In Crystal Field Theory (CFT), the crystal field splitting energy depends on the geometry of the complex. For the same metal ion, oxidation state and ligand, tetrahedral crystal field splitting energy is approximately four-ninths of octahedral crystal field splitting energy.

Formula:

Δt = (4/9) Δo

Or,

Δo = (9/4) Δt

Where,

Δt = Tetrahedral crystal field splitting energy

Δo = Octahedral crystal field splitting energy

Numerical Example:

Question: If the octahedral crystal field splitting energy (Δo) is 18,000 cm⁻¹, calculate the tetrahedral crystal field splitting energy (Δt).

Solution:

Given,

Δo = 18,000 cm⁻¹

We know that,

Δt = (4/9) Δo

Substituting the value,

Δt = (4/9) × 18,000

Δt = 8,000 cm⁻¹

Answer: Δt = 8,000 cm⁻¹

Important Relation to Remember:

Δt : Δo = 4 : 9

Therefore, tetrahedral crystal field splitting energy is approximately 4/9 of octahedral crystal field splitting energy.