Here our problem is to prove that the Bohr hydrogen atom approaches classical conditions when n becomes very large and small quantum jumps are involved.
To prove this let us compute the frequency of a photon that is emitted in the transition between the adjacent state and when .
we define Rydberg’s constant as
Therefore the frequency of the emitted photon is
, so for we have
According to classical theory of electromagnetism , a rotating charge with a frequency will emit a radiation of frequency . On the other hand , using the Bohr hydrogen model , the orbital frequency of the electron around the nucleus is
, which is identical to