A doubly ionised lithium atom (Li2+, Z=3) is initially in the n=5 state.
(i) Derive an expression for the wavelength λ of a photon emitted when an electron in a hydrogen-like ion of atomic number Z makes a transition from an initial level ni to a lower level nf (ni>nf).
(ii) Using your expression, calculate the longest and the shortest wavelengths among all photons that can be emitted while the ion in the n=5 state eventually reaches the ground state.
(iii) Find the ratio of the energies of the most energetic to the least energetic photons obtained in part (ii).
(iv) Identify the spectral region (ultraviolet, visible or infrared) to which each of the two photons in part (ii) belongs.