An octahedral complex of Mn³⁺ is found to have a spin-only magnetic moment of 2.83 B.M. The Crystal Field Stabilization Energy (CFSE) of this complex is: (where _o is the octahedral crystal field splitting energy and P is the pairing energy)

Step-by-step solution

The spin-only magnetic moment is given by = n(n+2) B.M., where n is the number of unpaired electrons. Given = 2.83 B.M., we have n(n+2) = 2.83 , which gives n = 2 (since 8 2.83 ). Manganese in the +3 oxidation state has a d^4 electronic configuration. In an octahedral field, a d^4 ion can either be high-spin ( t_ 2g ^3 e_g^1 ) with 4 unpaired electrons, or low-spin ( t_ 2g ^4 e_g^0 ) with 2 unpaired electrons. Since the complex has 2 unpaired electrons, it must be a low-spin complex with the configuration t_ 2g ^4