Past exam of the chemistry A course of the University of Cambridge / 2024 / Paper 2 / A8 / c

For the two field-sensitive orientations alone, choose the unsplit excited-manifold energy as reference and put $x=\mu B/(k_{\mathrm{B}}T)$. The restricted single-molecule partition function isIf the ground-manifold zero used above is retained, this restricted contribution is instead $2e^{-\beta \Delta }\cosh x$. The extra factor is independent of $B$, so it does not change magnetization conditional on occupying the excited manifold.

There are two magnetic states total; multiplying this expression by another factor of two would double count them. For the full thermal ensemble, the nonmagnetic ground states must be added:Although the omitted ground-state term has no direct field dependence, it affects normalization inside $\ln q$. Thus the restricted expression describes molecules constrained to the excited manifold; it cannot by itself give the magnetization of all thermally equilibrated NO molecules.