Find the quantum number n corresponding to nth excited state of `He^(++)` ion if on transition to the ground state the ion emits two photons in succession with wavelength 108.5 nm and 30.4 nm. The ionization energy of the hydrogen atom is 13.6 eV.

Explanation

The energy of the `He^(+)` ion in the`nth` state `=(13.6Z^(2))/(n^(2))eV`
Here `Z=Z`
`:. E_(n)=-(54.4)/(n^(2))eV`
The energy in the ground state `=-54.4eV`
`:. 54.4(1-(1)/(n^(2)))=(hc)/(1.6xx10^(-19)) ((1)/(lambda_(1))+(1)/(lambda_(2)))=52.35eV`.
`:. 1-(1)/(n^(2))=(52.35)/(54.4)`
`rArr n=5`