In hydrogen spectrum the ratio of wavelengths of the last line of Lyman series and the last line of Balmer series is

Step-by-step solution

The wavelength of a spectral line in the hydrogen spectrum is given by Rydberg's formula: 1 = R ( 1 n₁^2 - 1 n₂^2 ) For the last line of the Lyman series, the transition is from n₂ = to n₁ = 1 . 1 _L = R ( 1 1^2 - 1 ^2 ) = R _L = 1 R For the last line of the Balmer series, the transition is from n₂ = to n₁ = 2 . 1 _B = R ( 1 2^2 - 1 ^2 ) = R 4 _B = 4 R The ratio of the wavelengths is: _L _B = 1 R 4 R = 1 4 = 0.25 Answer: 0.25