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 5.29Γ10β11 m Imperial or US units 2.08Γ10β9 in Natural units 2.68Γ10β4 /eV 3.27Γ1024 βP

The Bohr radius in SI unit is given by-

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

Where,

• ao is the Bohr radius.
• me is the rest mass of electron.
• Ξ΅o is the permittivity of the free space
• $$\begin{array}{l}\left ( \frac{h}{2\pi } \right )\end{array}$$
= Δ§ is the reduced Planck constant.
• c is the velocity of light in vacuum.
• Ξ± is the fine structure constant.
• e is the elementary charge.

The Bohr radius can be expressed in Gaussian units as –

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

## 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

Physics Related Topics:

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

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