Read the passage carefully and answer the questions:

The degeneracy of the d orbitals has been removed due to ligand electron-metal electron repulsions in the octahedral complex to yield three orbitals of lower energy, $t_{2g}$ set and two orbitals of higher energy, $e_g$ set. This splitting of the degenerate levels due to the presence of ligands in a definite geometry is termed as crystal field splitting and the energy separation is denoted by Δo. Thus energy of the two $e_g$ orbitals will increase by (3/5) Δo and that of three $t_{2g}$ will decrease by (2/5) Δo. The crystal field splitting Δo depends upon the field produced by the ligand and charge on the metal ion. Some ligands are able to produce strong fields, in which case the splitting will be large, whereas others produce weak fields and consequently result in small splitting of d orbitals. Relative magnitude of crystal field splitting energy Δo and pairing energy, P (energy required for electron pairing in a single orbital) determine the formation of low spin (Δo > P) or high spin (Δo < P) complex. In tetrahedral coordination entity formation, the d-orbital splitting is inverted and is smaller as compared to the octahedral field splitting. The crystal field theory attributes the colour of the complex to d-d transition of the electron. The colour of the coordination compounds depends on the crystal field splitting. In the absence of ligand, crystal field splitting does not occur and hence the substance is colourless.

Which of the following relations is correct for the splitting of d orbitals in octahedral and tetrahedral crystal fields, considering same metal, the same ligands and metal-ligand distances?

$Δ_t=\frac{4}{9}Δ_o$

The correct answer is Option (1) → $Δ_t=\frac{4}{9}Δ_o$

In crystal field theory, for the same metal ion, same ligands and same metal–ligand distance, the splitting in a tetrahedral field is always smaller than that in an octahedral field.

The correct relation is:

$\Delta_t = \frac{4}{9}\,\Delta_o$​