Bohr radius

$$\begin{array}{rl}{\alpha }_0& =\frac{4\pi {ϵ}_0{\hslash }^2}{e^2{m}_e}\\ & =\frac{\hslash }{m_{e}c\alpha }\\ & \approx 5.2_E(-11)\text{m}\end{array}$$

, where

• ${ϵ}_0$ is the vacuum permittivity.
• $\hslash$ is the reduced planck constant
• $m_e$ is the mass of an electron
• $e$ is the elementary charge
• $c$ is the speed of light
• $\alpha$ is the fine-structure constant

The Bohr radius is the most likely distance between the nucleus and the electron in the hydrogen atom when it is in a Ground state.