In a hydrogen like atom electron make transition from an energy level with quantum number $$n$$ to another with quantum number $$\left( {n - 1} \right).$$  If $$n > > 1,$$  the frequency of radiation emitted is proportional to :

Solution :
$$\eqalign{ & \frac{\nu }{x} = \frac{1}{\lambda } = R{Z^2}\left[ {\frac{1}{{n_1^2}} - \frac{1}{{n_2^2}}} \right] \cr & \left[ {\because n > > 1} \right] \cr & \nu = RC{Z^2}\left[ {\frac{1}{{{{\left( {n - 1} \right)}^2}}} - \frac{1}{{{n^2}}}} \right] \cr & RC{Z^2}\left[ {\frac{{2n - 1}}{{{n^2}{{\left( {n - 1} \right)}^2}}}} \right] \cr} $$