# 3*p* orbitals

**The shape of the three 3 p orbitals.** From left to right: 3

*p*

*, 3*

_{y}*p*

*, and 3*

_{z}*p*

*. For each, the yellow zones are where the wave functions have positive values and the white zones denote negative values.*

_{x}For any atom, there are three 3*p* orbitals. These orbitals have the same shape but are aligned differently in space. The three 3*p* orbitals normally used are labelled 3*p** _{x}*, 3

*p*

*, and 3*

_{y}*p*

*since the functions are "aligned" along the*

_{z}*x*,

*y*, and

*z*axes respectively.

Each 3*p* orbital has four lobes. There is a planar node normal to the axis of the orbital (so the 3*p*_{x} orbital has a *yz* nodal plane, for instance). Apart from the planar node there is also a spherical node that partitions off the small inner lobes. The higher *p*-orbitals (4*p*, 5*p*, 6*p*, and 7*p*) are more complex still since they have more spherical nodes.

The origin of the planar node becomes clear when inspecting the wave equations which, for instance, includes an *x* term in the case of the 4*p** _{x}* orbital. When

*x*= 0, then there is a node, and this by definition is the

*yz*plane.

The origin of the spherical node becomes clear when inspecting the wave equations which, for instance, include (4 - ρ) terms. When (4 - ρ) = 0, then there is a node. Since for any 3*p* orbital ρ = 2*Zr*/3 (*Z* = effective nuclear charge, *r* = radius in atomic units), then the nodes are at the radius for which (4 - 2*Zr*/3) = 0, that is, *r* = 6/Z atomic units.

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.