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

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-

a0=4πε0(h/2π)2mee2=(h/2π)mecα

Where,

• a_o is the Bohr radius.
• m_e is the rest mass of electron.
• ε_o is the permittivity of the free space
• ( h /2 π )

• = 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 = ( h /2 π ) 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