Question

Ionization potential of hydrogen atom is 13.6 V. Hydrogen atoms in the ground state are excited by monochromatic radiation of photon energy 12.1 eV. The spectral lines emitted by hydrogen atoms according to Bohr’s theory will be ______.

Options

• one

• two

• three

• four

Answer 1

Ionization potential of hydrogen atom is 13.6 V. Hydrogen atoms in the ground state are excited by monochromatic radiation of photon energy 12.1 eV. According to Bohr’s theory, the spectral lines emitted by hydrogen atoms will be three.

Explanation:

En = −13.6 eV + 12.1 e V 

= −1.5 eV

Using Bohr's formula for energy levels,

`E_n = -13.6/n^2`

− 1.5 = `-13.6/n^2`

`n^2 = 13.6/1.5`

n² = 9

∴ n = 3

The electrons are excited to the third energy level (n = 3).

When electrons transition back from n = 3 to the ground state, the number of possible spectral lines is given by the formula:

Number of lines = `(n(n - 1))/2`

= `(3(3 - 1))/2`

= `(9 - 3)/2`

= `6/2`

= 3