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

According to Bohr's theory of hydrogen atom, frequency of radiation emitted,
`v=(DeltaE)/h=K[1/((n-1)^(2)-1/(n^(2)))]`,
where K is a constant
`=K[(n^(2)-(n-1)^(2))/(n^(2)(n-1)^(2))]`
`=K ((n+n-1)(n-n+1))/(n^(2)(n-1)^(2))=((2n-1))/(n^(2) (n-1)^(2))`
As `ngt gt1, therefore, v=(K(2n))/(n^(4)), i.e., v prop1/(n^(3))`