What type of rotation is associated with the symmetry operator Cn?

The symmetry operator Cn represents a proper rotation axis in molecular symmetry. Specifically, Cn indicates that a molecule can be rotated around a specific axis by an angle of 360/n degrees, where n is the order of the rotation. This means that after rotating the molecule by this angle, its appearance is indistinguishable from its original position, effectively resulting in a symmetrical configuration.

This concept is crucial in the context of molecular symmetry because it allows chemists to categorize and predict the behavior of molecules based on their symmetry elements. Proper rotations, like Cn, play a significant role in understanding molecular shape, reactivity, and interactions.

The other options reflect different types of symmetry operators. For instance, rotation by any arbitrary angle does not correlate with the fixed increments of symmetry operations denoted by Cn. Inversion of the molecule refers to the operation where each point in the molecule is reflected through a central point, whereas reflection across a plane describes a different symmetry operation entirely. Thus, the accurate definition of the Cn operator aligns specifically with rotation by 360/n degrees.