Explain crystal field splitting in octahedral complexes.

(N/A) In an octahedral coordination entity with $6$ ligands surrounding the metal atom/ion,there will be repulsion between the electrons in $d$-orbitals of metal and the electrons of the ligands.
The $d$-orbitals $[d_{x^{2}-y^{2}}$ and $d_{z^{2}}]$ experience greater repulsions as they are pointed towards the axes along the direction of ligands while the $d$-orbitals $[d_{xy}, d_{yz}$ and $d_{xz}]$ which are directed between the axes,comparatively experience less repulsions. As a result,the energy of orbitals $d_{xy}, d_{yz}$ and $d_{xz}$ will be lowered relative to the average energy in a spherical crystal field while the energy of $d_{x^{2}-y^{2}}$ and $d_{z^{2}}$ will be raised.
The metal electron-ligand electron repulsions cause the loss in degeneracy of the $d$-orbitals in an octahedral complex to yield $3$ orbitals of lower energy,the $t_{2g}$ set,and $2$ orbitals of higher energy,the $e_{g}$ set. This splitting of the degenerate levels due to the presence of ligands in a definite geometry is called crystal field splitting and the energy separation is denoted by $\Delta_{o}$ (the subscript $o$ is for octahedral).
The energy of the $2$ $e_{g}$ orbitals will increase by $\frac{3}{5} \Delta_{o}$ and that of the $3$ $t_{2g}$ will decrease by $\frac{2}{5} \Delta_{o}$.