The wavefunctions of the five degenerate d orbitals of a free ion are, in Cartesian coordi- nates, 01 = 2(x+iy)zf(r), 02 = 2(x-iy)zf(r), 03 = (x+iy)?f(r), 04 = (r-iy)?f(r), 05 = + (322p2)f(r). where f(r) is the radial wavefunction. Show that these functions transform into one another under the elements E, A and K representative of the classes of the group 32. Hence, deduce that the five-fold degeneracy of the d orbitals splits into two doublets and a singlet when the ion is placed in a site of symmetry 32. 32 (D3) E 3. [2] 2y [3] 1 1 1 1 1 2 2 3 1 1 -1 2+y2, 22 Z, R, (x, y), (x2-y?, y), (yz, xz), (Rx, R,) 2 -1 O The wavefunctions of the five degenerate d orbitals of a free ion are, in Cartesian coordi- nates, 01 = 2(x+iy)zf(r), 02 = 2(x-iy)zf(r), 03 = (x+iy)?f(r), 04 = (r-iy)?f(r), 05 = + (322p2)f(r). where f(r) is the radial wavefunction. Show that these functions transform into one another under the elements E, A and K representative of the classes of the group 32. Hence, deduce that the five-fold degeneracy of the d orbitals splits into two doublets and a singlet when the ion is placed in a site of symmetry 32. 32 (D3) E 3. [2] 2y [3] 1 1 1 1 1 2 2 3 1 1 -1 2+y2, 22 Z, R, (x, y), (x2-y?, y), (yz, xz), (Rx, R,) 2 -1 O