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 ao or rBohr. Due to his prime role in building the Bohr model, This physical constant is named after him.

Bohr Radius (ao or rBohr)

The value of the Bohr radius is

5.2917721067 * 10-11m

Bohr Radius In Different Units

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

ao 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
3.27×1024 ℓP

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,

  • ao is the Bohr radius.
  • me is the rest mass of electron.
  • εo 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