Question

The tetrahedral crystal field splitting is only____of the octahedral splitting. 

• A. \(\frac{1}{9}\)
• B. \(\frac{2}{9}\)
• C. \(\frac{3}{9}\)
• D. \(\frac{4}{9}\)
• E. \(\frac{5}{9}\)

Answer 1

The Correct Option is D

Crystal Field Theory Comparison:

• Tetrahedral splitting energy (Δ_tet) is smaller than octahedral (Δ_oct)
• Mathematically related as: Δ_tet = (4/9)Δ_oct
• Reason: Fewer ligand interactions and different geometry in tetrahedral

Thus, the correct option is (D): \(\frac{4}{9}\).

Answer 2

1. Understanding crystal field splitting:

In crystal field theory, the energy difference between the split d-orbitals in a coordination complex depends on the geometry of the complex. For an octahedral field, the splitting is denoted as \( \Delta_o \), and for a tetrahedral field, it is denoted as \( \Delta_t \).

2. Relationship between tetrahedral and octahedral splitting:

• In a tetrahedral field, the ligands approach the central metal ion at angles, resulting in weaker interactions compared to the direct approach in an octahedral field.
• The tetrahedral splitting (\( \Delta_t \)) is generally smaller than the octahedral splitting (\( \Delta_o \)).
• Experimentally and theoretically, it is established that:
  • \[ \Delta_t = \frac{4}{9} \Delta_o \]

3. Interpretation of the result:

• The tetrahedral crystal field splitting is \( \frac{4}{9} \) of the octahedral splitting.

5. Final answer:

The correct option is (D) 4/9.