4f radial distribution function

Schematic plot of the 4f radial distribution function r²R_4f² (R_4f = 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 R_4f by r². By definition, it is independent of direction.

In addition to three planar or conical nodes, f-orbitals (n > 4) 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, 6f, and 7f).