Question

The crystal field splitting energy for octahedral $\left( {{\Delta _{\text{O}}}} \right)$ and tetrahedral $\left( {{\Delta _{\text{t}}}} \right)$ complexes are related as:
A.${\Delta _{\text{t}}} = \dfrac{4}{9}{\Delta _{\text{O}}}$
B.${\Delta _{\text{t}}} = \dfrac{1}{2}{\Delta _{\text{O}}}$
C.${\Delta _{\text{O}}} = 2{\Delta _{\text{t}}}$
D.${\Delta _{\text{O}}} = \dfrac{4}{9}{\Delta _{\text{t}}}$

Answer 1

The splitting energy in octahedral complexes is higher than that of tetrahedral complexes. There are 4 ligands in tetrahedral complexes.

Complete step by step answer:
According to valence bond theory co-ordinate bond is formed between metal and ligand. The metals have vacant orbits and the ligands have electron pairs. The ligands donate their electron pair in the vacant d orbitals of metal. Valence bond theory could not explain the behaviour of strong field and weak field ligand and the colour shown by the complex compounds. It gave no account for the spectrochemical series.
So the crystal field theory was introduced, according to crystal field theory ionic bond is formed between metal and ligand and ligands approach the metal. The d orbitals of metal undergo splitting to form two sets of orbitals, one with the lower energy than the d orbitals and one with the higher energy than the degenerate d orbitals. The two sets formed are named as ${{\text{e}}_{\text{g}}}$ and ${{\text{t}}_{2{\text{g}}}}$ . If the approaching ligand is strong then the energy difference between ${{\text{e}}_{\text{g}}}$ and ${{\text{t}}_{2{\text{g}}}}$ will be high causing pairing of electrons in d orbitals. If the approaching ligand is weak then energy difference between ${{\text{e}}_{\text{g}}}$ and ${{\text{t}}_{2{\text{g}}}}$ orbitals is low. The relationship between crystal field splitting for octahedral and tetrahedral complexes is as:
${\Delta _{\text{t}}} = \dfrac{4}{9}{\Delta _{\text{O}}}$
Here ${\Delta _{\text{t}}}$ is crystal field splitting for tetrahedral complexes and ${\Delta _{\text{O}}}$ is splitting energy for octahedral complexes.

Hence, the correct option is A.

Note:
The valence bond theory considered that the bond formed between metal and ligand as purely ionic and CFT considered the bond formed as purely ionic. A bond can neither be purely ionic nor purely covalent. After that molecular orbital theory came that assumes the formation of ionic bonds followed by covalent bonds.