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Atomic orbitals: 2p wave function

Schematic plot of the 2px wave function ψ2px. 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 while the surface plot on the right shows values of ψ2px on a slice drawn through the nucleus, here the xy plane.

There are three 2p orbitals. These functions have the same shape but are aligned differently in space. They are labelled 2px, 2py, and 2pz since the functions are "aligned" along the x, y, and z axes. The orbital plotted above is a 2px orbital. The equations for the 2p orbitals (ψ2p) 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.

There is a planar node normal to the axis of the orbital (so the 2px orbital has a yz nodal plane, for instance). 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 2p-orbital has (2 - 2) = 0 radial nodes. The higher p-orbitals (3p, 4p, 5p, 6p, and 7p) are more complex since they do have spherical nodes.

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Document served: Friday 27th November, 2020