Bohr Radius

The Bohr model of the atom predicted the radius of the lowest-energy electron orbit. It is a physical constant which represents the most probable distance between the electron and the nucleus in a hydrogen atom in its ground state. We denote it by aₒ or rBohr. It is named after the Danish physicist Niels Bohr.

Bohr Radius (ao or rBohr)

The value of the Bohr radius is

5.2917721067 * 10-11m

Value of Bohr Radius In Different Units

Refer to 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

Bohr Radius Formula

The Bohr radius in the SI unit is given by-

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


  • ao is the Bohr radius.
  • me is the rest mass of electron.
  • εo is the permittivity of the free space
  • h/2π = ħ is the reduced Planck constant.
  • c is the velocity of light in a vacuum.
  • α is the fine structure constant.
  • e is the elementary charge.

The Bohr radius can be expressed in Gaussian units as –

\(\begin{array}{l}a_{0}=\frac{\left ( \frac{h}{2\pi } \right )^{2}}{m_{e}e^{2}}\end{array} \)

Uses of Bohr Radius

Bohr’s radius is only relevant to atoms and ions with a single electron, such as hydrogen. Although the model itself is now obsolete, the Bohr radius for the hydrogen atom is still regarded as an essential physical constant.

Physics Related Topics:

Rydberg Constant
Band Theory Of Solids
Value Of Planck’s Constant
Permittivity And Permeability

The video discusses Bohr’s atomic model, its postulates, limitations and more.

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