Find the quantum number `n` corresponding to the excited state of `He^(+)` ion, if on transition to the ground state that ion emits two photons in succession with wave lengths `108.5` and `30.4 nm`.

Answer

`n=5`

Explanation

Total energy of radiation
`E=(hc)/(lambda_(1))+(hc)/(lambda_(2))`
`13.6xx4xx(1-(1)/n^(2))=((1240)/(108.5)+(1240)/(30.4))eV`
`1-(1)/(n^(2))=(1)/(13.6xx4)xx52.22`