In Balmer series, wavelength of first line is ' λ 1 ' and in Brackett series wavelength of first line is ' λ 2 ' then λ 1 λ 2 is

Step-by-step solution

The wavelength of a line in Balmer series is given by 1 λ = R 1 2 2 - 1 n 2 [for n = 3, 4, 5,….] Where, R= Rydberg constant. For first line, n = 3 ⇒ 1 λ 1 = R 1 4 - 1 9 ⇒ λ 1 = 35 5 R ….(i) The wavelength of a line in Brackett series is given by 1 λ = R 1 4 2 - 1 n 2 [for n = 5, 6, 7] For first line, n = 5 ⇒ 1 λ 2 = R 1 16 - 1 25 ⇒ λ 2 = 400 9 R ……(ii) Dividing Eq. (i) by Eq. (ii), we get λ 1 λ 2 = 36 5 R × 9 R 400 = 81 500 = 0.162