Answer the following with reference to the hydrogen spectrum:
(a) Show that, for any fixed lower quantum number n1, the wavelength of the emitted radiation approaches a finite limit as the upper quantum number n2 tends to infinity.
(b) Explain physically why this limiting wavelength is associated with the ionisation of the atom from the level n1.
(c) Using suitable arguments, justify why the Lyman series lines fall in the ultraviolet region, the Balmer series in the visible region and the Paschen series in the infrared region of the electromagnetic spectrum.