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Atomic orbitals: 7p

The shape of the three 7p orbitals. From left to right: 7pz, 7px, and 7py. For each, the copper zones are where the wave functions have negative values and the green zones denote positive values.

For any atom, there are three 7p orbitals. These orbitals have the same shape but are aligned differently in space. The three 7p orbitals normally used are labelled 7px, 7py, and 7pz since the functions are "aligned" along the x, y, and z axes respectively.

Each 7p orbital has 12 lobes. There is a planar node normal to the axis of the orbital (so the 7px orbital has a yz nodal plane, for instance). Apart from the planar node there are also five spherical node that partition off the small inner lobes.

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 7px orbital. Clearly When x = 0, then we must have a node, and this by definition is the yz plane.

The origin of the spherical nodes becomes clearer if we examine the wave equations, which include a (6720 - 8400ρ + 3360ρ2 - 420ρ3 + 40ρ4 - ρ5) term. When (6720 - 8400ρ + 3360ρ2 - 420ρ3 + 40ρ4 - ρ5) = 0, then we must have nodes. Whil not trivial, we can solve this on a case-by-case basis to determine the position of the nodes.

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