# Atomic orbitals: 6*s* radial distribution function

**Schematic plot of the 6 s radial distribution function 4πr^{2}ψ_{1s}^{2}**

For *s*-orbitals, the radial distribution function is given by multiplying the *electron density* by 4π*r*^{2}. By definition, it is independent of direction. In the case of the hydrogen atom, the maximum value of the radial distribution function corresponds to *r* = 1 AU, 52.9 pm.

The 6*s* radial distribution function has four spherical nodes but the higher *s* orbitals have more. The number of nodes is related to the principal quantum number, *n*. In general, the *ns* orbital have (*n* - 1) radial nodes. Therefore, the 6*s*-orbital has (6 - 1) = 5 radial nodes, as shown in the above plot. Additional radial nodes become evident in higher *s*-orbitals (
7*s*) while lower orbitals (
1*s*,
2*s*,
3*s*,
4*s*,
5*s*,
6*s*, and) have fewer.

The Orbitron

^{TM}, a gallery of orbitals on the WWW: https://winter.group.shef.ac.uk/orbitron/

Copyright 2002-2023 Prof. Mark Winter [The University of Sheffield]. All rights reserved.