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Atomic orbitals: 7p wave function

Schematic plot of the 7p wave function ψ7p. 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 ψ7p on a slice drawn through the nucleus including x axis.

There are three 7p orbitals. These functions have the same shape but are aligned differently in space. They are labelled 7px, 7py, and 7pz since the functions are "aligned" along the x, y, and z axes. The orbital plotted above is a 7px orbital. The equations for the 7p orbitals (ψ7p) 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 7p orbitals are quite complex. Each has a total of twelve lobes, the inner ten of which are small. There is a planar node normal to the axis of the orbital (so the 7px orbital has a yz nodal plane, for instance). There are also five spherical nodes that partition off the ten 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 7p-orbital has (7 - 2) = 5 radial nodes.

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Document served: Wednesday 21st October, 2020