If ' ₁ ' and ' ₂ ' are the wavelengths of the first member of the Balmer and Paschen series, in hydorgen atom respectively, then the ratio of respective frequencies, f₁ / f₂ , is

Step-by-step solution

The ratio of frequencies f₁/f₂ for the first members of the Balmer and Paschen series in hydrogen is determined using the Rydberg formula: 1 = RZ^2 ( 1 n_f^2 - 1 n_i^2 ) For the Balmer series ( n_f = 2 ), the first member corresponds to n_i = 3 : 1 ₁ = R ( 1 2^2 - 1 3^2 ) = 5R 36 The frequency is f₁ = c/ ₁ = 5Rc/36 . For the Paschen series ( n_f = 3 ), the first member corresponds to n_i = 4 : 1 ₂ = R ( 1 3^2 - 1 4^2 ) = 7R 144 The frequency is f₂ = c/ ₂ = 7Rc/144 . The ratio becomes: f₁ f₂ = 5Rc/36 7Rc/144 = 5 36