# Physical Constants

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Physical Constants Unit
Atomic mass unit (u) 1 u = 1.66053906660 × 10−24 g
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 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 u
= 1.6749273 × 10−24 g
Mass of proton (mp) 1.0072765 u
= 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.)

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