magnetism, and Circuits Copyright © 2018 by Daryl Janzen is licensed under a Creative Commons Attribution 4.0 International License, except where otherwise noted.