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 \(\omega \rightarrow \omega_{n}\).