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.
The energy of radiation at level n is given by the relation:
…(i)
Where v1 is the frequency of radiation at level n
H is Planck’s constant
m is mass of hydrogen atom
e is charge on electron
ε0 is permittivity of free space
The energy of radiation at level (n-1) is given by the relation:
……………(ii)
Where v2 is the frequency of radiation at level n-1
Due to deexcitation of the electrons, the energy released is:
E =E2- E1
hv = E2- E1…………………..(iii)
Putting equation (i) and (ii) in equation (iii), we get
v =
v = 
For large values of n, (n-1)≈n
v = 
Frequency of revolution of an electron is given by
Vc = v/2πr……………..(vi)
Velocity of electron in nth orbit is given by the following relation
…………………….(iv)
The radius of nth orbit is given by the following relation
r =
………………….(v)
Substituting the values of equation (iv) and (v) in equation (vi), we get
