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Appendix C: Fundamental Constants

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    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.

    * c  is the speed of light

    Quantity Symbol Value
    Atomic mass unit u

    1.660 538 782 (83) x 10−27 kg

    931.494 028 (23) MeV/c*

    Avogadro’s number NA 6.022 141 79 (30) x 1023 particles/mol
    Bohr magneton $$\mu_{B} = \frac{e \hbar}{2 m_{e}}$$ 9.274 009 15 (23) x 10−24 J/T
    Bohr radius $$a_{0} = \frac{\hbar^{2}}{m_{e} e^{2} k_{e}}$$ 5.291 772 085 9 (36) x 10−11 m
    Boltzmann’s constant $$k_{B} = \frac{R}{N_{A}}$$ 1.380 650 4 (24) x 10−23 J/K
    Compton wavelength $$\lambda_{C} = \frac{h}{m_{e} c}$$ 2.426 310 217 5 (33) x 10−12 m
    Coulomb constant $$k_{e} = \frac{1}{4 \pi \varepsilon_{0}}$$ 8.987 551 788... x 109 N • m2/C2 (exact)
    Deuteron mass md

    9.109 382 15 (45) x 10−31 kg

    5.485 799 094 3(23) x 10−4 u

    0.510 998 910 (13) MeV/c2 *

    Electron mass me

    9.109 382 15 (45) x 10−31 kg

    5.485 799 094 3(23) x 10−4 u

    0.510 998 910 (13) MeV/c2 *

    Electron volt eV 1.602 176 487 (40) x 10−19 J
    Elementary charge e 1.602 176 487 (40) x 10−19 C
    Gas constant R 8.314 472 (15) J/mol • K
    Gravitational constant G 6.674 28 (67) x 10−11 N • m2/kg2
    Neutron mass mn

    1.674 927 211 (84) x 10−27 kg

    1.008 664 915 97 (43) u

    939.565 346 (23) MeV/c2 *

    Nuclear magneton $$\mu_{n} = \frac{e \hbar}{2 m_{p}}$$ 5.050 783 24 (13) x 10−27 J/T
    Permeability of free space $$\mu_{0}$$ 4\(\pi\) x 10−7 T • m/A (exact)
    Permittivity of free space $$\varepsilon_{0} = \frac{1}{\mu_{0} c^{2}}$$ 8.854 187 817... x 10−12 C2/N • m2 (exact)
    Planck’s constant h 6.626 068 96 (33) x 10−34 J • s
    Reduced Planck's constant $$\hbar = \frac{h}{2 \pi}$$ 1.054 571 628 (53) x 10−34 J • s
    Proton mass mp

    1.672 621 637 (83) x 10−27 kg

    1.007 276 466 77 (10) u

    938.272 013 (23) MeV/c2 *

    Rydberg constant RH 1.097 373 156 852 7 (73) x 107 m−1
    Speed of light in vacuum c 2.997 924 58 x 108 m/s (exact)

    Useful combinations of constants for calculations:

    • hc = 12,400 eV • Å = 1240 eV • nm = 1240 MeV • fm
    • \(\hbar\)c = 1973 eV • Å = 197.3 eV • nm = 197.3 MeV • fm
    • kee2 = 14.40 eV • Å = 1.440 eV • nm = 1.440 MeV • fm
    • kBT = 0.02585 eV at T = 300 K

    Contributors

    • Samuel J. Ling (Truman State University), Jeff Sanny (Loyola Marymount University), and Bill Moebs with many contributing authors. This work is licensed by OpenStax University Physics under a Creative Commons Attribution License (by 4.0).