# Bohr Radius

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.

## Bohr Radius (a_{o} or r_{Bohr})

The value of the Bohr radius is

### Bohr Radius In Different Units

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} |

## Bohr Radius Formula

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 –

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

## Use

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