Question

Will someone please explain the dz² orbital? I want to know how it is possible and what all is going on.

Answer 1

For each atom, there are five 3d orbitals. These are labelled 3d_xy, 3d_xz, 3d_yz, 3d_x²-y² and 3d_z². Four of these functions have the same shape but are aligned differently in space. The fifth function (3d_z²) has a different shape.

Each 3d_xy, 3d_xz, 3d_yz, and 3d_x²-y² orbital has four lobes. There are two planar node normal to the axis of the orbital (so the 3d_xy orbital has yz and xz nodal planes, for instance). The 3d_z² orbital is different and has two conical nodes.

The origin of the planar nodes becomes clear if we examine the wave equations which, for instance, includes an xy term in the case of the 3d_xy orbital. Clearly when either x = 0 or y = 0, then we must have a node, and this by definition is the case for the yz and a xz planes.