Physical Constants

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Feb 27, 2023
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- Conversion Factors & Units to Memorize
- Organic Chemistry Glossary

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Physical Constants	Unit
Atomic mass unit (u)	1 u = 1.66053906660 × 10⁻²⁴ g
Atomic mass unit (u)	1 g = 6.0221407621 × 10²³ u
Avogadro’s number (NA)	6.022142 × 10²³/mol
Boltzmann’s constant (k)	1.380651 × 10⁻²³ J/K
Charge on electron (e)	1.60217634 × 10⁻¹⁹ C
Faraday’s constant (F)	9.6485338 × 10⁴ C/mol
Gas constant (R)	R=k N_A
Gas constant (R)	0.0820575 (L atm)/(mol K) = 8.31447 J/(mol K)
Mass of electron (mn)	5.485799 × 10⁻⁴ amu
Mass of electron (mn)	= 9.109383 × 10⁻²⁸ g
Mass of neutron (mn)	1.0086649 u
Mass of neutron (mn)	= 1.6749273 × 10⁻²⁴ g
Mass of proton (mp)	1.0072765 u
Mass of proton (mp)	= 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^-7T²·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 / g_e) A [G] A [MHz] = 28.0249 (g / g_e) 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.)

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