If the series limit of the Lyman series for the hydrogen emission spectrum is , then the wavelength of the first line of the Balmer series is:

Step-by-step solution

The wavelength of a spectral line in the hydrogen emission spectrum is given by the Rydberg formula: 1 = R ( 1 n₁^2 - 1 n₂^2 ) For the series limit of the Lyman series, the transition is from n₂ = to n₁ = 1 . 1 = R ( 1 1^2 - 1 ^2 ) = R For the first line of the Balmer series, the transition is from n₂ = 3 to n₁ = 2 . Let its wavelength be ' . 1 ' = R ( 1 2^2 - 1 3^2 ) 1 ' = R ( 1 4 - 1 9 ) = R ( 5 36 ) Substituting R = 1 : 1 ' = 1 ( 5 36 ) ' = 36 5 Answer: 36 5