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

So,

and

Therefore the frequency of the emitted photon is

, so for we have

and

Therefore ,

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

or

, which is identical to