In a hydrogen like atom electron makes transition from an energy level with quantum number n to another with quantum number (n - 1). If `n gt gt 1,` 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

Energy of radius emitted
`E=hv=E_(0)Z^(2)[1/((n-1)^(2))-1/n^(2)]=E_(0)Z^(2)[(2n-1)/(n^(2)(n-1)^(2))]`
`hv~~E_(0)Z^(2) [(2n)/n^(4)]implies v prop 1/n^(3)`