Find the ratio of energies of photons produced due to the transition of an electron of a hydrogen atom from its (i) second permitted energy level to the first level, and (ii) the highest permitted energy level to the first permitted level.

Step-by-step solution

(a) Since the second permitted energy level = E 2 − E 1 The energy of the photon produced = ( − 13.6 eV 2 2 ) − ( − 13.6 eV 1 2 ) = − 3.4 + 13.6 = 10.2 eV ( b ) The highest permitted energy level to the first permitted level = E ∞ − E 1 = 0 − ( − 13.6 ) = 13.6 eV ∴ The ratio of energies of photon = 10.2 13.6 = 3 4 = 3 : 4