Question

Distinguise proper and improper rotations

Answer 1

proper rotation
Proper Rotation (Cn)

The rotation operations occur with respect to line called an axis of rotation. A proper rotation is performed by rotating the molecule 360°/n, where n is the order of the axis. If the resulting configuation is indistinguishable from the original, we say there exists ann-fold proper rotation axis (or Cn axis) in the molecule.

Each of the following molecules contains one or more proper axes:

The water molecule contains a C2 axis

Ethane contains both C2 and C3 axes

Improper rotation

In geometry, an improper rotation, also called rotoreflection, rotary reflection, or rotoinversion is, depending on context, a linear transformation or affine transformation which is the combination of a rotation about an axis and a reflection in a plane perpendicular to that axis.