# Fundamental Physical Constants / Naturkonstanten

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(without warranty / ohne Gewähr)
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
$\left\{h2 \pi \right\}$ = 1.05457266e-34 J s
Boltzmann constant / Boltzmannsche Konstante
$k$B: 1.380658e-23 J/K
1.60217733e-19 C
$N$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 me}
9.2740154e-24 J/T
Nuclear magneton / Kernmagneton

$\mu$N = {e h 4 π mp}
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 ge μB h}
1.7608592e11 1/s T
$\left\{\gamma$e 2 π} = 28.024944 GHz/T
Electron magnetic moment / magnetisches Moment des Elektrons

$\mu$e = -{12} ge μB
-9.2847701e-24 J/T
Proton gyromagnetic ratio (H2O) / gyromagnetisches Verhältnis der Protonen in Wasser

$\gamma$p = 2.67515255e8 1/s T
$\left\{\gamma$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

$\left\{m$p me} = 1836.152701
$\left\{\mu$e μp} = 658.2106881
$\left\{\gamma$e γp} = 658.2275841 (protons in water)

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

$\left\{em$e} = 1.75880e11 C/kg
Atomic mass unit / Einheit der Atommasse amu:
1.66057e-27 kg
$a$0: 5.29177e-11 m
$r$e: 2.81792e-15 m

R = $N$A kB
8.31451 $m2kg/s2K mol$
Molar volume / Molvolumen
$V$mol: 22.41383 $m3/kmol$

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 me c}
2.42631e-12 m

## Further Useful Constants / Weitere nützliche Konstanten

Atomic energy unit / atomare Energieeinheit Hartree

1 Hartree = $\left\{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 = {γp 2 π} B
$\nu$p = 42.5764 MHz/T ($H$2O)

### EPR (Electron Paramagnetic Resonance, ESR)

Electron Larmor frequency

$\nu$e = {γe 2 π} {g ge} B
$\nu$e / GHz = 13.9962 g B / T
g = 0.07144775 $\left\{\nu$e / GHz B / T}
g = 3.04199 $\left\{\nu$e / GHz νp / 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 $\left\{gg$e} A / G
A / MHz = 28.0249 $\left\{gg$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

Note: Physical quantities should be typeset in an italic font, whereas units should be typeset in a regular (non-italic) font. Due to problems with currently available browsers, this page (or parts of it) may not be rendered according to these rules.

Burkhard Kirste, 1996-10-28