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In a hydrogen like atom electron makes t...

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

A

`(1)/(n^(2)`

B

`(1)/(n^(3))`

C

`n^(2)`

D

`(1)/(n^(4))`

Text Solution

Verified by Experts

The correct Answer is:
B
`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)
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