For a given metal ion and set of ligands, is the crystal-field splitting energy larger for a tetrahedral or an octahedral geometry?

Verified step by step guidance

1. Understand the concept of crystal-field splitting, which occurs when metal ions are surrounded by ligands in a coordination complex, causing the degenerate d-orbitals to split into groups of different energies.
2. Recognize that the geometry of the coordination complex (such as tetrahedral or octahedral) significantly affects the extent of this splitting.
3. Note that in an octahedral field, the d-orbitals split into two groups: the lower energy t2g (three orbitals) and the higher energy eg (two orbitals).
4. In a tetrahedral field, the d-orbitals also split into two groups but in reverse order: the higher energy e (two orbitals) and the lower energy t2 (three orbitals).
5. Compare the magnitude of splitting: octahedral complexes generally have a larger crystal-field splitting energy ( Δ_oct ) compared to tetrahedral complexes ( Δ_tet ), which is typically smaller due to the fewer number of ligands and their arrangement around the metal ion.

Key Concepts

Crystal Field Theory

Crystal Field Theory (CFT) explains how the arrangement of ligands around a central metal ion affects the energy levels of the d-orbitals. In this theory, ligands create an electric field that splits the degenerate d-orbitals into different energy levels, influencing the color, magnetism, and stability of the complex.

Tetrahedral vs. Octahedral Geometry

In tetrahedral geometry, four ligands are arranged around a central metal ion, leading to a specific splitting pattern of the d-orbitals. In contrast, octahedral geometry involves six ligands, resulting in a different splitting pattern. The arrangement of ligands directly affects the magnitude of crystal-field splitting energy (Δ).

Crystal Field Splitting Energy (Δ)

Crystal Field Splitting Energy (Δ) is the energy difference between the split d-orbitals in a coordination complex. In general, Δ is larger in octahedral complexes compared to tetrahedral ones due to the stronger interaction between the ligands and the d-orbitals, which results from the greater number of ligands in octahedral geometry.