# 4p orbitals

The shape of the three 4p orbitals. From left to right: 4py, 4pz, and 4px. For each, the yellow zones are where the wave functions have positive values and the white zones denote negative values.

For any atom, there are three 4p orbitals. These orbitals have the same shape but are aligned differently in space. The three 4p orbitals normally used are labelled 4px, 4py, and 4pz since the functions are "aligned" along the x, y, and z axes respectively.

Each 4p orbital has six lobes. There is a planar node normal to the axis of the orbital (so the 4px orbital has a yz nodal plane, for instance). Apart from the planar node there are also two spherical node that partition off the small inner lobes. The higher p-orbitals (5p, 6p, and 7p) are more complex as they have additional spherical nodes.

The origin of the planar node becomes clear when inspecting the wave equations which, for instance, includes an x term in the case of the 3px orbital. When x = 0, then there is a node, and this by definition is the yz plane.

The origin of the spherical nodes becomes clear when inspecting the wave equations which includes a (20 - 10ρ + ρ2) term. When (20 - 10ρ + ρ2) = 0, then there are nodes. When solved this shows nodes at ρ = 2.5 + √(5/4) and 2.5 - √(5/4). Since for the 4p orbital ρ = 2Zr/4 (Z = effective nuclear charge, r = radius in atomic units), then the nodes are at the radii r, = (5 + √5)/Z and (5 - √5)/Z atomic units.

The OrbitronTM, a gallery of orbitals on the WWW: https://winter.group.shef.ac.uk/orbitron/