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^(2)`
B. `(1)/(n^(3))`
C. `n^(2)`
D. `(1)/(n^(4))`

Answer

B

Explanation

`E_(n)-E_(n-1)`
`=(-13.6 Z^(2))/(n^(2))+(-13.6Z^(2))/((n-1)^(2))=[(1)/((n-1)^(2))-(1)/(n^(2))]`
`hv=13.6 Z^(2)[(n^(2)-(n-1)^(2))/(n^(2)(n-1)^(2))]`
`=(13.6Z^(2))/(n^(2))[(1)/((1-1//n)^(2))-1]`
`=(13.6Z^(2))/(n^(2))[a+(2)/(n)-1]=(2xx13.6Z^(2))/(n^(3))v prop(1)/(n^(3))` (b)