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Constants library

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

Universal & Atomic 13

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 energy equivalent measured

mec2=8.187105788×10−14 Jm_{\mathrm{e}} c^{2} = 8.187105788 \times 10^{-14}\ \text{J}

JThe electron's rest energy, 8.187 105 788 × 10⁻¹⁴ J or 510.999 keV — the photon energy of every positron annihilation.

Proton mass measured

mp=1.67262192595×10−27 kgm_{\mathrm{p}} = 1.67262192595 \times 10^{-27}\ \text{kg}

kgThe rest mass of the proton, 1.672 621 926 × 10⁻²⁷ kg — 1.007 276 u, 938.272 MeV/c², and 1836 times the electron.

Proton mass energy equivalent measured

mpc2=1.50327761802×10−10 Jm_{\mathrm{p}} c^{2} = 1.50327761802 \times 10^{-10}\ \text{J}

JThe proton's rest energy, 1.503 277 618 × 10⁻¹⁰ J or 938.272 MeV — the yardstick for accelerator and nuclear energies.

Neutron mass measured

mn=1.67492750056×10−27 kgm_{\mathrm{n}} = 1.67492750056 \times 10^{-27}\ \text{kg}

kgThe rest mass of the neutron, 1.674 927 501 × 10⁻²⁷ kg — 1.008 665 u or 939.565 MeV/c², just heavier than the proton.

Neutron mass energy equivalent measured

mnc2=1.50534976514×10−10 Jm_{\mathrm{n}} c^{2} = 1.50534976514 \times 10^{-10}\ \text{J}

JThe neutron's rest energy, 1.505 349 765 × 10⁻¹⁰ J or 939.565 MeV — exceeding the proton's by the 1.293 MeV that drives beta decay.

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.

Neutron-proton mass ratio measured

mn/mp=1.00137841946m_{\mathrm{n}}/m_{\mathrm{p}} = 1.00137841946

dimensionlessThe neutron is heavier than the proton by just 0.1378 % — the 1.293 MeV difference that makes free neutrons decay and stars burn.

Proton charge-to-mass quotient measured

e/mp=95788331.43 C/kge/m_{\mathrm{p}} = 95788331.43\ \text{C/kg}

C/kg9.578 833 143 × 10⁷ C/kg — the proton's charge-to-mass ratio, smaller than the electron's by the full factor of 1836.

Proton rms charge radius measured

rp=8.4075×10−16 mr_{\mathrm{p}} = 8.4075 \times 10^{-16}\ \text{m}

mThe root-mean-square radius of the proton's charge distribution, 8.4075 × 10⁻¹⁶ m — 0.841 femtometres, and recently controversial.

Nuclear radius constant

r0=1.2×10−15 mr_{0} = 1.2 \times 10^{-15}\ \text{m}

mThe empirical coefficient in R = r₀A^(1/3), about 1.2 × 10⁻¹⁵ m — the constant that says nuclear matter has a fixed density.

Barn (nuclear cross-section unit) exact

b=1×10−28 m2\mathrm{b} = 1 \times 10^{-28}\ \text{m}^{2}

m²Exactly 10⁻²⁸ m², or 100 fm²: the unit every nuclear cross section is quoted in, and roughly the geometric area of a uranium nucleus.

Electromagnetic 4

Nuclear magneton measured

μN=5.0507837393×10−27 J/T\mu_{\mathrm{N}} = 5.0507837393 \times 10^{-27}\ \text{J/T}

J/TThe magnetic-moment unit for nuclei, eħ/2mₚ — smaller than the Bohr magneton by the full proton-to-electron mass ratio of 1836.

Proton magnetic moment measured

μp=1.41060679545×10−26 J/T\mu_{\mathrm{p}} = 1.41060679545 \times 10^{-26}\ \text{J/T}

J/TThe magnetic moment of the proton, 2.79 nuclear magnetons rather than the 1 a point particle would show — evidence of quark structure.

Neutron magnetic moment measured

μn=−9.6623653×10−27 J/T\mu_{\mathrm{n}} = -9.6623653 \times 10^{-27}\ \text{J/T}

J/TA neutral particle with a magnetic moment of −1.913 nuclear magnetons — proof on its own that the neutron has charged internal structure.

Proton gyromagnetic ratio measured

γp=267522187.08 s−1⋅T−1\gamma_{\mathrm{p}} = 267522187.08\ \text{s}^{-1}{\cdot}\text{T}^{-1}

s⁻¹·T⁻¹The proton's precession rate per unit magnetic field in angular frequency — the constant that turns a magnet strength into an NMR frequency.