Problem 23
Show that a molecule with a \(C_{n}\) axis cannot have a dipole moment perpendicular to the axis.
Problem 24
The \(C_{4 \mathrm{v}}\) group has the following classes: \(E, 2 C_{4}\) \(C_{2}, 2 \sigma_{\mathrm{v}}\) and \(2 \sigma_{d} .\) How many irreducible representations does this group have and what is the dimensionality of each? \(\sigma_{d}\) refers to a dihedral mirror plane. For example in the molecule \(\mathrm{BrF}_{5},\) the \(\sigma_{\mathrm{v}}\) mirror planes each contain two of the equatorial \(F\) atoms, whereas the dihedral mirror planes do not contain the equatorial \(F\) atoms.
