An isolated atom of a certain element emits light of wavelength λ_m1 when the atom falls from its state with quantum number m into its ground state of quantum number 1. The atom emits a photon of wavelength λ_n1 when the atom falls from its state with quantum number n into its ground state.

(a) Find the wavelength of the light radiated when the atom makes a transition from the m state to the n state.

(b) Show that k_mn = |k_m1 - k_n1|, where k_ij = 2π/λ_ij is the wave number of the photon. This problem exemplifies the Ritz combination principle, an empirical rule formulated in 1908.