4p orbitals

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

The three 4p orbitals. Use the previous and next icons to see other views

The three 4p orbitals including orbital nodes. Use the previous and next icons to see other views

Nodes of the three 4p orbitals. Use the previous and next icons to see other views

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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 4p_x, 4p_y, and 4p_z 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 4p_x 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 3p_x 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.