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Problem 2 - Entrance Test

The magnetic moment (in Bohr magneton, μB) of a tetrahedral complex [NiCl₄]²⁻ is 2.83 μB. Which of the following statements is correct regarding its electronic configuration and ligand field stabilization energy (LFSE)? (A) The complex has a high-spin d⁸ configuration with zero LFSE. (B) The complex has a high-spin d⁸ configuration with LFSE = −0.6Δt. (C) The complex has a low-spin d⁸ configuration with LFSE = −1.2Δt. (D) The complex has a high-spin d⁸ configuration with LFSE = −0.8Δt.

Correct: D

Ni²⁺ is d⁸. In a tetrahedral field, the e set (higher energy) is doubly degenerate and the t₂ set (lower energy) is triply degenerate. For d⁸ in tetrahedral geometry, the electron configuration is e⁴ t₂⁴. The magnetic moment of 2.83 μB corresponds to 2 unpaired electrons (μ = √[n(n+2)] = √8 ≈ 2.83), confirming a high-spin configuration. The LFSE for d⁸ tetrahedral is: LFSE = (4 × 0.6Δt) − (4 × 0.4Δt) = 2.4Δt − 1.6Δt = 0.8Δt. However, since the e set is higher in energy, the stabilization is negative relative to the barycenter: LFSE = −0.8Δt. Thus, the correct answer is D.