In a hydrogen like atom electron make transition from an energy level with quantum number `n` to another with quantum number `(n - 1)` if `n gtgt1` , the frequency of radiation emitted is proportional to :

Options

A. `(1)/(n)`
B. `(1)/(n^(2))`
C. `(1)/(n((3)/(2)))`
D. `(1)/(n^(3))`

Answer

D

Explanation

`Delta E=hv`
`v=(Delta E)/(h)=k[(1)/((n-1)^(2))-(1)/(n^(2))]`
`=(k2n)/(n^(2)(n-1)^(2))~~ (2k)/(n^(3)) prop (1)/(n^(3))`