Using Bohr's atomic model, the orbital period of electron in hydrogen atom in the n^ th orbit is ( ₀ =permittivity of free space, h=Planck's constant, m = mass of electron, e = electronic charge)

Step-by-step solution

The radius of the n^ th orbit in Bohr's model is given by r = ₀ n^2 h^2 m e^2 . The velocity of the electron in the n^ th orbit is given by v = e^2 2 ₀ n h . The orbital period T is the time taken to complete one revolution, which is T = 2 r v . Substituting the values of r and v : T = 2 ( ₀ n^2 h^2 m e^2 ) e^2 2 ₀ n h T = 2 ₀ n^2 h^2 m e^2 2 ₀ n h e^2 T = 4 ₀^2 n^3 h^3 m e^4 Answer: 4 , ₀^2 n^3 h^3 me^4