In atomic, physics, Bohr Radius is a physical constant, expressing the most probable distance between the electron and the nucleus in a Hydrogen atom in the ground state. Denoted by a_{o} or r_{Bohr}. Due to his prime role in building the Bohr model, This physical constant is named after him.

The value of the Bohr radius is

5.2917721067 * 10^{-11}m |

Refer the table given below for the value of Bohr Radius in various units

a_{o} in |
Bohr radius |

SI units | 5.29×10^{−11} m |

Imperial or US units | 2.08×10^{−9} in |

Natural units | 2.68×10^{−4 }/eV |

3.27×10^{24} ℓ_{P} |

The Bohr radius in SI unit is given by-

\(a_{0}=\frac{4\pi \varepsilon _{0}\left ( \frac{h}{2\pi } \right )^{2}}{m_{e}e^{2}} =\frac{\left( \frac{h}{2\pi } \right )}{m_{e}c\alpha }\) |

Where,

- a
_{o}is the Bohr radius. - m
_{e}is the rest mass of electron. *ε*_{o}is the permittivity of the free space- \(\left ( \frac{h}{2\pi } \right )\) =
*ħ*is the reduced Planck constant. - c is the velocity of light in vacuum.
*α*is the fine structure constant.- e is the elementary charge.

The Bohr radius can be expressed in Gaussian units as –

\(a_{0}=\frac{\left ( \frac{h}{2\pi } \right )^{2}}{m_{e}e^{2}}\) |

Although the Bohr model is no longer used in physics, the Bohr radius is highly used due to its promising presence in calculating other fundamental physical constants.

For example

- Atomic unit
- Fine structure constant