# 3*s* atomic orbital

**The shape of the 3 s orbital.** The blue zone is where the wave function has positive values while the white zone is where values are positive.

For any atom there is just one 3*s* orbital. The image on the top is deceptively simple as the interesting feature is buried within the orbital. That on the left is sliced in half to show that there the two spherical nodes of the 3*s* orbital. The shape on the right shows the nodal structure of the 3*s*-orbital.

The origin of the spherical node becomes clear if we examine the wave equation, which includes a (2 - ρ) term. When (2 - ρ) = 0, then we must have a node. Since for the 2*s* orbital ρ = 2*Zr*/2 = *Zr* (*Z* = effective nuclear charge, *r* = radius in atomic units), then the node is at the radius for which (2 - *Zr*) = 0, that is, *r* = 2/Z atomic units.

While still spherical, the higher *s*-orbitals (4*s*, 5*s*, 6*s*, and 7*s*) are more complex since they have more spherical nodes. While still spherical, the lower *s*-orbitals (2*s* and
1*s*) are simpler since they have fewer spherical nodes.

The Orbitron

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

Copyright 2002-2021 Prof. Mark Winter [The University of Sheffield]. All rights reserved.