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The crystal field splitting energy for octahedral (\Delta _{0}) and tetrahedral (\Delta _{t}) complexes is related as

Option: 1

\mathrm{\Delta_{t}=\frac{2}{9} \Delta_{0}}


Option: 2

\mathrm{\Delta_{t}=\frac{5}{9} \Delta_{0}}


Option: 3

\mathrm{\Delta_{t}=\frac{4}{9} \Delta_{0}}


Option: 4

\mathrm{\Delta_{t}=2 \Delta_{0}}


Answers (1)

best_answer

The crystal field splitting energy for octahedral (\Delta _{0}) and tetrahedral (\Delta _{t}) complexes is related as 

\mathrm{\Delta _{_{t}}=\frac{4}{9}\; \Delta _{0}}

This is because of the following reasons:

(1) Number of ligands in a tetrahedra complex is 4 whereas that in an octahedral complex is 6. This accounts for a factor of \frac{2}{3} roughly

(2) No ligands directly approach the d- orbitals of the metals in a Tetrahedral field whereas in an Octahedral field, the \mathrm{e_g} orbitals \mathrm{(d_{x^2-y^2}\ and\ d_{z^2})} directly face the incoming ligands which roughly accounts for another factor of  \frac{2}{3}.

Hence, the correct answer is Option (3)

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