= Solution
\Image[/past-exam-of-the-chemistry-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2021/paper-1-q2-molecular-orbitals.png]
{title=Qualitative valence molecular-orbital occupancies for nitrogen, oxygen, lithium and beryllium dimers}
Suppress the filled 1s core pair, which contributes zero net <bond order>. For N$_2$, use the valence ordering
$$
\sigma_{2s}<\sigma_{2s}^*<\pi_{2p}<\sigma_{2p_z}
<\pi_{2p}^*<\sigma_{2p_z}^*
$$
and occupy it as $(\sigma_{2s})^2(\sigma_{2s}^*)^2(\pi_{2p})^4(\sigma_{2p_z})^2$.
For O$_2$, the ordering of the bonding 2p levels is reversed: $\sigma_{2p_z}<\pi_{2p}$. Occupancy is $(\sigma_{2s})^2(\sigma_{2s}^*)^2(\sigma_{2p_z})^2(\pi_{2p})^4(\pi_{2p_x}^*)^1(\pi_{2p_y}^*)^1$, with parallel <spins> in the two degenerate antibonding pi orbitals.
Li$_2$ has $(\sigma_{2s})^2$; Be$_2$ has $(\sigma_{2s})^2(\sigma_{2s}^*)^2$ in the elementary valence description. Empty 2p-derived levels must also be included to discuss mixing and Be$_2$'s weak bonding; their precise energies are not set by this qualitative diagram.
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