Question

Do the rotations about two perpendicular C₂ axes constitute a group? If not, what additional operations are required? Show that the defining conditions for a group are satisfied by the operations that you list.

Answer 1

A symmetry operation is a movement of the molecule in such a way that the resulting configuration of the molecule is indistinguishable from the original molecule,that is identical.

Rotational axis symmetery- If a rotation around an axis by 360°/n results in a molecule indistinguishable from the original. n is known as the order of the axis. here n=2 , so it is writen as C2,example is water. 360°/2 = 180^o.

A particular symmetry element generates many symmetry operations. ACn axis generatesa set of operationsCn1....Cn^n.here C2^2 operation result in identical.

if we rotate molecule by 180^o identical molecule we get. since molecule has two fold of symmetry one in the plane of the molecule itself and other perpendicular to it.