Question

We used crystal field theory to order the energy-level splittings induced in the five d orbitals. The same procedure could be applied to p orbitals. Predict the level splittings (if any) induced in the three p orbitals by octahedral and square-planar crystal fields.

Short answer

The P orbital does not split in the octahedral or square planar field.

Step-by-step solution

 Step 1: The octahedral splitting.

Crystal fieldsplitting in an octahedral complex split the d orbitals into two sets

• The high energy set $\mathbf{\left(}{\mathbf{e}}_g\mathbf{\right)}$ has a set of two orbitals
• The low energy set $\mathbf{\left(}{\mathbf{t}}_{2g}\mathbf{\right)}\mathbf{)}$ has a set of three orbitals

Square planar splitting.

In the crystal field splitting in a square planar complex, the ligand with the xy components faces more repulsion, which will increase its energy, and the ligand with the z component faces less repulsion, hence lower energy.

The p orbital splitting. 

Applying the octahedral crystal field and square planar crystal field around the p orbital increases the energy of p orbitals $\left({\text{p}}_{\text{x}}{\text{,p}}_{\text{y}}{\text{,p}}_{\text{z}}\right)$more than the normal ground state.

The p orbital does not split further into sets like the d orbital split into two energy states because they have the same term ${\text{T}}_{\text{1g}}$ (triple degenerate), making its splitting impossible.