## H atom orbitals in 3D

The various pictures of H atom orbitals in the text or elsewhere on our web site are important places to turn to learn how atomic orbital quantum numbers control the size, shape, orientation, and nodal patterns of orbitals in general. It is important to remember, however, that orbitals really are three-dimensional objects, and it is often helpful to see three-dimensional pictures of them to reinforce their shapes and nodal patterns. Since the World Wide Web's technology is not yet capable of projecting a 3D holographic image into space à la Star Wars movies, we'll have to settle for animations of 3D images. A few of these are collected here in the form of QuickTime movies or static pictures of 3D drawings.

We start with the three 2p orbitals, px, py, and pz. The movie below spins these around the z axis. The flat nodal planes, one per orbital because l = 1 and the number of nodal planes equals l, are shown in gray. The orbitals (the wavefunctions) are shown in red and blue to distinguish their algebraic signs. The red parts have the opposite algebraic sign of the blue parts. As you play the movie, you will notice that the pz orbital in the middle doesn't seem to move. That's because this orbital has m = 0, and all m = 0 orbitals are cylindrically symmetric about the z axis; they look the same as they spin around the z axis of symmetry.

If we look at similar pictures for a d and an f orbital, we can see how these pick up one extra nodal plane for each step up in l.

The orbitals shown here have only flat planar nodes, but among the five d and seven f orbitals, one of each type has m = 0, and these are cylindrically symmetric with two (for d) or three (for f) planar nodes, as shown below in comparison to the pz orbital. For the pz orbital, the one nodal plane is the flat xy plane. For the d orbital, the two nodal planes are cones (shown in two different shades of gray). For the f orbital, two of the three nodal planes are cones, but the third is a flat plane, the xy plane again.