Physical Constants
- Page ID
- 9060
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)| 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.)