Question

Calculate the shortest wavenumber in hydrogen spectrum of Lyman series. (R_H = 109677 cm⁻¹)

Options

• 12064.5 cm⁻¹

• 82257.8 cm⁻¹

• 6854.8 cm⁻¹

• 4387.1 cm⁻¹

Answer 1

82257.8 cm⁻¹

Explanation:

The shortest wavenumber corresponds to the maximum wavelength and minimum energy.

For Lyman series, n₁ = 1

The shortest wavenumber (maximum wavelength) in the hydrogen spectrum of the Lyman series corresponds to the transition from n = 2 to n = 1.

Therefore, n₂ = 2

`barV = R_H [1/n_1^2 - 1/n_2^2]` cm⁻¹

`= 109677 [1/1^2 - 1/2^2]` cm⁻¹

`= 109677 [1 - 1/4]` cm⁻¹

`= 109677 [3/4]` cm⁻¹

= 82257.8 cm⁻¹