KCET · Chemistry · Coordination Compounds

For the crystal field splitting in octahedral complexes,

A the energy of the \(e_{g}\) orbitals will decrease by (3/5) \(\Delta_{o}\) and that of the \(t_{2 g}\) will increase by \((2 / 5) \Delta_{o}\)
B the energy of the \(e_{g}\) orbitals will increase by \((3 / 5) \Delta_{o}\) and that of the \(t_{2 g}\) will decrease by \((2 / 5) \Delta_{o}\)
C the energy of the \(e_{g}\) orbitals will increase by (3/5) \(\Delta_{0}\) and that of the \(t_{2 g}\) will increase by (2/5) \(\Delta_{o}\)
D the energy of the \(e_{g}\) orbitals will decrease by \((3 / 5) \Delta_{o}\) and that of the \(t_{2 g}\) will decrease by \((2 / 5) \Delta_{o}\)

Verified Solution

Answer & Solution

Correct Answer

(B) the energy of the \(e_{g}\) orbitals will increase by \((3 / 5) \Delta_{o}\) and that of the \(t_{2 g}\) will decrease by \((2 / 5) \Delta_{o}\)

Step-by-step Solution

Detailed explanation

For crystal field splitting in octahedral complexes, the energy of \(e_{g}\) orbitals will increase by \(\left(\frac{3}{5}\right) \Delta_{o}\) and that of \(t_{2 g}\) will decrease by \(\left(\frac{2}{5}\right) \Delta_{o}\).
The splitting of degenerate \(d\)-orbital is as follows.

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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