The correct answer is option 'D', which indicates that the signal at 39.7 ppm in the 13C NMR spectrum of DMSO-d6 is a septet. This means that the signal is split into seven peaks with different intensities.

Explanation:

DMSO-d6 is a deuterated form of dimethyl sulfoxide (DMSO), which is commonly used as a solvent in NMR spectroscopy. The deuterium atom in DMSO-d6 replaces one of the hydrogen atoms in the methyl groups of DMSO, resulting in a different chemical environment for the carbon atoms.

In the 13C NMR spectrum, each unique carbon atom in a molecule gives rise to a distinct signal. The chemical shift, measured in parts per million (ppm), indicates the relative position of the carbon atom in the molecule. The splitting pattern of the signal provides information about the neighboring atoms.

In the case of DMSO-d6, the signal at 39.7 ppm corresponds to the carbon atom in the methyl group that is attached to the deuterium atom. This carbon atom has three neighboring protons (two methyl groups and one methylene group), which generate a splitting pattern in the NMR spectrum.

The splitting pattern is determined by the concept of spin-spin coupling. The protons on neighboring carbon atoms can have different spin states, either aligned with or against the external magnetic field. These different spin states can interact with the spin states of the observed carbon atom, leading to splitting of the signal.

In this case, the carbon atom in the methyl group has three neighboring protons, which can be arranged in different spin combinations. The number of possible combinations determines the splitting pattern. For a system with three equivalent protons, the splitting pattern follows the (n+1) rule, where n is the number of protons.

So, for three equivalent protons, the splitting pattern is a quartet (4+1=5 peaks), which is not the correct answer. However, the signal is a septet, which suggests the presence of two additional protons. These two additional protons are part of the methylene group adjacent to the methyl group.

Therefore, the correct answer is option 'D', indicating that the signal at 39.7 ppm in the 13C NMR spectrum of DMSO-d6 is a septet, which arises from the interaction with two neighboring protons.