Answer one of the two questions in this section.

Do not answer more than the required number of questions in this section. Extra answers will not be marked.

1.

(a)

Briefly describe the photoelectron spectroscopy experiment. In particular, explain what needs to be measured to obtain the final result. [6 marks]

Notes: While it may help to write down a formula or two to guide your discussion, very little mathematical detail is expected. In particular, you need not give any detail about how any relevant quantities are measured.

(b)

Predict the photoelectron spectrum of N₂ using Koopmans's theorem. [9 marks]

2.

(a)

Using an argument based on LCAO-MO theory, predict the bond order in the molecular ion HHe⁺. [3 marks]

Hint: If it helps, treat this case by analogy to an isoelectronic homonuclear diatomic molecule.

(b)

Compute the bond length in HHe⁺. [5 marks]

(c)

Predict the frequencies of the first several lines of the rotational absorption spectrum of $\isotope{1}{}{H}\isotope{4}{}{He}$ given that the isotopic mass of $\isotope{1}{}{H}$ is 1.0078250321amu while the mass of $\isotope{4}{}{He}$ is 4.0026032497amu. [7 marks]