Solid-state nuclear magnetic resonance (NMR) spectroscopy finds growing application to inorganic and organic materials, biological samples, polymers, proteins, and cellular membranes. However, this technique is often neither included in laboratory curricula nor typically covered in undergraduate courses. On the other hand, spectroscopy and molecular structure taught in second-semester undergraduate physical chemistry courses meet the minimal background prerequisites for interpreting data obtained in many solid-state NMR experiments. A solid-state [superscript 2]H NMR experiment is described in which the student obtains and interprets the spectrum of a powder sample of hexamethylbenzene-d[subscript 18] using a solution NMR spectrometer as found in many undergraduate institutions. A quadrupolar-echo pulse sequence is applied to the sample to obtain the [superscript 2]H NMR spectrum. The spectrum of a randomly oriented powder sample consists of two spectral branches with broad shoulders. The quadrupolar frequencies corresponding to the nuclear spin transitions are interpreted in terms of molecular mobility in the solid state, that is, 3-fold rotation of the methyl groups and 6-fold rotation of the hexamethylbenzene ring. In this way, students discover that solid substances may have significant molecular motions. This undergraduate investigation employing solid-state [superscript 2]H NMR provides an informative exposure to state-of-the-art research techniques by using facilities that are already in place at many undergraduate institutions. Furthermore, it demonstrates a real-life manifestation of quantum mechanics as explained in physical chemistry courses, as well as fundamentals of molecular motions such as rotation of aromatic ring compounds and methyl groups in the solid state. (Contains 2 tables and 7 figures.)