 Solution

A spectral component shifts by the difference between its upper- and lower-level Stark shifts. With $\Delta J=+1$, $\Delta K=0$ and $\Delta M=q$, the supplied energy formula givesFor radiation polarized parallel to the static field, $q=0$, soThus the assigned $K=0$ feature has no first-order splitting, whereas the $K\ne 0$ features acquire symmetrically arranged magnetic-sublevel components with spacings proportional to $|K|$. With perpendicular radiation, $q=\pm 1$ gives the corresponding different allowed pattern. Recording field-dependent spectra with specified polarization would test both the J values and the K sequence; using an individual level's shift alone would not predict the observed line positions. Higher-order shifts of the nominally unsplit feature are outside this first-order test.