An energy–level diagram for the hydrogen atom is drawn on a vertical energy axis, taking the ground state as −13.6eV and the ionisation limit as 0eV. Answer the following:
(i) Write the mathematical expression that gives the energy En of the nth stationary state of a hydrogen atom.
(ii) Using the result of part (i), explain why the vertical spacing between successive energy levels becomes smaller as n increases when the levels are plotted on a uniform energy scale.
(iii) On such a diagram, a student shades the entire region between the n=1→n=2 and n=2→n=3 vertical drops to represent ultraviolet radiation. Justify whether this shading is correct. State, with reasons, which principal quantum number transitions in hydrogen mainly fall in the visible region of the spectrum.