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Atomic orbitals: 4d wave function
This page addresses the 4dxy, 4dxz, 4dyz, and 4dx2-y2 wave functions. See the 4dz2 page for information about its wave function.
Schematic plot of the 4dxy wave function ψ4dxy. The blue zones are where the wave function has negative values and the red zones denote positive values.
The graph on the left is a plot of values along a single line along the x=y line drawn through the nucleus while the surface plot on the right shows values of ψ4dxy on the xy plane drawn through the nucleus.
The plot above is labelled for the 4dxy orbital but the form of the plots for the 4dxz, 4dyz, and 4dx2-y2 orbitals is similar, differing only in orientation. See the 4dz2 page for comparable information about its wave function.
In general, apart from the two nodal planes, d-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 nd orbital has (n - 3) radial nodes, so 4d-orbitals have (4 - 3) = 1 radial node.
The equations for the 4d orbitals (ψ4d) show that in addition to a radial dependency, there is a dependency upon direction. This is why d 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 Orbitron is a gallery of orbitals on the WWWThe OrbitronTM, a gallery of orbitals on the WWW, URL: http://winter.group.shef.ac.uk/orbitron/
Copyright 2002-2015 Prof Mark Winter [The University of Sheffield]. All rights reserved.
Document served: Sunday 16th February, 2020