The correct order of the complexes $\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_5\left(\mathrm{H}_2 \mathrm{O}\right)\right]^{3+}(\mathrm{A}),\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_6\right]^{3+}(\mathrm{B}),\left[\mathrm{Co}(\mathrm{CN})_6\right]^{3-}(\mathrm{C})$ and $\left[\mathrm{CoCl}\left(\mathrm{NH}_3\right)_5\right]^{2+}(\mathrm{D})$ in terms of wavelength of light absorbed is

<p>The energy of absorbed light by a complex can be expressed as $E = hv = \frac{hC}{\lambda}$, where $E$ is the energy, $h$ is Planck's constant, $v$ is the frequency, $C$ is the speed of light, and $\lambda$ is the wavelength of the absorbed light. This formula demonstrates that energy ($E$) is inversely proportional to the wavelength ($\lambda$). </p> <p>In this context, all cobalt complexes are in the +3 oxidation state. The Crystal Field Stabilization Energy (CFSE) is influenced by the strength of the ligands surrounding the metal ion. As the ligand field strength increases, the CFSE also increases.</p> <p>The order of field strength for the ligands in this case is:</p> <p>$ \text{CN}^- > \text{NH}_3 > \text{H}_2\text{O} > \text{Cl}^- $</p> <p>This implies the following order for CFSE in the given complexes:</p> <p>$ \text{C} > \text{B} > \text{A} > \text{D} $</p> <p>Because energy is inversely proportional to wavelength, complexes absorbing at higher energies will absorb at shorter wavelengths. Therefore, the order of the complexes in terms of the wavelength of light absorbed, from longest to shortest wavelength, is:</p> <p>$ \text{D} > \text{A} > \text{B} > \text{C} $</p>