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

Step-by-step solution

The Rydberg formula for hydrogen spectral lines is given by 1 = R ( 1 n_f^2 - 1 n_i^2 ) where R is the Rydberg constant, n_f is the final quantum number, and n_i is the initial quantum number. For series limit transitions, n_i = , simplifying the formula to 1 = R n_f^2 . The Lyman series limit corresponds to n_f = 1 , giving _L = 1 R . The Balmer series limit corresponds to n_f = 2 , giving _B = 4 R . The ratio of wavelengths is _L _B = 1 R 4 R = 1 4 = 0.25 . Final answer: 0.25