Question

The correct order of the wavelength of light absorbed by the following complexes is:

• \( [\mathrm{Co}(\mathrm{NH}_3)_6]^{3+} \)
• \( [\mathrm{Co}(\mathrm{CN})_6]^{3-} \)
• \( [\mathrm{Cu}(\mathrm{H}_2\mathrm{O})_4]^{2+} \)
• \( [\mathrm{Ti}(\mathrm{H}_2\mathrm{O})_6]^{3+} \)

Choose the correct answer from the options given below:

• A. \( \text{C} < \text{D} < \text{A} < \text{B} \)
• B. \( \text{C} < \text{A} < \text{D} < \text{B} \)
• C. \( \text{B} < \text{D} < \text{A} < \text{C} \)
• D. \( \text{B} < \text{A} < \text{D} < \text{C} \)

Hint:

To solve wavelength absorption questions instantly, look at the extremes of the spectrochemical series. Since \(\text{CN}^-\) is one of the strongest field ligands available, it maximizes splitting (\(\Delta\)), which guarantees it will absorb the shortest wavelength. Thus, complex B must be at the starting end of a increasing order sequence, letting you narrow options down immediately!

Answer 1

The Correct Option is D

Concept: According to Crystal Field Theory (CFT), the color of a coordination complex arises from electronic transitions between split \(d\)-orbitals (\(d\text{-}d\) transitions). The energy absorbed during this transition (\(\Delta\)) is inversely proportional to the wavelength (\(\lambda\)) of the absorbed light: \[ \Delta = \frac{hc}{\lambda} \implies \lambda \propto \frac{1}{\Delta} \] The magnitude of crystal field splitting (\(\Delta\)) depends primarily on:
• The Spectrochemical Series (Ligand Strength): Strong field ligands split orbitals further apart, resulting in a higher \(\Delta\) value: \[ \text{I}^- < \text{Br}^- < \text{S}^{2-} < \text{Cl}^- < \text{F}^- < \text{OH}^- < \text{H}_2\text{O} < \text{NH}_3 < \text{en} < \text{NO}_2^- < \text{CN}^- < \text{CO} \]
• Oxidation State of Central Metal: A higher positive charge on the metal ion increases electrostatic attraction for the ligands, increasing \(\Delta\).
• Nature of Central Metal: Elements belonging to different groups or transition series split fields differently under similar constraints.

Step 1: Comparing the Cobalt complexes (A and B) using ligand strength.
Let us compare \( [\text{Co}(\text{NH}_3)_6]^{3+} \) (A) and \( [\text{Co}(\text{CN})_6]^{3-} \) (B). Both complexes feature the same central metal ion (\(\text{Co}^{3+}\)) in an octahedral environment.
• In the spectrochemical series, Cyanide (\(\text{CN}^-\)) is a significantly stronger field ligand than Ammonia (\(\text{NH}_3\)).
• Therefore, the crystal field splitting energy (\(\Delta_{\circ}\)) follows the order: \(\Delta_{\circ}(\text{B}) > \Delta_{\circ}(\text{A})\).
• Since \(\lambda \propto \frac{1}{\Delta}\), the order of wavelength absorbed is: \(\lambda(\text{B}) < \lambda(\text{A})\).

Step 2: Comparing splitting between different metal ions with aqua ligands (C and D).
Let us evaluate \( [\text{Ti}(\text{H}_2\text{O})_6]^{3+} \) (D) and compare its parameters with the others.
• \( \text{Ti}^{3+} \) belongs to the early part of the \(3d\) series (\(3d^1\)). It has a higher oxidation state (\(+3\)) compared to \( \text{Cu}^{2+} \), causing stronger ligand-metal overlap than typical \(M^{2+}\) complexes.
• For \( [\text{Cu}(\text{H}_2\text{O})_4]^{2+} \) (C), Copper has a lower oxidation state (\(+2\)), and the coordination number is 4. Splitting energies for tetrahedral or square planar complexes with weak ligands like water are fundamentally lower than those of octahedral \(M^{3+}\) ions.
• Additionally, the spectrochemical field splitting sequence for identical ligands across these configuration changes trends such that: \[ \Delta_{\circ}(\text{Co}^{3+}) > \Delta_{\circ}(\text{Ti}^{3+}) > \Delta(\text{Cu}^{2+}) \]

Step 3: Establishing the comprehensive overall order.
Combining the splitting field magnitudes derived across the configurations: \[ \text{Splitting Energy }(\Delta): \quad \text{B } (\text{Co}^{3+}, \text{CN}^-) > \text{A } (\text{Co}^{3+}, \text{NH}_3) > \text{D } (\text{Ti}^{3+}, \text{H}_2\text{O}) > \text{C } (\text{Cu}^{2+}, \text{H}_2\text{O}) \] Taking the inverse relation to arrive at the correct sequence for absorbed wavelengths (\(\lambda\)): \[ \lambda: \quad \text{B} < \text{A} < \text{D} < \text{C} \] This precisely matches option (D).