How does the crystal field splitting energy in a tetrahedral complex (Δt) quantitatively relate to that in an octahedral complex (Δo) for identical metal ions and ligands?

Answer and explanation

Correct answer: C. Δt = (4/9) Δo

  1. Step 1: In a tetrahedral complex, there are only 4 ligands compared to 6 in an octahedral complex, reducing the electrostatic field strength by a factor of .
  2. Step 2: None of the tetrahedral ligand approach directions point directly at the metal d-orbitals, which reduces the orbital overlap efficiency by another factor of .
  3. Step 3: Combining both geometric factors yields: .
  4. Step 4: Because is always substantially smaller than the pairing energy , tetrahedral complexes are virtually always high-spin.
Answer
Δt = (4/9) Δo
Why not the others: 'Δt = (9/4) Δo' inverts the ratio, falsely suggesting tetrahedral splitting is larger; 'Δt = (2/3) Δo' accounts only for the ligand count reduction while ignoring the angular geometry factor; 'Δt = (3/2) Δo' is mathematically and physically incorrect.

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