Understanding Ligand Field Strength

Ligand field strength refers to the ability of a ligand to cause splitting in the energy levels of metal d-orbitals within a coordination complex. This splitting energy, often denoted as $\Delta_o$ (crystal field splitting energy in octahedral complexes) or $10 Dq$, influences the complex's properties like color and magnetism.

Ligands are ranked based on their field strength in a spectrochemical series. Ligands that cause a larger splitting are considered strong-field ligands, while those causing smaller splitting are weak-field ligands.

The Spectrochemical Series

The spectrochemical series arranges ligands in order of increasing field strength. A portion of this series, relevant to the given ligands, is:

• Weak Field Ligands: $I^{-} < Br^{-} < S^{2-} < SCN^{-} < Cl^{-} < F^{-}$
• Intermediate Field Ligands: $OH^{-} < H_{2}O < NCS^{-}$
• Strong Field Ligands: $NH_{3} < en < bipy < phen < NO_{2}^{-} < CN^{-} < CO$

Note that $NCS^{-}$ (thiocyanate) can coordinate through N or S, influencing its position, but generally falls before ethylenediamine.

Analyzing the Given Ligands

Let's classify the provided ligands based on their position in the spectrochemical series:

• (A) $S^{2-}$ (Sulfide ion): Considered a weak-field ligand.
• (B) Ethylenediamine (en): A bidentate amine ligand, considered a strong-field ligand.
• (C) $NCS^{-}$ (Thiocyanate ion): Typically considered a medium-field ligand, stronger than $S^{2-}$ but weaker than ethylenediamine.
• (D) $CN^{-}$ (Cyanide ion): A very strong-field ligand, among the strongest.

Determining the Decreasing Order of Field Strength

We need to arrange these ligands from the strongest field to the weakest field (decreasing order). Based on the spectrochemical series:

1. Strongest Field Ligand: $CN^{-}$ (D)
2. Next Strongest: Ethylenediamine (B)
3. Weaker Ligand: $NCS^{-}$ (C)
4. Weakest Field Ligand: $S^{2-}$ (A)

Therefore, the decreasing order of field strength is:

$CN^{-} >$ Ethylenediamine $>$ $NCS^{-} > S^{2-}$

Corresponding to the labels, this order is (D), (B), (C), (A).

Matching with Options

Comparing this order with the given options:

• Option 1: (A), (C), (B), (D) - Incorrect
• Option 2: (A), (B), (C), (D) - Incorrect
• Option 3: (D), (B), (C), (A) - Correct
• Option 4: (D), (C), (B), (A) - Incorrect

The correct order is (D), (B), (C), (A).