JEE Main 2023 — Coordination Compounds Question with Solution

In order to match these complexes with their respective crystal field splitting energies (CFSE), we need to understand the coordination number, the geometry of the complex, and the nature of the ligand.

The crystal field splitting energy, often denoted as Δ₀ or Δ, is the energy difference between the higher-energy and lower-energy sets of d-orbitals in a transition metal ion when in a crystal field created by a set of ligands.

The sign of CFSE is often taken as negative because it represents a lowering in energy due to the field of the ligands. The magnitude of CFSE depends on the nature of the ligand, with ligands causing larger splitting being known as strong-field ligands and those causing smaller splitting being known as weak-field ligands.

Based on spectrochemical series, we know the strength of ligands as follows: F⁻ < H₂O < NH₃ < CN⁻

The crystal field splitting energy also depends on the configuration of the d electrons in the transition metal ion. For octahedral complexes, the d orbitals split into two sets with an energy difference Δ₀: a lower-energy set (dxy, dyz, dxz) called t₂g, and a higher-energy set (dz², dx²-y²) called eg.

Now let's analyze each complex:

1. [Cu(NH₃)₆]²⁺: Cu²⁺ ion has a d⁹ configuration. It is an octahedral complex with a strong field ligand (NH₃), hence the splitting will be large.

2. [Ti(H₂O)₆]³⁺: Ti³⁺ ion has a d¹ configuration. It is an octahedral complex with a weak field ligand (H₂O), hence the splitting will be small.

3. [Fe(CN)₆]³⁻: Fe³⁺ ion has a d⁵ configuration. It is an octahedral complex with a very strong field ligand (CN⁻), hence the splitting will be very large.

4. [NiF₆]⁴⁻: Ni²⁺ ion has a d⁸ configuration. It is an octahedral complex with a very weak field ligand (F⁻), hence the splitting will be very small.

So, the correct order of CFSE values for these complexes should be:

[NiF₆]⁴⁻ < [Ti(H₂O)₆]³⁺ < [Cu(NH₃)₆]²⁺ < [Fe(CN)₆]³⁻

Therefore, the correct answer is:

A-I, B-IV, C-II, D-III