For a hypothetical tetrahedral complex [ML₄]²⁻ , the crystal field splitting energy ( _t ) is 4000 cm ⁻¹ . The crystal field splitting energy ( _o ) for the corresponding octahedral complex [ML₆]⁴⁻ with the same metal and ligands will be

Step-by-step solution

The relationship between the crystal field splitting energy of a tetrahedral complex ( _t ) and an octahedral complex ( _o ) having the same metal, the same oxidation state, and the same ligands is given by: _t = 4 9 _o Rearranging the formula to solve for _o gives: _o = 9 4 _t Substituting the given value of _t = 4000 cm ⁻¹ : _o = 9 4 4000 cm ⁻¹ = 9000 cm ⁻¹ Answer: 9000 cm ⁻¹