Dilip Jha

working in the frame of the heavy(so assumed relative to the electron) nucleus and there fore non accelerating-the centripetal force is provided by the inward electrostatic force of attraction between the electron and the nucleus, so equating these two we get one equation connecting speed of electron v and radius of orbit r. we can get another equation between these two from Bohr's second postulate of quantization of angular momentum. this later equation will involve the principal quantum number n whose value for first and second orbit is 1 and 2 respectively. from these two equations we can solve for v and r.. then the time period would be T=2(pi)r/v. it will then turn out that T is directly proportional to n^3. THUS THE SOUGHT RATION WOULD BE 1^3/2^3=1/8.