(a) Show that in the Bohr model, the frequency of revo-lution of an electron in its circular orbit around a stationary hydrogen nucleus is f = me4/4ε02n3h3 (b) In classical physics, the frequency of revolution of the electron is equal to the frequency of the radiation that it emits. Show that when n is very large, the fre-quency of revolution does indeed equal the radiated frequency cal-culated from Eq. (39.5) for a transition from n1 = n + 1 to n2 = n.
v = e2/2ε0nh
r = ε0n2h2/πme2
The Attempt at a Solution
I managed to solve part (a). But for part (b), I'm not sure how to find the energy of the photon. I tried
E = -13.6eV (1/n2 - 1/(n+1)2) which I expanded to get
E = -13.6eV ((2n+1)/n2(n+1)2) but doesn't this tend to 0 as n approaches infinity? Since E = hf this implies that f tends to 0 as well? Does anybody know how to prove the relationship in part (b)? Thanks! :)