Question

Arrange the following complex ions in increasing order of their wavelength of light absorbed: 
(A) \([\text{Co}(\text{CN})_6]^{3-}\) 
(B) \([\text{Co}(\text{NH}_3)_6]^{3+}\) 
(C) \([\text{CoF}_6]^{3-}\) 
(D) \([\text{Co}(\text{C}_2\text{O}_4)_3]^{3-}\) 
Choose the correct answer from the options given below: 
 

• A. (A), (B), (D), (C)
• B. (A), (D), (B), (C)
• C. (D), (B), (A), (C)
• D. (C), (D), (B), (A)

Hint:

Remember: Stronger ligand field \(\rightarrow\) Larger \(\Delta_o\) \(\rightarrow\) Shorter absorbed wavelength (\(\lambda\)).
Spectrochemical series order: Halides \(<\) Oxygen donors \(<\) Nitrogen donors \(<\) Carbon donors.

Answer 1

The Correct Option is A

Concept:
In octahedral coordination complexes of a transition metal ion, the absorption of light corresponds to the promotion of an electron from the lower \(t_{2g}\) energy level to the higher \(e_g\) level (a \(d\text{--}d\) transition).
The energy of the absorbed photon (\(\Delta_o\)) is inversely related to its wavelength (\(\lambda\)) via the Planck-Einstein relation:
\[ \Delta_o = \frac{hc}{\lambda} \implies \lambda \propto \frac{1}{\Delta_o} \] Therefore, a ligand that generates a stronger crystal field causes a larger crystal field splitting energy (\(\Delta_o\)) and leads to the absorption of light at a shorter wavelength.

Step 1: Ranking Ligand Field Strengths via the Spectrochemical Series:
All four complexes involve the identical central metal ion, \(\text{Co}^{3+}\) (\(3d^6\)).
Hence, the magnitude of \(\Delta_o\) depends exclusively on the field strength of the coordinated ligands.
According to the spectrochemical series, the crystal field strength of the ligands increases in the order:
\[ \text{F}^- < \text{C}_2\text{O}_4^{2-} < \text{NH}_3 < \text{CN}^- \]

Step 2: Determining the Order of Crystal Field Splitting Energy (\(\Delta_o\)):
Because \(\Delta_o\) increases with ligand field strength, the complexes arrange in order of increasing \(\Delta_o\) as:
\[ [\text{CoF}_6]^{3-} < [\text{Co}(\text{C}_2\text{O}_4)_3]^{3-} < [\text{Co}(\text{NH}_3)_6]^{3+} < [\text{Co}(\text{CN})_6]^{3-} \] In terms of the given labels, this sequence is:
\[ \text{(C)} < \text{(D)} < \text{(B)} < \text{(A)} \]

Step 3: Calculating the Relative Wavelengths of Absorbed Light:
Since absorbed wavelength is inversely proportional to \(\Delta_o\) (\(\lambda = hc/\Delta_o\)), the complex with the highest \(\Delta_o\) absorbs at the shortest wavelength, and the complex with the lowest \(\Delta_o\) absorbs at the longest wavelength.
Inverting the \(\Delta_o\) sequence gives the increasing order of absorbed wavelength:
\[ \lambda_{(\text{A})} < \lambda_{(\text{B})} < \lambda_{(\text{D})} < \lambda_{(\text{C})} \] Thus, the increasing order of wavelength of light absorbed is (A), (B), (D), (C).
Final Answer:
The correct increasing order is (A), (B), (D), (C), which corresponds to option (A).