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Atomic orbitals: 3p wave function

Schematic plot of the 3px wave function ψ3px. Note the line plot uses the x axis as the horizontal axis. Blue represents negative values for the wave function and red represents positive values. 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 ψ3p on a slice drawn through the nucleus including x axis.

There are three 3p orbitals. These functions have the same shape but are aligned differently in space. They are labelled 3px, 3py, and 3pz since the functions are "aligned" along the x, y, and z axes. The orbital plotted above is a 3px orbital. The equations for the 3p orbitals (ψ3p) 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 3p orbitals are quite complex. Each has a total of four lobes, the inner two of which are small. There is a planar node normal to the axis of the orbital (so the 3px orbital has a yz nodal plane, for instance). There is also a spherical node that partitions off the 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 3p-orbital has (3 - 2) = 1 radial node. The higher p-orbitals (4p, 5p, 6p, and 7p) are more complex since they have more spherical nodes.

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Document served: Monday 28th September, 2020