Electron in hydrogen atom first jumps from third excited state to second excited state and then form second excited state to first excited state. The ratio of wavelength `lambda_(1): lambda_(2)` emitted in two cases is

Options

A. `7//5`
B. `27//20`
C. `27//5`
D. `20//7`

Answer

D

Explanation

Here, for wavelength `lambda_(1)`
`n_(1)=4 and n_(2)=3`
and for `lambda_(2)n_(1)=3 and n_(2)=2`
We have `(hc)/(lambda)=-13.6[(1)/(n_(2)^(2))-(1)/(n_(1)^(2))]` So, for `lambda_(1)`
`rArr(hc)/(lambda_(1))=-13.6[(1)/((4)^(2))-(1)/((3)^(2))]`
`rArr(hc)/(lambda_(1))=13.6[(7)/(144)]" " ....(i)`
Similary, for `lambda_(2)`
`rArr(hc)/(lambda_(2))=13.6[(1)/((3)^(2))-(1)/((2)^(2))]`
`rArr(hc)/(lambda_(2))=13.6[(5)/(36)]" " ....(ii)`
Hence, from Eqs. (i), and (ii), we get
`(lambda_(1))/(lambda_(2))=(20)/(7)`