Find out the quantum number 'n' coresponding to the exited state of `He^(+)` ion if on transition to the ground state that ion emits two photons in sucession with wavelengths 1026.7 and 304 Å `(R_(H)=1.096xx10^(7)m^(-1))`.

Explanation

For two successive transitions say from n to `n_(1)` and then `n_(1)` to 1
`DeltaE=(E_(n)-E_(n_(1)))+(E_(n_(1))-E_(1))=E_(n)-E_(1)=(hcR_(H)Z^(2))/(1^(2))=hcR_(H)Z^(2)[(n^(2)-1)/(n^(2))] " "…(i)`
Also, `DeltaE_(1)=(hc)/(lambda_(1))+(hc)/(lambda_(2)) =hc[(lambda_(1)+lambda_(2))/(lambda_(1)lambda_(2))]" "...(ii)`
From equations (i) and (ii) `[(n^(2)-1)/(n^(2))] =(1)/(R_(H)Z^(2))[(lambda_(1)+lambda_(2))/(lambda_(1)lambda_(2))]`
`[(n^(2)-1)/(n^(2))]=(1)/(1.097xx10^(7)xx4)[((1026.7+304)xx10^(-10))/(1026xx304xx10^(-20))]=0.9716 " " :.n=6`