The first, second and third excited energies for hydrogen atom are
E’1 = E2 – E1 = -3.4 – [-13.6] = 10.2 eV,
E’2 = E3 – E1= -1.51 – [-13.6] = 12.09 eV,
and E’3 = E4 – E1 = -0.85 – [-13.6] = 12.75 eV
It follows that when a 12.5 eV electron beam is used to bombard gaseous hydrogen at room temperature, the H – atoms at the most will be raised to n = 3 level. The H – atoms may come to ground state directly or via n = 2 level. Therefore, the wavelengths emitted will lie in Balmer series [for de-excitation from n = 3 level to n = 2 and 1 level] and Lyman series [for dexadexcitation from n = 2 level to n = 1 level].
