Which of these crystal-field splitting diagrams represents:
a. a weak-field octahedral complex of Fe³⁺ ,
b. a strong-field octahedral complex of Fe³⁺ 
c. a tetrahedral complex of Fe³⁺
d. a tetrahedral complex of Ni²⁺ (The diagrams do not indicate the relative magnitudes of ∆. ) [Find more in Section 23.6.]

Verified step by step guidance

1. Identify the electron configuration of Fe³⁺ and Ni²⁺. Fe³⁺ has an electron configuration of 3d^5, and Ni²⁺ has an electron configuration of 3d^8.
2. Understand the concept of crystal field splitting in different geometries. In octahedral complexes, the d-orbitals split into two energy levels: t2g (lower energy) and eg (higher energy). In tetrahedral complexes, the splitting is reversed with eg (lower energy) and t2g (higher energy).
3. For a weak-field octahedral complex of Fe³⁺, the electrons will fill the t2g and eg orbitals according to Hund's rule and the Aufbau principle, with minimal pairing due to the lower crystal field splitting energy.
4. For a strong-field octahedral complex of Fe³⁺, the electrons will first fill the lower energy t2g orbitals completely before occupying the higher energy eg orbitals, showing more electron pairing due to higher crystal field splitting energy.
5. For tetrahedral complexes of Fe³⁺ and Ni²⁺, distribute the electrons in the eg and t2g orbitals according to their respective electron configurations, considering the reversed order of energy levels compared to octahedral complexes.

Key Concepts

Crystal Field Theory

Crystal Field Theory (CFT) explains the electronic structure of transition metal complexes by considering the interaction between the metal ion's d-orbitals and the electric fields produced by surrounding ligands. This theory helps predict the splitting of d-orbitals into different energy levels, which is crucial for understanding the color, magnetism, and stability of the complexes.

Octahedral vs. Tetrahedral Complexes

In coordination chemistry, octahedral complexes have six ligands symmetrically arranged around a central metal ion, leading to a specific pattern of d-orbital splitting. Tetrahedral complexes, on the other hand, have four ligands and exhibit a different splitting pattern. The geometry of the complex significantly influences the energy difference between the split d-orbitals, denoted as Δ.

Weak-field vs. Strong-field Ligands

Ligands can be classified as weak-field or strong-field based on their ability to split the d-orbitals. Weak-field ligands cause a small splitting (Δ), leading to high-spin configurations, while strong-field ligands cause larger splitting, resulting in low-spin configurations. The nature of the ligands affects the electronic arrangement of the metal ion, influencing the properties of the complex.