Past exam of the chemistry course of the year 3 of the natural sciences course of the University of Cambridge / 2021 / Paper 2A / Section B / 21 / d / Solution

The inferred dipole moment is approximately $0.626\mathrm{D}$. With the static field parallel to the radiation electric field, the microwave selection rule is $\Delta M_J=0$. A fully resolved three-component first-order rotational Stark effect pattern naturally identifies the $J=1\to 2$, $|K|=1$ transition: the three initial $M_J=-1,0,1$ values give the three components. $K=0$ would have no first-order shift.

Subtract the lower-state field shift from the upper-state field shift, rather than equating a transition shift to one level's shift:For $J=1$ and $|K|=1$, neighbouring components are separated by $\mu E_{\mathrm{field}}/(3h)$. HenceThis assignment assumes the stated splitting resolves all allowed first-order components, rather than three accidentally unresolved groups of a higher-$J$ transition.