Question

The crystal field splitting energy for octahedral $\left({\Delta }_0\right)$ and tetrahedral $\left({\Delta }_t\right)$ complexes are related as :

• A. ${\Delta }_t=\frac{4}{9}{\Delta }_0$
• B. ${\Delta }_t=\frac{1}{2}{\Delta }_0$
• C. ${\Delta }_0=2{\Delta }_t$
• D. ${\Delta }_0=\frac{4}{9}{\Delta }_t$

Answer 1

The correct option is A ${\Delta }_t=\frac{4}{9}{\Delta }_0$

Since splitting in tetrahedral complex is$\frac{2}{3}$rd of octahedral complex, so for one ligand splitting on $Oh=\frac{{\Delta }_0}{6}$, then for one lignd splitting in tetrahedral is $\frac{2}{3}\left(\frac{{\Delta }_0}{6}\right).$ So for 4 ligand, $\Delta t=4\times \frac{2}{3}\times \frac{{\Delta }_0}{6}$$=\frac{4}{9}{\Delta }_0$
$\Delta t=\frac{4}{9}{\Delta }_0$