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Constants library

15 values, each with its units, its uncertainty, and where it came from.

Universal & Atomic 12

Electronvolt (in joules) exact

eV=1.602176634×10−19 J\mathrm{eV} = 1.602176634 \times 10^{-19}\ \text{J}

JThe energy one electron gains crossing one volt: exactly 1.602 176 634 × 10⁻¹⁹ J, the working currency of atomic physics.

Avogadro constant exact

NA=6.02214076×1023 mol−1N_{\mathrm{A}} = 6.02214076 \times 10^{23}\ \text{mol}^{-1}

mol⁻¹Exactly 6.022 140 76 × 10²³ entities per mole — the fixed number that has defined the mole since the 2019 SI revision.

Atomic mass constant (unified atomic mass unit) measured

mu=1.66053906892×10−27 kgm_{\mathrm{u}} = 1.66053906892 \times 10^{-27}\ \text{kg}

kgOne twelfth of the mass of a free carbon-12 atom at rest, 1.660 539 069 × 10⁻²⁷ kg — the dalton used in every mass spectrum.

Atomic mass constant energy equivalent measured

muc2=1.49241808768×10−10 Jm_{\mathrm{u}} c^{2} = 1.49241808768 \times 10^{-10}\ \text{J}

JThe rest energy of one dalton, 1.492 418 088 × 10⁻¹⁰ J or 931.494 MeV — the conversion factor behind every mass-defect calculation.

Electron mass measured

me=9.1093837139×10−31 kgm_{\mathrm{e}} = 9.1093837139 \times 10^{-31}\ \text{kg}

kgThe rest mass of the electron, 9.109 383 714 × 10⁻³¹ kg — equivalently 5.485 799 091 × 10⁻⁴ u or 0.510 999 MeV/c².

Deuteron mass measured

md=3.3435837768×10−27 kgm_{\mathrm{d}} = 3.3435837768 \times 10^{-27}\ \text{kg}

kgThe mass of the deuteron, one proton bound to one neutron: 3.343 583 777 × 10⁻²⁷ kg, or 2.013 553 u and 1875.613 MeV/c².

Alpha particle mass measured

mα=6.644657345×10−27 kgm_{\alpha} = 6.644657345 \times 10^{-27}\ \text{kg}

kgThe mass of the helium-4 nucleus, 6.644 657 345 × 10⁻²⁷ kg — 4.001 506 u, 3727.379 MeV/c², and the most tightly bound light nucleus.

Proton-electron mass ratio measured

mp/me=1836.152673426m_{\mathrm{p}}/m_{\mathrm{e}} = 1836.152673426

dimensionlessThe proton outweighs the electron by 1836.152 673 4 — a pure number, known to 17 parts per trillion, that shapes all of chemistry.

Rydberg constant measured

R∞=10973731.568157 m−1R_{\infty} = 10973731.568157\ \text{m}^{-1}

m⁻¹The wavenumber scale of atomic spectra, 10 973 731.568 157 m⁻¹ — the most precisely measured constant in all of physics.

Rydberg energy (hcR∞) measured

hcR∞=2.179872361103×10−18 JhcR_{\infty} = 2.179872361103 \times 10^{-18}\ \text{J}

JThe ionisation energy of ground-state hydrogen, 2.179 872 361 × 10⁻¹⁸ J or 13.605 693 eV — the natural unit of atomic energy.

Bohr radius measured

a0=5.29177210544×10−11 ma_{0} = 5.29177210544 \times 10^{-11}\ \text{m}

mThe most probable electron-proton distance in ground-state hydrogen, 5.291 772 105 × 10⁻¹¹ m — the natural size of an atom.

Classical electron radius measured

re=2.8179403205×10−15 mr_{\mathrm{e}} = 2.8179403205 \times 10^{-15}\ \text{m}

mr_e = α²a₀ = 2.817 940 321 × 10⁻¹⁵ m — the radius a classical sphere of charge e would need to have rest energy m_e c².

Electromagnetic 3

Bohr magneton measured

μB=9.2740100657×10−24 J/T\mu_{\mathrm{B}} = 9.2740100657 \times 10^{-24}\ \text{J/T}

J/TThe natural quantum of magnetic moment for an electron, eħ/2mₑ — the yardstick for atomic magnetism and electron spin.

Electron magnetic moment measured

μe=−9.2847646917×10−24 J/T\mu_{\mathrm{e}} = -9.2847646917 \times 10^{-24}\ \text{J/T}

J/TThe magnetic moment of a free electron, negative because its charge is, and about 0.116% larger than one Bohr magneton.

Electron gyromagnetic ratio measured

γe=1.76085962784×1011 s−1⋅T−1\gamma_{\mathrm{e}} = 1.76085962784 \times 10^{11}\ \text{s}^{-1}{\cdot}\text{T}^{-1}

s⁻¹·T⁻¹The electron's spin precession rate per tesla, 658 times the proton's — the basis of electron spin resonance and of spin-qubit control.