The frequency of revolution of an electron in the n ^ th orbit of hydrogen atom is

Step-by-step solution

The velocity of an electron in the n th orbit of a hydrogen atom is v_n = Ze^2 2 ₀ nh , which simplifies to v_n 1 n for hydrogen ( Z=1 ). The corresponding orbital radius is r_n = ₀ n^2 h^2 m Z e^2 , giving r_n n^2 . The frequency of revolution is the velocity divided by the orbital circumference: f = v_n 2 r_n . Substituting the proportional relationships yields f 1/n n^2 = 1 n^3 . The frequency is inversely proportional to n^3 .