Question

How do orbitals split in an octahedral crystal field?

Answer 1

Hint: The electrons in the d-orbitals and ligands repel each other due to repulsion between the charges. Thus the d-orbitals which are nearer to the ligands will have higher energy than those which further result in the splitting of d orbitals.

Complete step by step answer: Let us consider a molecule with octahedral geometry. Here the ligand is treated as point negative charge and the metal ion is treated as a point positive charge. Since the ligand approaches the metal ion along the x, y, z-axis. Therefore, the electron in ${d_{{z^2}}}$ and ${d_{{x^2} - {y^2}}}$ orbitals, which lies along the x, y, z axes experience greater repulsion as compared to the remaining three orbitals ${d_{xy}},{d_{yz}}{\text{ and }}{d_{zx}}$ whose lobes lie between the axes as a result the energy of ${d_{xy}},{d_{yz}}{\text{ and }}{d_{zx}}$ orbitals are lower than those of ${d_{{z^2}}}$ and ${d_{{x^2} - {y^2}}}$ orbitals. The former three orbitals of lower energy are called ${t_{2g}}$ orbitals and the latter two of higher energy orbitals are called ${e_g}$ orbitals. These names are derived from spectroscopic terms.
The splitting of the d orbitals into two sets of orbital in octahedral complexes may be represented as

The difference between the two sets of d orbitals is called crystal field splitting energy or crystal field stabilization energy (CFSE). It is represented by ${\Delta _o}$. Here subscript o stands for the octahedral complex.

So, the correct answer is “Option A”.

Note: The ligand with a small value ${\Delta _o}$ are called weak ligands whereas the ligands with a higher value ${\Delta _o}$ are called strong ligands. The crystal field splitting theory was successful in explaining the colour magnetic properties and the effect of weak and strong field ligands etc. in a coordination compound.