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

Step 1: Understanding the Concept:
Crystal Field Splitting energy (\(\Delta\)) is inversely proportional to the wavelength of absorbed light (\(\lambda\)).
\[ \Delta = \frac{hc}{\lambda} \implies \lambda \propto \frac{1}{\Delta} \]
\(\Delta\) depends on the strength of the ligand (Spectrochemical series) and the oxidation state of the metal.
Step 2: Detailed Explanation:
Order of Ligand Strength: \(H_2O<NH_3<CN^-\).
1. Compare A and B (Both \(Co^{3+}\)): Since \(CN^-\) is stronger than \(NH_3\), \(\Delta(B)>\Delta(A) \implies \lambda(B)<\lambda(A)\).
2. Compare metal ions: Higher oxidation states increase \(\Delta\). So, \([Co(NH_3)_6]^{3+}\) (A) has higher splitting than aqua complexes of +2 metals or early transition +3 metals.
3. \([Ti(H_2O)_6]^{3+}\) (D) vs \([Cu(H_2O)_4]^{2+}\) (C): The +3 oxidation state of \(Ti\) causes more splitting than +2 of \(Cu\), and tetrahedral/square complexes generally have lower splitting than octahedral ones. Thus \(\Delta(D)>\Delta(C) \implies \lambda(D)<\lambda(C)\).
Overall Splitting Order: B > A > D > C.
Wavelength order (inverse): B < A < D < C.
Step 3: Final Answer:
The wavelength order is B < A < D < C, which matches option (D).