Problem 6.20

Demonstrate that the frequency $\omega$ of a photon emerging when an electron jumps between neighbouring circular orbits of a hydrogen-like ion satisfies the inequality $\omega_{n}>\omega>\omega_{n+1},$ where $\omega_{n}$ and $\omega_{n+1}$ are the frequencies of revolution of that electron around the nucleus along the circular orbits. Make sure that as $n \rightarrow \infty$ the frequency of the photon $\omega \rightarrow \omega_{n}$.