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Atomic orbitals: 3d wave function

This page addresses the 3dz2 wave function. See the 3dxy, 3dxz, 3dyz, and 3dx2-y2 page for information about the other 3d wave functions.

Schematic plot of the 3dz2 wave function ψ3dz2. 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 drawn through the nucleus along the z-axis, while the surface plot on the right shows values of ψ3dxy on a slice in the xz plane drawn through the nucleus.

The plot above is for the 3dz2 orbital - see the 3dxy, 3dxz, 3dyz, and 3dx2-y2 page for comparable information about their wave functions.

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 3d-orbitals have (3 - 3) = 0 radial nodes.

The equations for the 3d orbitals (ψ3d) 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.

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