Fundamental Physical Constants / Naturkonstanten

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Exponent (base 10) of decimal numbers: e n = $10n$ .
Units are separated by spaces, positive numbers denote powers, all units to the right of the slash are in the denominator (negative powers).

Planck constant / Plancksches Wirkungsquantum h:

6.6260755e-34 J s
$\{h2\; \pi \}$ = 1.05457266e-34 J s

Boltzmann constant / Boltzmannsche Konstante

$k$_B: 1.380658e-23 J/K

Elementary charge / Elementarladung e:

1.60217733e-19 C

Avogadro number / Avogadrosche Zahl

$N$_A: 6.0221367e23 particles/mol

Speed of light / Lichtgeschwindigkeit c:

2.99792458e8 m/s

Permeability of vacuum / Permeabilität des Vakuums

$\mu$₀ = 4 π e-7 $T2m3/J$
12.566370614e-7 $T2m3/J$

Permittivity of vacuum / Dielektrizitätskonstante

$\epsilon$₀ = {1 μ₀ c²}
8.854187817e-12 $C2/J\; m$

Fine structure constant / Feinstrukturkonstante

$\alpha$ = 1 / 137.0359895

Electron rest mass / Elektronenruhemasse

$m$_e: 9.1093897e-31 kg

Proton rest mass / Protonenruhemasse

$m$_p: 1.6726231e-27 kg

Neutron rest mass / Neutronenruhemasse

$m$_n: 1.6749286e-27 kg

Bohr magneton / Bohrsches Magneton

$\mu$_B = {e h 4 π m_e}
9.2740154e-24 J/T

Nuclear magneton / Kernmagneton

$\mu$_N = {e h 4 π m_p}
5.0507866e-27 J/T

Free electron g factor / g-Faktor des freien Elektrons

$g$_e = 2.002319304386

Free electron gyromagnetic ratio / gyromagnetisches Verhältnis des freien Elektrons

$\gamma$_e = {2 π g_e μ_B h}
1.7608592e11 1/s T
$\{\gamma$_e 2 π} = 28.024944 GHz/T

Electron magnetic moment / magnetisches Moment des Elektrons

$\mu$_e = -{12} g_e μ_B
-9.2847701e-24 J/T

Proton gyromagnetic ratio (H₂O) / gyromagnetisches Verhältnis der Protonen in Wasser

$\gamma$_p = 2.67515255e8 1/s T
$\{\gamma$_p 2 π} = 42.576375 MHz/T

Proton magnetic moment / magnetisches Moment des Protons

$\mu$_p = 1.41060761e-26 J/T

Proton-electron ratios / Proton-Elektron-Verhältnisse

$\{m$_p m_e} = 1836.152701
$\{\mu$_e μ_p} = 658.2106881
$\{\gamma$_e γ_p} = 658.2275841 (protons in water)

Charge-to-mass ratio for electron / Ladungs-Masse-Verhältnis des Elektrons

$\{em$_e} = 1.75880e11 C/kg

Atomic mass unit / Einheit der Atommasse amu:

1.66057e-27 kg

Bohr radius / Bohrscher Radius

$a$₀: 5.29177e-11 m

Electron radius / Elektronenradius

$r$_e: 2.81792e-15 m

Gas constant / Gaskonstante R:

R = $N$_A k_B
8.31451 $m2kg/s2K\; mol$

Molar volume / Molvolumen

$V$_mol: 22.41383 $m3/kmol$

Faraday constant / Faradaysche Konstante F:

F = $N$_A e
9.64846e4 C/mol

Proton g factor (Lande factor) / g-Faktor des Protons

$g$_H: 5.585

Gravitational constant / Gravitationskonstante G

(6.673 +- 0.010)e-11 $m3/kg\; s2$ (CODATA)

Acceleration due to gravity / Erdbeschleunigung g:

9.80665 $m/s2$

Compton wavelength of the electron / Compton-Wellenlänge des Elektrons

$\lambda$_c = {h m_e c}
2.42631e-12 m

Further Useful Constants / Weitere nützliche Konstanten

Atomic energy unit / atomare Energieeinheit Hartree

1 Hartree = $\{e24\; \pi \; \epsilon$₀ a₀}
1 Hartree = 2.625501e+06 J/mol (approx. 627.5 kcal/mol)

Useful Conversion Factors / Nützliche Umrechnungsfaktoren

NMR (Nuclear Magnetic Resonance)

Proton Larmor frequency

$\nu$_p = {γ_p 2 π} B
$\nu$_p = 42.5764 MHz/T ($H$₂O)

EPR (Electron Paramagnetic Resonance, ESR)

Electron Larmor frequency

$\nu$_e = {γ_e 2 π} {g g_e} B
$\nu$_e / GHz = 13.9962 g B / T
g = 0.07144775 $\{\nu$_e / GHz B / T}
g = 3.04199 $\{\nu$_e / GHz ν_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 $\{gg$_e} A / G
A / MHz = 28.0249 $\{gg$_e} A / mT
A / MHz = 13.9962 g A / mT
A / MHz = 2.99792e4 A / $cm-1$
A / $cm-1$ = 0.333564e-4 A / MHz
A / $cm-1$ = 4.66863e-4 g A / mT

• The NIST Reference on Constants, Units, and Uncertainty
  • CODATA Internationally recommended values of the Fundamental Physical Constants
• Fundamental constants C Header File, FORTRAN Data File
• Conversion of units / Umrechnung von Einheiten
• Physical Constants and Astronomical Data (U Wisconsin)
  • Astro-Physical Calculator
• Table of Fundamental Physical Constants
• Index General chemistry / Allgemeine Chemie