## What is the difference between the \(d_{x^{2}-y^{2}}\) and \(d_{x y}\) orbitals of the same n?

Answer:

The \(d_{x^{2}-y^{2}}\) has two vertical nodal planes \(\text{bisecting}\) the \(x\) and \(y\) axes, and the \(d_{x y}\) has an \(xz\) and \(yz\) nodal plane.

The only difference between these two orbitals is that the \(d_{x^{2}-y^{2}}\) lobes are along the axes and the \(d_{x y}\) is rotated \(45^{\circ}\) counterclockwise.

You can spot the two nodal planes by constructing vertical planes between lobes of opposite phases.

Since there are alternating phases all the way around, there must be two nodal planes, and they must be perpendicular to each other.