Bohr radius
| Value | 5.29177210544e-11 m |
| Status | Measured: ± 8.20e-21 m (1.5e-10 relative) |
| Source | CODATA 2022 |
| Categories | Universal & Atomicphysicsatomic |
| femtometer | 52,917.721 fm |
| picometer | 52.917721 pm |
| nanometer | 0.052917721 nm |
| micrometer | 0.000052917721 μm |
| millimeter | 5.2917721e-08 mm |
| centimeter | 5.2917721e-09 cm |
| decimeter | 5.2917721e-10 dm |
| meter | 5.2917721e-11 m |
| kilometer | 5.2917721e-14 km |
| inch | 2.0833748e-09 in |
| foot | 1.7361457e-10 ft |
| yard | 5.7871523e-11 yd |
| mile | 3.2881547e-14 mi |
| nautical mile | 2.8573284e-14 nmi |
| astronomical unit | 3.5373312e-22 AU |
| light-year | 5.5934075e-27 ly |
| parsec | 1.7149465e-27 pc |
Learning zone
In Bohr's 1913 model a₀ is the radius of the first allowed orbit; in real quantum mechanics the electron has no orbit, but a₀ survives as the decay length of the 1s wavefunction and the radius at which the radial probability density peaks. Either way it sets the scale of the atomic world: about 0.53 ångström, so atoms are roughly 1 Å across and a solid packs about 10²⁹ of them per cubic metre.
Written as a₀ = ħ/(m_e c α), it is α times smaller than the reduced Compton wavelength and α⁻² times bigger than the classical electron radius — the same three lengths, separated twice over by 137. Two cautions: a₀ is defined for infinite nuclear mass, and it scales as 1/Z for hydrogen-like ions, so a ground-state electron in U⁹¹⁺ sits 92 times closer in and moves at two-thirds the speed of light, which is why heavy-element chemistry needs relativistic corrections.