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Atomic orbitals: 3d radial distribution function

Schematic plot of the 3d radial distribution function r2R3d2 (R3d = radial wave function).

For 3d-orbitals, the radial distribution function is related to the product obtained by multiplying the square of the radial wave function R3d by r2. By definition, it is independent of direction and so is the same for all five 3d orbitals.

In addition to two planar nodes (or two conical nodes in the case of the 3dz2 orbital), d-orbitals, display a number of radial nodes that separate the largest, outer, component from the inner components. The number of nodes is related to the principal quantum number, n. In general, the nd orbital has (n - 3) radial nodes, so the 3d-orbitals have (3 - 3) = 0 radial nodes, as shown in the above plot. Radial nodes do become evident, however, in the higher d-orbitals (4d, 5d, and 6d).

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Document served: Thursday 24th May, 2018