Question

The energy of an electron revolving in the n^th orbit in Bohr model of hydrogen atom is proportional to ______.

Options

• n²

• n

• `1/n`

• `1/n^2`

Answer 1

The energy of an electron revolving in the n^th orbit in Bohr model of hydrogen atom is proportional to `bbunderline(1/n^2)`.

Explanation:

The energy of the n^th orbit is given by:

E_n = `-(m e^4)/(8 e_0^2 h^2 n^2)`

For a hydrogen atom, this expression simplifies to:

E_n = `-13.6/n^2` eV

From this relation, we observe that:

E_n ∝ `1/n^2`

As n increases, the energy becomes less negative (i.e., increases) and approaches zero as n → ∞.

∴ The energy is proportional to `1/n^2`.