Bohr radius - Aetherwisp

The Bohr radius $a_{0}$ is a constant representing the distance from the nucleus of a hydrogen atom at which the wave function of an electron in the ground state has maximum Probability.

It is defined as

a_{0}=\frac{4\pi\varepsilon_{0}\hbar^{2}}{e^{2}m_{e}}=\frac{\hbar}{m_{e}c\alpha}=5.29177210903(80)\times10^{−11}\text{ m}\simeq0.53\ \mathring{\text{A}}

where

$\hbar$ is the reduced Planck constant
$\varepsilon_{0}$ is the vacuum permittivity
$e$ is the elementary charge
$m_{e}$ is the electron mass
$c$ is the speed of light
$\alpha$ is the fine-structure constant

It was originally discovered through the Bohr model of the hydrogen atom as the orbit radius of an electron in the ground state. A more precise value can be obtained by solving the Bohr model without assuming that the nucleus is stationary. This leads to the modified Bohr radius

a_{\mu}=\frac{m_{e}}{\mu}a_{0}

where $\mu=m_\text{nucleus}m_{e}/(m_\text{nucleus}+m_{e})$ is the reduced mass of the hydrogen atom.