(a) Show that in the Bohr model, the frequency of revolution of an electron in its circular orbit around a stationary hydrogen nucleus is $f=m e^{4} / 4 \epsilon_{0}^{2} n^{3} h^{3}$ . (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 frequency of revolution does indeed equal the radiated frequency calculated from Eq. $(39.5)$ for a transition from $n_{1}=n+1$ to $n_{2}=n .$ (This illustrates Bohr's correspondence principle, which is often used as a check on quantum calculations. When $n$ is small, quantum physics gives results that are very different from those of classical physics. When $n$ is large, the differences are not significant, and the two methods then "correspond." In fact, when Bohr first tackled the hydrogen atom problem, he sought to determine $f$ as a function of $n$ such that it would correspond to classical results for large $n . )$