The complexes are $\left[\mathrm{Co}(\mathrm{CN})_6\right]^{3-},\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_6\right]^{3+}$, $\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_5 \mathrm{H}_2 \mathrm{O}\right]^{3+}$ and $\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_5 \mathrm{Cl}\right]^{2+}$

It is based on the ligand strength. In spectrochemical series, ligands are weak or strong stronger ligands will split $d$-orbital energies in transition metal complexes. So, strong ligands cause larger splitting. and result in shorter wavelengths of absorbed light. For weak ligands, the splitting is lesser and wavelength is maximum.

For the given ligands, $\mathrm{CN}^{-}, \mathrm{NH}_3, \mathrm{H}_2 \mathrm{O}, \mathrm{Cl}^{-}$, the older of increasing field (ligand) strength is $Cl^-<\mathrm{H}_2 \mathrm{O}<\mathrm{NH}_3<\mathrm{CN}^{-}$(splitting is inversely. proportional to wavelength): $C N^{-}$is a strong-field ligand. So, it will cause a larger splitting and absorb light at a shorter wavelength (higher energy).

So, the complex $\left[C_0(\mathrm{CN})_6\right]^{3^-}$ has shorter wavelength

$\mathrm{NH}_3$ ligand strength is lower than $C{N}^{-}$ but higher than $\mathrm{Cl}^{-}$and $\mathrm{H}_2 \mathrm{O}$. The splitting caused by $\mathrm{NH}_3$ is lesser than $\mathrm{CN}^{-}$. So, the wavelength is higher than $\left[\mathrm{CO}(\mathrm{CN})_6\right]^{3-}$ complex.

$$ \mathrm{Co}\left(\mathrm{NH}_3\right)_6^{3+} \text { has wavelength higher than }\left[\mathrm{CO}(\mathrm{CN})_6\right]^{3-} \text { - } $$

$\mathrm{H}_2 \mathrm{O}$ is a weaker ligand than $\mathrm{NH}_3$ so, the complex $\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_5 \mathrm{H}_2O\right]^{3+}$ has higher wavelength than $\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_6\right]^{3+}$

Cl is the weak field ligand than $^{}$ $\mathrm{H}_2 \mathrm{O}$ and $\mathrm{NH}_3$

So, the wavelength is maximum for the complex containing $C^{-}$.

$$ \left[\mathrm{Co}\left(\mathrm{NH}_3\right)_5 \mathrm{Cl}\right]^{2+} \text { has highest wavelength. } $$

The correct order of wavelength maxima of the absorption band is.

$$ \left[\mathrm{Co}(\mathrm{CN})_6\right]^{3-}<\left[\mathrm{C}_0\left(\mathrm{NH}_3\right)_6\right]^{3+}<\left[\mathrm{C}_0\left(\mathrm{NH}_3\right)_5 \mathrm{H}_2 \mathrm{O}\right]^{3+} \leq\left[\mathrm{C}_0\left(\mathrm{NH}_3\right)_5 \mathrm{Cl}\right]^{2+} $$

$$ \text { Answer: Option (A) } $$