The frequencies for series limit of Balmer and Paschen series are ' v₁ ^ and ' v₃ ' respectively. If frequency of first line of Balmer series ' v₂ ' then the relation between v₁, v₂ and v₃ is

Step-by-step solution

The frequencies of spectral lines in hydrogen are given by the Rydberg formula: v = R c ( 1 n_f^2 - 1 n_i^2 ) . Series limit of Balmer series : n_i = to n_f = 2 , so v₁ = Rc 4 . First line of Balmer series : n_i = 3 to n_f = 2 , yielding v₂ = 5Rc 36 . Series limit of Paschen series : n_i = to n_f = 3 , giving v₃ = Rc 9 . The energy difference E_ - E₂ equals the sum (E_ - E₃) + (E₃ - E₂) . Dividing by Planck's constant h gives v₁ = v₃ + v₂ , or equivalently v₁ - v₂ = v₃ . Verifying numerically: Rc 4 - 5Rc 36 = 9Rc -