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Why are different colours observed in octahedral and tetrahedral complexes for the same metal and same ligands?

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In octahedral complex, the lower wavelength of light is absorbed more than tetrahedral complex for a same metal and ligand. Formation of the d-orbital splitting is inverted in tetrahedral coordination entity and it is smaller than the octahedral field splitting. It can be shown as below for a same metal ligand.

\Delta _{t}=\left ( \frac{4}{9} \right )\Delta _{o}.

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