The wave number of light absorbed for the d-d transition by an octahedral complex [M(H₂O)₆]²⁺ is 9000 cm ⁻¹ . If the metal ion M²⁺ has a d^7 electronic configuration, the magnitude of the crystal field stabilization energy (CFSE) for the corresponding tetrahedral complex [M(H₂O)₄]²⁺ is ________ cm ⁻¹ .

Step-by-step solution

The octahedral crystal field splitting energy is given by the absorption wave number: _o = 9000 cm ⁻¹ The tetrahedral splitting energy _t is related to _o by: _t = 4 9 _o = 4 9 9000 = 4000 cm ⁻¹ For a tetrahedral complex, the d -orbital splitting results in lower energy e orbitals and higher energy t₂ orbitals. Tetrahedral complexes are generally high-spin. The electronic configuration for a d^7 metal ion in a tetrahedral field is e^4 t₂^3 . The CFSE for a tetrahedral complex is calculated as: CFSE = (-0.6 n_e + 0.