An atom's electron distribution will have an electric quadrupole moment if the distribution is a nonspherical ellipsoid. The matrix element for an electric quadrupole transition is proportional to the electric quadrupole operator \(Q=x^{2}+y^{2}-2 z^{2}=r^{2}-3 z^{2}\).

(a) What is the parity of \(Q\) ?

(b) What does the parity of \(Q\) imply about the parity of the initial and final states of an allowed electric quadrupole transition?