How will you account for the simultaneous appearance of large number of lines in the hydrogen spectrum?

When an electric discharge is passed through a tube containing hydrogen gas at low pressure, hydrogen molecules dissociate to form hydrogen atoms. These hydrogen atoms absorb different amounts (quanta or photons) of energy and the electrons are accordingly promoted to different higher energy states (n = 2, 3, 4, 5.....). All these excited states are metastable states and electrons soon radiate energy and come back to the lower energy levels in one or more jumps. Some come back to the ground state (n = 1) and others to n = 2, n = 3, n = 4 ....etc. from higher energy levels. Each of these different return jumps which are occurring simultaneously, emit radiations of different frequencies or wave numbers and thus produce large number of lines in the hydrogen spectrum.