Question: 57. The correct order of the wavelength of light absorbed by the following complexes is,
A. \left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]^{3+}
B. \left[\mathrm{Co}(\mathrm{CN})_{6}\right]^{3-}
C. \left[\mathrm{Cu}\left(\mathrm{H}_{2} \mathrm{O}\right)_{4}\right]^{2+}
D. \left[\mathrm{Ti}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{3+}
Choose the correct answer from the options given below:
(1) B < D < A < C
(2) B < A < D < C
(3) C < D < A < B
(4) C < A < D < B
Answer: Option (2)
Explanation:
The wavelength of light absorbed during a d\text{-}d transition is inversely proportional to the crystal field splitting energy \Delta.
\Delta \propto \frac{1}{\lambda}Stronger ligand field results in larger \Delta and hence absorption of light with shorter wavelength.
Now, compare the ligands and metal ions in the given complexes.
Complex B, \left[\mathrm{Co}(\mathrm{CN})_{6}\right]^{3-},
contains \mathrm{CN}^{-}, which is a very strong-field ligand.
Therefore, it has the largest \Delta and absorbs light of the shortest wavelength.
Complex A, \left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]^{3+},
contains \mathrm{NH_{3}}, a strong-field ligand but weaker
than \mathrm{CN}^{-}.
Hence, its \Delta is smaller than B but larger than the aqua complexes.
Complex D, \left[\mathrm{Ti}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{3+}, has the weak-field ligand \mathrm{H_{2}O}.
However, the metal ion is \mathrm{Ti}^{3+}, which has higher oxidation state than \mathrm{Cu}^{2+},
resulting in slightly larger \Delta than C.
Complex C, \left[\mathrm{Cu}\left(\mathrm{H}_{2} \mathrm{O}\right)_{4}\right]^{2+},
also has weak-field ligand \mathrm{H_{2}O} and lower metal oxidation state,
so it has the smallest \Delta and absorbs light of the longest wavelength.
Therefore, the correct order of wavelength absorbed is
B < A < D < C
Hence, the correct answer is Option (2).