Fundamental Physical Constants / Naturkonstanten
English/German
Exponent (base 10) of decimal numbers: e n = 10^n . 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
- h/(2 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
- mu_0 = 4 pi e-7 T2 m3/J
- 12.566370614e-7 T2 m3/J
- Permittivity of vacuum / Dielektrizitätskonstante des Vakuums epsilon_0
- epsilon_0 = 1 / (mu_0 c^2)
- 8.854187817e-12 C2/J m
- Fine structure constant / Feinstrukturkonstante 1 / alpha
- 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
- mu_B = eh/(4 pi m_e)
- 9.2740154e-24 J/T
- Nuclear magneton / Kernmagneton mu_N
- mu_N = eh/(4 pi 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
- gamma_e = 2 pi g_e mu_B / h
- 1.7608592e11 1/s T
- gamma_e/(2 pi) = 28.024944 GHz/T
- Electron magnetic moment / magnetisches Moment des Elektrons mu_e
- mu_e = -(1/2) g_e mu_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 pi) = 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/mu_p = 658.2106881
- gamma_e/gamma_p = 658.2275841 (protons in water)
Charge-to-mass ratio for electron / Ladungs-Masse-Verhältnis des Elektrons e / m_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
- 8.3143 m2 kg/s2 K 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
- 6.6732e-11 m3/kg s2
- Acceleration due to gravity / Erdbeschleunigung g
- 9.80665 m/s2
- Compton wavelength of the electron / Compton-Wellenlänge des Elektrons lambda_c
- lambda_c = h / (m_e c)
- 2.42631e-12 m
Further Useful Constants / Weitere nützliche Konstanten
- Atomic energy unit / atomare Energieeinheit Hartree
- 1 Hartree = e^2 /(4 pi epsilon_0 a_0)
- 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 = gamma_p/(2 pi) B
- nu_p = 42.5764 MHz/T (H2O)
EPR (Electron Paramagnetic Resonance, ESR)
- Electron Larmor frequency
- nu_e = gamma_e/(2 pi) 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]/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] = 2.99792e4 A[1/cm]
- A[1/cm] = 0.333564e-4 A[MHz]
- A[1/cm] = 4.66863e-4 g A[mT]
