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Atomic orbitals: 4p wave function

Schematic plot of the 4p wave function ψ4p. Red shows where thewave function is positive and blue where it is negative. Click on the "Show nodal structure" button to get a clearer view of the nodal structure for this orbital.

The graph on the left is a plot of values along a single line drawn through the nucleus along the x axis, while the surface plot on the right shows values of ψ4p on a slice drawn through the nucleus including x axis.

There are three 4p orbitals. These functions have the same shape but are aligned differently in space. They are labelled 4px, 4py, and 4pz since the functions are "aligned" along the x, y, and z axes. The orbital plotted above is a 4px orbital. The equations for the 4p orbitals (ψ4p) show that in addition to a radial dependency, there is a dependency upon direction. This is why p orbitals are not spherical. This behaviour is unlike that of the s orbitals for which the value of the wave function for a given value of r is the same no matter what direction is chosen.

The 4p orbitals are quite complex. Each has a total of six lobes, the inner four of which are small. There is a planar node normal to the axis of the orbital (so the 4px orbital has a yz nodal plane, for instance). There are also two spherical nodes that partition off the four small inner lobes. Use the "Show nodal structure" button above to help see this.

In general, apart from a nodal plane, p-orbitals have a number of radial nodes that separate the largest, outer, component from the inner components. The number of radial nodes is related to the principal quantum number, n. In general, a np orbital has (n - 2) radial nodes, so the 4p-orbital has (4 - 2) = 2 radial nodes. The higher p-orbitals (5p, 6p, and 7p) are more complex still since they have more spherical nodes.

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Document served: Wednesday 21st October, 2020