Question

What is meant by crystal field splitting energy ? On the basis of crystal field theory, write the electronic configuration of $d^4$ in terms of $t_{2g}$ and $e_g$ in an octahedral field when
(i) ${\Delta }_0>P$
(ii) ${\Delta }_0<P$

Answer 1

d-orbital is degenerate which split into two levels $e_g$ and $t_{2g}$ in the presence of ligands. This splitting is due to the presence of ligands. This is called the crystal-field splitting and the energy difference between the two levels ($e_g$ and $t_{2g}$) is called the crystal-field splitting energy, ${\Delta }_0$

Electrons are singly filled in the $t_{2g}$ energy levels first and the remaining electrons are filled based on the crystal field splitting energy and pairing energy.
Filling up of the remainig electrons takes place in two ways.

(i) If the CFSE (${\Delta }_0$) is greater than that of the pairing energy ($p$), electrons will be filled in the '$e_g$' orbitals.
(ii) If the CFSE (${\Delta }_0$) is lesser than that of the pairing energy ($p$), electrons will be paired up in the $t_{2g}$ energy levels.