In a hydrogen spectrum λ be the wavelength of first transition line of Lyman series. The wavelength difference will be " a λ " between the wavelength of 3 rd transition line of Paschen series and that of 2 nd transition line of Balmer Series where a = _____.

Step-by-step solution

Using Rydberg formula, 1 λ = R 1 n f 2 - 1 n i 2 , where, R is Rydberg constant and n is quantum number. For first line of Lyman series 1 λ = R 1 - 1 4 = R 3 4 ⇒ λ = 4 3 R             . . . 1 For 3 rd   line of Paschen series 1 λ 3 = R 1 3 2 - 1 6 2 = R 9 × 3 4 For 2 nd line of Balmer series 1 λ 2 = R 1 2 2 - 1 4 2 = R 4 × 3 4 Thus, a λ = λ 3 - λ 2 = 12 R - 16 3 R = 20 3 R Putting equation 1 a 4 3 R = 20 3 R ⇒ a = 5