| Plancksches Wirkungsquantum h | 6,6260755·10−34 J s h / (2π) = 1.05457266·10−34 J s |
| Boltzmannsche Konstante kB | 1,3806503·10−23 J/K |
| Elementarladung e | 1,60217733·10−19 C |
| Avogadrosche Zahl NA | 6,0221367·1023 Partikel/mol |
| Lichtgeschwindigkeit im Vakuum c | 2,99792458·108 m/s |
| Permeabilität des Vakuums mu0 = μ0 | μ0 = 4π·10−7 T2 m3/J 12,566370614·10−7 T2 m3/J |
| Dielektrizitätskonstante des Vakuums epsilon0 = ε0 | ε0 = 1 /(μ0 c2) 8,854187817·10−12 C2/J m |
| Feinstrukturkonstante1 / alpha = 1 / α | 137,0359895 |
| Elektronenruhemasse me | 9,1093897·10−31 kg |
| Protonenruhemasse mp | 1,6726231·10−27 kg |
| Neutronenruhemasse mn | 1,6749286·10−27 kg |
| Bohrsches Magneton muB = μB | muB =e h / (4 π me) 9,2740154·10−24 J/T |
| Kernmagneton μN | μN =e h / (4 π mp) 5,0507866·10−27 J/T |
| atomare Energieeinheit Hartree | 1 Hartree =e2 / (4 π ε0 a0) 1 Hartree = 2,625501·106 J/mol (etwa 627,5 kcal/mol) |
| g-Faktor des freien Elektrons ge | 2,002319304386 |
| magnetisches Moment des Elektrons mue = μe | μe = -(1/2)ge μB -9,2847701·10−24 J/T |
| gyromagnetisches Verh. des freien Elektrons gammae | gammae =2 π ge muB / h 1,7608592·1011 1/s T γe / (2π) = 28,024944 GHz/T |
| gyromagnetisches Verh. der Protonen in Wasser gammap | 2,67515255e8 1/s T γp / (2π) = 42,576375 MHz/T |
| Proton magnetic moment/magn. Moment des Protons mup | 1,41060761·10−26 J/T |
| Proton-Elektron-Verhältnisse | mp / me = 1836,152701 μe / μp = 658,2106881 γe / γp = 658,2275841 (protons in water) |
| Ladungs-Mass e-Verhältnis des Elektrons e / me | 1,75880·1011 C/kg |
| Einheit der Atommasse amu | 1,66057·10−27 kg |
| Bohrscher Radius a0 | 5,29177·10−11 m |
| Elektronenradius re | 2,81792·10−15 m |
| Gaskonstante R | R =NA kB 8,31451 m2 kg/s2 k mol |
| Molvolumen Vmol | 22,41383 m3/kmol |
| Faradaysche Konstante F | F =NA e 9,64846e4 C/mol |
| g-Faktor des Protons gH | 5,585 |
| Compton-Wellenlänge des Elektrons lambdac = λc | λc = h / (me c) 2,42631·10−12 m |
| Erdbeschleunigung g | 9,80665 m/s2 |
| Gravitationskonstante G | 6,673 +/- 0,010)·10−11 m3/kg s2 |
| Name | Symbol | Number | Exp | CGS Units | Relative Error (ppm) |
| speed of light in a vacuum | c | 2,99792458 | 10 | cm s-1 | exact |
| Planck constant | h | 6,6260755(40) | -27 | erg s | 0,60 |
| h / 2 · π | hbar | 1,05457266(63) | -27 | erg s | 0,60 |
| Gravitational constant | G | 6,67259(85) | -8 | cm3 g-1 s-2 | 128 |
| Electron charge | e | 4,8032068(14) | -10 | esu | 0,30 |
| Mass of electron | me | 9,1093897(54) | -28 | g | 0,59 |
| Mass of proton | mp | 1,6726231(10) | -24 | g | 0,59 |
| Mass of neutron | mn | 1,6749286(10) | -24 | g | 0,59 |
| Mass of hydrogen | mH | 1,6733 | -24 | g | ? |
| Atomic mass unit | amu | 1,6605402(10) | -24 | g | 0,59 |
| Avagadro's number | NA | 6,0221367(36) | 23 | 0,59 | |
| Boltzmann constant | k | 1,380658(12) | -16 | erg K -1 | 8,5 |
| Electron volt | eV | 1,6021772(50) | -12 | erg | ~0,60 |
| Radiation density constant | a | 7,5646 | -15 | erg cm-3 K-4 | ? |
| Stefan-Boltzmann constant | σ | 5,67051(19) | -5 | erg cm-2 K-4 s-1 | 34 |
| Fine structure constant | α | 7,29735308(33) | -3 | 0,045 | |
| Rydberg constant | R\inf | 2,1798741(13) | -11 | erg | 0,60 |
| atomic mass constant | m u | 1.660539 · 10-27 kg |
| Avogadro constant | N A | 6.022142 · 1023 /mol |
| Bohr magneton | m B | 9.274009 · 10-24 J/T |
| Bohr radius | a0 | 5.291772 · 10-11 m |
| Boltzmann constant | k | 1.3806503 · 10-23 J/K |
| conductance quantum | G 0 | 7.748092 · 10-5 S |
| electric permittivity constant | e 0 | 1/( m 0 · c 2 ) = 8.85418781...·10-12 F/m |
| electron Compton wavelength | l c | 2.426310 · 10-12 m |
| electron magnetic moment | m e | 9.284764 · 10-24 |
| electron radius (classical) | r e | 2.817940 · 10-15 m |
| electron rest mass | m e | 9.109382 · 10-31 kg |
| electron volt | eV | 1.602176 · 10-19 J |
| elementary charge | 1.602176 · 10-19 C | |
| Euler's constant | g | 0.577215664901532... |
| Faraday constant | F | 9.648524 · 104 C/mol |
| fin e-structure constant | 7.297353 · 10-3 | |
| first radiation constant | c 1 | 3.741771 · 10-16 W/m2 |
| golden ratio | f | 1.618033988749894... |
| gravitational constant | G | 6.6732 · 10-11 N-m2 /kg2 |
| Josephson constant | K J | 4.835979 · 1014 Hz/V |
| magnetic flux quantum | F 0 | 2.067834 · 10-15 Wb |
| magnetic permeability constant | m 0 | 4 p x10-7 = 1.2566370614... · 10-6 H/m |
| natural log base | e | 2.718281828459045... |
| neutron magnetic moment | m n | 9.662364 · 10-27 J/T |
| neutron rest mass | m n | 1.674927 · 10-27 kg |
| nuclear magneton | m N | 5.050783 · 10-27 J/T |
| π | p | 3.14159265358979323846264... |
| Planck constant | h | 6.626069 · 10-34 J-s |
| proton Compton wavelength | l c,p | 1.321410 · 10-15 m |
| proton magnetic moment | m p | 1.410607 · 10-26 J/T |
| proton rest mass | m p | 1.672622 · 10-27 kg |
| Rydberg constant | 1.09737316 · 107 /m | |
| second radiation constant | c2 | 1.438775 · 10-2 m-K |
| speed of light in a vacuum | c | 2.99792458 · 108 m/s |
| standard volume of ideal gas | V 0 | 2.24136 · 10-2 m3 /mol |
| Stefan-Boltzmann constant | s | 5.670400 · 10-8 W/m2 -K4 |
| universal gas constant | R | 8.314472 J/mol-K |
| Wien displacement law constant | b | 2.897769 · 10-3 m-K |
Die Fallbeschleunigung auf Meereshöhe ist am Äquator etwa g = 9,780 m/s2, am 45. Breitengrad g = 9,80665 m/s2 und an den
Polen etwa g = 9,832 m/s2. Je h = 1 Meter Höhe nimmt g um etwa 3·10-6 m/s2 ab, solange h klein gegen den Erdradius ist.
| Name | Symbol und Formel | Zahlenwert | Zehnerpotenz und Einheit |
relative Unsicherheit |
| Lichtgeschwindigkeit im leeren Raum (Vakuum) |  |
2,997 924 58 | 108 m·s-1 | (exakt) |
| Magnetische Feldkonstante |  |
4 p = 12,566 370 614 | 107 N·A-2 | (exakt) |
| Elektrische Feldkonstante |  |
8,854 187 817 | 1012 F·m-1 | (exakt) |
| Gravitationskonstante |  |
6,6742(10) | 10-11 m3 ·kg-1 ·s-2 | 1,0·10-4 |
| Plancksches Wirkungsquantum, Planck- Konstante |
 |
6,626 0693(11) | 10-34 J·s | 1,7·107 |
| Plancksches Wirkungsquantum, Planck- Konstante |
 |
1,054 571 68(18) | 10-34 J·s | 1,7·107 |
| Elementarladung |  |
1,602 176 53(14) | 10-19 C | 8,5·108 |
| Elementarladung |  |
2,417 989 40(21) | 1014 A·J1 | 8,5·108 |
| Sommerfeld-Feinstrukturkonstante |  |
7,297 352 568(24) | 10-3 | 3,3·109 |
| Sommerfeld-Feinstrukturkonstante |  |
137,035 999 11(46) | 3,3·109 | |
| (magnetisches) Flußquant |  |
2,067 833 72(18) | 10-15 Wb | 8,5·108 |
| Josephson-Konstante |  |
483 597,879(41) | 109 Hz·V-1 | 8,5·108 |
| von Klitzing-Konstante |  |
25 812,807 449(86) |  |
3,3·109 |
| Ruhemasse des Elektrons |  |
9,109 3826(16) | 10-31 kg |
1,7·107 |
| Ruhemasse des Elektrons | 5,485 799 0945(24) | 10-4 u | 4,4·1010 | |
| - Energieäquivalent in MeV | 0,510 998 918(44) | MeV | 8,6·108 | |
| Rydberg-Konstante |  |
1,097 373 156 8525(73) | 107 m-1 | 6,6·1012 |
| Ruhemasse des Protons |  |
1,672 621 71(29) | 10-27 kg | 1,7·107 |
| Ruhemasse des Protons | 1,007 276 466 88(13) | u | 1,3·1010 | |
| - Energieäquivalent in MeV | 938,272 029(80) | MeV | 8,6·108 | |
| Verhältnis Ruhemasse des Protons zu Ruhemasse des Elektrons |
 |
1 836,152 672 61(85) | 4,6·1010 | |
| Ruhemasse des Neutrons |  |
1,674 927 28(29) | 10-27 kg | 1,7·107 |
| Ruhemasse des Neutrons | 1,008 664 915 60(55) | u | 5,5·1010 | |
| - Energieäquivalent in MeV | 939,565 360(81) | MeV | 8,6·108 | |
| Avogadro-Konstante |  |
6,022 1415(10) | 1023 mol-1 | 1,7·107 |
| Faraday-Konstante |  |
96 485,3383(83) | C·mol-1 | 8,6·108 |
| Universelle (molare) Gaskonstante |  |
8,314 472(15) | J·mol-11 ·K-1 | 1,7·106 |
| Boltzmann-Konstante |  |
1,380 6505(24) | 10-23 J·K-1 | 1,8·106 |
| Stefan-Boltzmann-Konstante |  |
5,670 400(40) | 108 W·m-2 ·K-4 | 7,0·106 |
| Quantity | Symbol | Value |
|---|---|---|
| speed of light in vacuum | c | 299 792 458 m·s-1 (defined) |
| permeability of vacuum | μ0 | 4π × 10-7 N A-2 (defined) |
| 4π × 10-7 = | 12.566 370 614... × 10-7 N A-2 | |
| permittivity of vacuum | ε0 = 1/(μ0c2) | 8.854 187 817 ... × 10-12 F·m-1 |
| characteristic impedance of vacuum | Z0 = μ0c | 376.730 313 461... Ω (defined) |
| gravitational constant | G | 6.672 59(85) × 10-11 m3·kg-1·s-2 |
| Planck's constant | h | 6.626 068 76(52) × 10-34 J·s |
| Dirac's constant | 1.054 571 596(82) × 10-34 J·s | |
| Planck mass | mp = ( |
2.1767(16) × 10-8 kg |
| Planck length | lp= ( |
1.6160(12) × 10-35 m |
| Planck time | tp = ( |
5.3906(40) × 10-44 s |
| elementary charge | e | 1.602 176 462(63) × 10-19 C |
| electron rest mass | me | 9.109 381 88(72) × 10-31 kg |
| proton rest mass | mp | 1.672 621 58(13) × 10-27 kg |
| neutron rest mass | mn | 1.674 927 16(13) × 10-27 kg |
| atomic mass constant, (unified atomic mass unit) | mu = 1 u | 1.660 538 73(13) × 10-27 kg |
| Avogadro's number | L, NA | 6.022 141 99(47) × 1023 |
| Boltzmann constant | k | 1.380 6503(24) × 10-23 J·K-1 |
| Faraday constant | F | 9.648 534 15(39) × 104 C·mol-1 |
| gas constant | R | 8.314 472(15) J·K-1·mol-1 |
| zero of the Celsius scale | 273.15 K (defined) | |
| molar volume, ideal gas, p = 1 bar, θ = 00C | 22.710 981(40) L·mol-1 | |
| standard atmosphere | atm | 101 325 Pa (defined) |
| fine-structure constant | α = μ0e2c / (2h) | 7.297 352 533(27) × 10-3 |
| α-1 | 137.035 999 76(50) | |
| Bohr radius | a0 | 5.291 772 083(19) × 10-11 m |
| Hartree energy | Eh | 4.359 743 81(34) × 10-18 J |
| Rydberg constant | R∞ | 1.097 373 156 8549(83) × 107 m-1 |
| Bohr magneton | μB | 9.274 008 99(37) × 10-24J·T-1 |
| electron magnetic moment | μe | -9.284 763 62(37) × 10-24 J·T-1 |
| Lande g-factor for free electron | ge | 2.002 319 304 386(20) |
| nuclear magneton | μN | 5.050 786 6(17) × 10-27 J·T-1 |
| proton magnetic moment | μp | 1.410 607 61(47) × 10-26 J·T-1 |
| proton magnetogyric ratio | γp | 2.675 221 28(81) × 108 s-1·T-1 |
| magnetic moment of protons in H20, μ'p | μ'p / μB | 1.520 993 129(17) × 10-3 |
| proton resonance frequency per field in H20 | γ'p / (2π) | 42.576 375 (13) M·Hz·T-1 |
| Stefan-Boltzmann constant | σ | 5.670 400(40) × 10-8 W·m-2·K-4 |
| first radiation constant | c1 | 3.741 774 9(22) × 10-16 W·m2 |
| second radiation constant | c2 | 1.438 769 (12) × 10-2 m·K |
| standard acceleration of free fall | gn | 9.80665 m·s-2 (defined) |
Einige dieser angenommenen physikalischen Konstanten stellen sich
als einfache "Umrechnungsfaktoren" heraus.
| How many truly fundamental constants are there? Why do they have the values they have? Just slight deviations in the values of some constants would make carbon based life impossible; this is where the so-called "anthropic principle" comes in. Will we eventually be able, with a "Theory of Everything" (TOE) to calculate all natural constants? Nobody knows. We run against the deepest physical questions at this point. So let's just look at what we have. Since it is customary to list as natural constants some quantities that are actually computable from others, we include some of these so-called "constants" here, too. |
| Symbol and formula |
Numerical value | Magnitude and unit | Remarks |
| Speed of light in vacuum | |||
| c0, c | 2.997 924 58 | 108 m·s−1 | Truly fundamental |
| Gravitational constant | |||
| G | 6.673 | 10−11 m3·kg−1·s−2 | Truly fundamental |
| Planck's constant | |||
| h | 6.626 068 76 | 10−34 J·s | Truly fundamental |
| 4.1356 | 10−15 eV·s | ||
| Elementary charge | |||
| e | 1.602 176 462 | 10−19 C | Truly fundamental? Maybe not |
| Fine structure constant | |||
| α = µ0·c·e2/2h | 7.297 352 533 | 10−3 | Unitless, maybe more fundamental than others. |
| Mass of a electron at rest | |||
| me | 9.109 381 88 | 10−31 kg |
Not truly fundamental; can be calculated in principle |
| 0.510 998 902 | MeV | ||
| Mass of a proton at rest | |||
| mp | 1.672 621 58 | 10−27 kg | Not truly fundamental, can be calculated in principle |
| 1.007 276 466 | u | ||
| 938.271 998(38) | MeV | ||
| Avogadro constant | |||
| NA | 6.022 141 99(47) | 1023 mol−1 | Not truly fundamental any more |
| Faraday constant | |||
| F = e·NA | 96 485.3415(39) | C·mol−1 | Not truly fundamental any more |
| Universal gas constant | |||
| R | 8.314 472(15) | J·mol−1·K−1 | Not truly fundamental any more |
| Boltzmann constant | |||
| k = R/NA | 1.380 6503 | 10−23 J·K−1 | Truly fundamental |
| 8.617269 | 10−5 eV·K−1 | ||
| Magnetic permeability of vacuum | |||
| µ0 = 1/e0c2 | 12.566 370 614 | 10−7 V·s·A−1m−1 | Not truly fundamental |
| Electric susceptibility of vacuum | |||
| ε0 = 1/µ0c2 | 8.854 187 817 | 10−12 A·s·V−1m−1 | Not truly fundamental |
| Magnetic flux quant | |||
| Π = h/2e | 2.067 833 636 | 10−15 Wb | Smallest possible magnetic flux Not truly fundamental |
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