If an electron is revolving in an orbit at frequency , classical electromagnetism predicts that it will radiate energy not only at this frequency but also at , , , and so on. We have to show that this is also predicted by Bohr’s theory of the hydrogen atom in the limiting case of large quantum numbers.

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We will use the following results of the Bohr’s theory of the hydrogen atom:

From these results we note that the frequency of rotation of the orbit with principal quantum number is

.

We will consider the limit of large quantum numbers that is we will assume that . The classical frequency of a Bohr orbit with will therefore be

.

We next consider Bohr transitions from the state with principal quantum number , , to states with principal quantum number .

The frequency of spectral lines when hydrogen atom makes transitions from state , , to states with principal quantum number .

Will be

We obtain the expression for in the limit .

We find

We thus note that in the limit of large quantum numbers, the correspondence limit, the quantum result agrees with the classical physics result.