# 4*p* orbitals

**The shape of the three 4 p orbitals.** From left to right: 4

*p*

*, 4*

_{y}*p*

*, and 4*

_{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 4*p* orbitals. These orbitals have the same shape but are aligned differently in space. The three 4*p* orbitals normally used are labelled 4*p** _{x}*, 4

*p*

*, and 4*

_{y}*p*

*since the functions are "aligned" along the*

_{z}*x*,

*y*, and

*z*axes respectively.

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

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

*yz*plane.

The origin of the spherical nodes becomes clear when inspecting the wave equations which includes a (20 - 10ρ + ρ^{2}) term. When (20 - 10ρ + ρ^{2}) = 0, then there are nodes. When solved this shows nodes at ρ = 2.5 + √(5/4) and 2.5 - √(5/4). Since for the 4*p* orbital ρ = 2*Zr*/4 (*Z* = effective nuclear charge, *r* = radius in atomic units), then the nodes are at the radii *r*, = (5 + √5)/Z and (5 - √5)/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.