In a hydrogen like atom electron makes transition from an energy level with quantum number n to another with quantum number `(n-1)`. If `ngtgt1`, The frequency of radiation emitted is proportional to

Options

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

Answer

A

Explanation

`(1)/(lamda_(ik))=R((1)/(n_(k)^(2))-(1)/(n_(i)^(2)))`
`(f_(ik))/(c)=R((1)/((n-1)^(2))-(1)/(n^(2)))" "[:.c=lamda_(ik)f_(ik)]`
`=R[(1)/(n^(2)(1-(1)/(n))^(2))-(1)/(n^(2))]`
`R=[(1)/(n^(2)){(1-(1)/(n))^(-2)-1}]`
`=R[(1)/(n^(2)){1+(2)/(n)-1}]`
First two terms of binomial expansion.
`R=[(2)/(n^(3))]`
`f_(ik)=(2Rc)/(n^(3))`
`:.f_(ik)prop(1)/(n^(3))" "` [2 Rc is constant]
`:.fprop(1)/(n^(3))`