# 7*p* orbitals

**The shape of the three 7 p orbitals.** From left to right: 7

*p*

*, 7*

_{y}*p*

*, and 7*

_{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 7*p* orbitals. These orbitals have the same shape but are aligned differently in space. The three 7*p* orbitals normally used are labelled 7*p** _{x}*, 7

*p*

*, and 7*

_{y}*p*

*since the functions are "aligned" along the*

_{z}*x*,

*y*, and

*z*axes respectively.

Each 7*p* orbital has 12 lobes. There is a planar node normal to the axis of the orbital (so the 7*p*_{x} orbital has a *yz* nodal plane, for instance). Apart from the planar node there are also five spherical nodes that partition off the small inner lobes.

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 2*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 clearer if we examine the wave equations, which include a (6720 - 8400*ρ* + 3360*ρ*^{2} - 420*ρ*^{3} + 40*ρ*^{4} - *ρ*^{5}) term. When (6720 - 8400*ρ* + 3360*ρ*^{2} - 420*ρ*^{3} + 40*ρ*^{4} - *ρ*^{5}) = 0, then there are 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.