Question -
Answer -
It is given that a hydrogen atomde-excites from an upper level (n) to a lower level (n−1).
We have the relation for energy (E1)of radiation at level n as:
Now, the relation for energy (E2) ofradiation at level (n − 1) is
givenas:
Energy (E) released as aresult of de-excitation:
E = E2−E1
hν = E2 − E1 …(iii)
Where,
ν = Frequency of radiationemitted
Putting values from equations (i)and (ii) in equation (iii), we get:
For large n, we can write
Classical relation of frequency of revolution of anelectron is given as:
Where,
Velocity of the electron inthe nth orbit is given as:
v =
And, radius of the nth orbitis given as:
r = 
Putting the values of equations(vi) and (vii) in equation (v), we get:
Hence, the frequency of radiationemitted by the hydrogen atom is equal to its classical orbital frequency.