question_answer 13)

Obtain an expression for the frequency of radiation emitted when a hydrogen atom de-excites from level n to level (n -1). For large n, show that this frequency equals the classical frequency of revolution of the electron in the orbit. 

Answer:

The energy of an electron in the nth orbit of hydrogen atom is given by Also, for the pth orbit, ?(2) The frequency of radiation emitted for the transition of electron from  to  orbit is  (Using eqns (1) & (2) For n = n and p = n - 1, we have For large value of n. In - 1 2n In and n - 1 n.       ?.(3) Now the classical frequency of revolution of electron is given by                            ?(4) But according to Bohr's angular momentum condition,   ?(5) Using eqn. (5) in eqn. (4), ?(6) But   from eqn. (6), for a large n,                                     (Using (3) and (7)) i.e. frequencies are equal. This is called the Bohr's correspondence principle.