In the spectrum of the hydrogen atom, the ratio of the wavelengths of the longest wavelength in L y m a n series to the longest wavelength in the B a l m e r series is

Step-by-step solution

When an electron jumps down from any higher energy level to the first energy level, then the emitted lines form the Lyman series   1 λ L = R 1 1 2 - 1 n 2 , where   R is the Rydberg constant. Similarly, when an electron jumps down from any higher energy level to the second energy level, then the emitted lines form the Balmer series 1 λ B = R 1 2 2 - 1 n 2 For maximum wavelength, the energy gap should be the smallest n = 2 , 1 λ L = R 1 - 1 2 2 = R 1 - 1 4 = 3 R 4 n = 3 , 1 λ B = R 1 2