# 2*s* atomic orbital

**The shape of the 2 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 2*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 is a spherical node in the 2*s* orbital. The shape on the right shows the nodal structure of the 2*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 (
3*s*,
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 (
1*s*) is simpler since it has no spherical nodes.

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.