Question

What is meant by crystal field splitting energy? On the basis of crystal field theory, write the electronic configuration of ${{\text{d}}^{\text{4}}}$ in terms of ${{\text{t}}_{{\text{2g}}}}$ and ${{\text{e}}_{\text{g}}}$ in an octahedral field when
A. ${\Delta _0} > {\text{P}}$
B. ${\Delta _0} < {\text{P}}$

Answer 1

Hint: ${\Delta _0}$ is the crystal field splitting energy and ${\text{P}}$ is the pairing energy. When ${\Delta _0} > {\text{P}}$, it is a strong field ligand. When ${\Delta _0} < {\text{P}}$, it is a weak field ligand.

Complete step by step answer:
The theory that explains the structure and the stability of the coordination complexes is known as the crystal field theory.
The assumptions of crystal field theory are as follows:
1. The metal ion is considered to be a positive charge.
2. The ligands are considered to be a negative charge.
The elements of the d-block of the periodic table have variable oxidation states and variable coordination number. Thus, the coordination complexes are formed by the d-block elements of the periodic table.
The d-subshell has five degenerate orbitals.
When the ligand bonds to the metal ion, the energy of the degenerate d-orbitals increases.
As the energy of the degenerate d-orbitals increases, the degenerate orbitals split into ${{\text{t}}_{{\text{2g}}}}$ and ${{\text{e}}_{\text{g}}}$ orbitals.
The difference in the energies of the ${{\text{t}}_{{\text{2g}}}}$ and ${{\text{e}}_{\text{g}}}$ orbitals is known as the crystal field splitting energy (CFSE). It is denoted by ${\Delta _0}$.
The splitting of degenerate d-orbitals is shown in the diagram below:

The splitting of the energy depends on the type of the ligand. If the ligand is a strong field ligand its splitting energy is high and if the ligand is a weak field ligand its splitting energy is low.
Write the electronic configuration of ${{\text{d}}^{\text{4}}}$ in terms of ${{\text{t}}_{{\text{2g}}}}$ and ${{\text{e}}_{\text{g}}}$ in an octahedral field when ${\Delta _0} > {\text{P}}$ as follows:
1.When ${\Delta _0} > {\text{P}}$ i.e. crystal field splitting energy is greater than the pairing energy, the ligand is a strong field ligand. When the ligand is a strong field ligand, the fourth electron pairs in the ${{\text{t}}_{{\text{2g}}}}$ orbital.
Thus, the electronic configuration is as follows:

Write the electronic configuration of ${{\text{d}}^{\text{4}}}$ in terms of ${{\text{t}}_{{\text{2g}}}}$ and ${{\text{e}}_{\text{g}}}$ in an octahedral field when ${\Delta _0} < {\text{P}}$ as follows:
2.When ${\Delta _0} < {\text{P}}$ i.e. crystal field splitting energy is smaller than the pairing energy, the ligand is a weak field ligand. When the ligand is a weak field ligand, the fourth electron jumps in the ${{\text{e}}_{\text{g}}}$ orbital.
Thus, the electronic configuration is as follows:

Note:
Strong field ligands form low spin complexes. The examples of strong field ligands are ${\text{C}}{{\text{O}}^ - }$, ${\text{C}}{{\text{N}}^ - }$. Weak field ligands form high spin complexes. The examples of weak field ligands are ${{\text{F}}^ - }$, ${\text{C}}{{\text{l}}^ - }$.