A hydrogen atom (Z = 1) is in the third excited state, and a photon is either emitted or absorbed. Concepts: 

(i) What is the quantum number of the third excited state? 

(ii) When an atom emits a photon, is the final quantum number nf of the atom greater than or less than the initial quantum number ni? 

(iii) When an atom absorbs a photon, is the final quantum number nf of the atom greater than or less than the initial quantum number ni? 

(iv) How is the wavelength of a photon related to its energy? 

Calculations: 

Determine the quantum number nf of the final state and the energy of the photon when the photon is

(a) Emitted with the shortest possible wavelength,

(b) Emitted with the longest possible wavelength, 

(c) Absorbed with the longest possible wavelength.