An octahedral complex of Mn ³⁺ has a spin-only magnetic moment of 2.83 BM . Ignoring the pairing energy, the magnitude of the crystal field stabilization energy (CFSE) for this complex is x ₀ . The value of 10x is _______.

Step-by-step solution

The central metal ion is Mn ³⁺ , which has a 3 d ⁴ electronic configuration. The spin-only magnetic moment is given by = n(n+2) BM , where n is the number of unpaired electrons. A value of 2.83 BM corresponds to n = 2 (since 2(2+2) = 8 2.83 ). In an octahedral field, a 3 d ⁴ ion can be either high-spin ( t _ 2 g ³ e _ g ¹ ) with 4 unpaired electrons, or low-spin ( t _ 2 g ⁴ e _ g ⁰ ) with 2 unpaired electrons. Since n = 2 , the complex must be low-spin with the configuration t _ 2 g ⁴ e _ g ⁰ . The CFSE for this co