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Atomic orbitals: 4f radial distribution function

Schematic plot of the 4f radial distribution function r2R4f2 (R4f = radial wave function).

For 4f-orbitals, the radial distribution function is related to the product obtained by multiplying the square of the radial wave function R4f by r2. By definition, it is independent of direction.

In addition to three planar nodes, (or one planar and two conical nodes in the case of the 4fx3, 4fy3, and 4fz3 orbitals), f-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 nf orbital has (n - 4) radial nodes, so the 4f-orbitals have (4 - 4) = 0 radial nodes, as shown in the above plot. Radial nodes do become evident, however, in the higher f-orbitals (5f).

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