= Solution
The coarse spacing is about $2\widetilde B$, so $\widetilde B\simeq0.25\ \mathrm{cm^{-1}}$. The two groups near 1.5 and $2.0\ \mathrm{cm^{-1}}$ therefore have \b[$J=2\to3$ and $J=3\to4$], respectively. For positive $\widetilde D_{JK}$, increasing $K^2$ moves a component to lower <wavenumber>. The assignments are
$$
\boxed{\begin{array}{c|c|c}
J\to J+1&K&\widetilde\nu\ /\mathrm{cm^{-1}}\\ \hline
2\to3&0&1.50130\\
&1&1.50128\\
&2&1.50122\\ \hline
3\to4&0&2.00171\\
&1&2.00168\\
&2&2.00160\\
&3&2.00147
\end{array}}
$$
Within one group, successive separations scale as $(K+1)^2-K^2=1,3,5,\ldots$. The observed gaps follow that pattern to their printed precision. There are $J+1$ distinct $|K|$ components because $|K|\leq J$ in the lower state; the $+K$ and $-K$ members remain coincident without an applied field. A high-resolution feature here is therefore not simply assigned to an arbitrary magnetic sublevel.
\Image[/past-exam-of-the-chemistry-course-of-the-year-3-of-the-natural-sciences-course-of-the-university-of-cambridge/2022/paper-2a-rotational.png]
{title=Derived stick assignments of the two rotational groups, showing the K-squared pattern}
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