Skip to main content
Chemistry LibreTexts

Physical Constants

[ "article:topic" ]
  • Page ID
    9060
  • Atomic mass unit (amu) 1 amu = 1.6605389 × 10−24 g
    1 g = 6.022142 × 1023 amu
    Avogadro’s number (NA) 6.022142 × 1023/mol
    Boltzmann’s constant (k) 1.380651 × 10−23 J/K
    Charge on electron (e) 1.6021765 × 10−19 C
    Faraday’s constant (F) 9.6485338 × 104 C/mol
    Gas constant (R) R=k NA

    0.0820575 (L atm)/(mol K)

    = 8.31447 J/(mol K)

    Mass of electron (mn) 5.485799 × 10−4 amu
    = 9.109383 × 10−28 g
    Mass of neutron (mn) 1.0086649 amu
    = 1.6749273 × 10−24 g
    Mass of proton (mp) 1.0072765 amu
    = 1.6726217 × 10−24 g
    Pi π = 3.1415927
    Planck’s constant (h)

    h = 6.626069 × 10 −34J s

    \(\hbar=\dfrac{h}{2\pi}\)=1.05457266·10-34 J·s

    Speed of light in vacuum (c) c = 2.99792458 × 108 m/s (exact)
    Permeability of vacuum \(\mu_0\)

    \(\mu_0 = 4\pi\) ·10-7 T2·m3/J

    12.566370614·10-7 T2·m3/J

    Permittivity of vacuum \(\epsilon_0\)

    \(\epsilon_0 = \dfrac{1}{\mu_o\, c^2}\)

    8.854187817·10-12 C2/J·m

    Fine structure constant \(\alpha\)
     
    \(\dfrac{1}{137.0359895}\)
    Bohr magneton \(\mu_B\)

    \(\mu_B = \dfrac{e h }{4 \pi \,m_e}\)

    9.2740154·10-24 J/T

    Nuclear magneton \(\mu_N\)

    \(\mu_N = \dfrac{e h }{4 \pi \,m_p}\)

    5.0507866·10-27 J/T

    Free electron g factor \(g_e\)

    2.002319304386

    Free electron gyromagnetic ratio \(\gamma_e\)

    \(\gamma_e = \dfrac{2 g_e B}{h}\)

    1.7608592·1011 1/s·T

    \(\dfrac{\gamma_e}{2\pi}\) = 28.024944 GHz/T

    Electron magnetic moment \(\mu_e\)

    \(\mu_e = \dfrac{- g_e \mu_B}{2}\)

    -9.2847701·10-24 J/T

    Proton gyromagnetic ratio (H2O) \(\gamma_p\)

    2.67515255·108 1/s·T

    \(\dfrac{\gamma_p}{2 \pi}\) = 42.576375 MHz/T

    Proton magnetic moment\(\mu_p\)

    1.41060761·10-26 J/T

    Charge-to-mass ratio for the electron \(\frac{e}{m_e}\)

    1.75880·1011 C/kg

    Bohr radius \(a_0\)

    5.29177·10-11 m

    Electron radius \(r_e\)

    2.81792·10-15 m

    Proton g factor (Landé factor) \(g_H\)
    5.585
    Gravitational constant G

    (6.673 ± 0.010)·10-11 m3/kg·s2 (CODATA)

    Acceleration due to gravity g

    9.80665 m/s2

    Compton wavelength of the electron \(\lambda_c\)
    2.42631·10-12 m
    Atomic energy unit Hartree

    1 Hartree = \(\dfrac{e^2}{4 \pi \epsilon_o\, a_0}\)

    1 Hartree = 2.625501·106 J/mol (approx. 627.5 kcal/mol)

    Proton Larmor frequency

    \(\nu_p = \gamma_p / 2\pi \, B\)

    \(\nu_p\) = 42.5764 MHz/T (H2O)

    Electron Larmor frequency
     

    \(\nu_e\) = \(\dfrac{\nu_e}{2\pi}\) (g / ge) B

    \(\nu_e\) [GHz] = 13.9962 g B [T]

    g = 0.07144775 \(\nu_e\) [GHz] / B [T]

    g = 3.04199\(\nu_e\) [GHz] / \(\nu_p\) [MHz]

    B [T] = 0.0234872 \(\nu_p\) [MHz]

    Conversion of Units

    1 G = 0.1 mT

    1 T = 10 kG

    1 mT = 10 G

    A [MHz] = 2.80249 (g / ge) A [G]

    A [MHz] = 28.0249 (g / ge) A [mT]

    A [MHz] = 13.9962 g A [mT]

    A [MHz] = 2.99792·104 A [cm-1]

    A [cm-1] = 0.333564·10-4 A [MHz]

    A [cm-1] = 4.66863·10-4 g A [mT]

     

    (Note that the use of brackets [ ] in the following expressions is not in accordance with standards which require the use of a slash, e.g. A/MHz.)