The emission spectra of He⁺ ions show 6 different photons (from transitions to ground state). The quantum number n of the state finally populated in He⁺ ions from the H–He⁺ mixture experiment (after H transfers excitation energy) is

H* (n=2) excitation energy = 10.2 eV. He⁺ (n=2) energy = −13.6 eV. After receiving 10.2 eV: total = −13.6 + 10.2 + 40.8 = 51 eV above ground. He⁺ ground = −54.4 eV. E₄(He⁺) = −54.4/16 × 4 = −3.4 eV. ΔE(1→4 for He⁺) = 51 eV. So n = 4.