The principle quantum number ' n ' corresponding to the exited state of He ⁺ ion, if on transition to the ground state two photons in succession with wavelength 1026 ~A ^ and 304 ~A ^ are emitted ( R =1.097 10^7 ~m ⁻¹ )

Step-by-step solution

For first photon, aligned & =304 Å, n ₁=1 & 1 = Rz ^2 ( 1 n ₁^2 - 1 n ₂^2 ) aligned aligned & 1 304 10⁻¹⁰ =1.097 10^7 (2)^2 ( 1 1^2 - 1 n ₂^2 ) & n ₂=2 aligned For second photon, aligned & =1026 Å, n ₁=2, n ₂= n & 1 1026 10⁻¹⁰ =1.097 10^7 (2)^2 ( 1 2^2 - 1 n ^2 ) & n =6 aligned