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Atomic orbitals: 4p

The shape of the three 4p orbitals. From left to right: 4pz, 4px, and 4py. For each, the copper zones are where the wave functions have negative values and the gold zones denote positive 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 still snce they have more spherical nodes.

The origin of the planar node becomes clear if we examine the wave equation which, for instance, includes an x term in the case of the 4px orbital. Clearly When x = 0, then we must have a node, and this by definition is the yz plane.

The origin of the spherical node becomes clearer if we examine the wave equation, which includes a (20 - 10ρ + ρ2) term. When (20 - 10ρ + ρ2) = 0, then we must have nodes. We can solve this to show nodes are 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.

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Document served: Wednesday 21st October, 2020