Determine Colour of Light Absorbed by Aqueous Copper Sulfate

An aqueous solution of copper sulfate ($\text{CuSO}_4$) contains hydrated copper(II) ions, primarily in the form of the hexaaquacoppper(II) complex, $[\text{Cu}(\text{H}_2\text{O})_6]^{2+}$.

1. Electronic Configuration and Crystal Field Splitting: The central copper ion ($\text{Cu}^{2+}$) has a $3d^9$ electronic configuration. In the presence of water molecules acting as weak field ligands, the five degenerate $d$-orbitals split into two sets of different energies in an octahedral crystal field:

   • Lower energy $t_{2g}$ set
   • Higher energy $e_g$ set

2. $d$-$d$ Transition and Wavelength Absorption: When visible light passes through the solution, an electron absorbs a photon with energy equal to the crystal field splitting energy ($\Delta_o$) and gets promoted from a lower energy orbital to a higher energy orbital ($d$-$d$ transition): $\Delta E = h\nu = \frac{hc}{\lambda}$

3. Complementary Color Relationship: The observed color of a solution is the complementary color of the light absorbed by it:

   • Aqueous $\text{CuSO}_4$ appears blue to blue-green because light of these wavelengths is transmitted/reflected.
   • Using the complementary color wheel, the complementary color to blue / blue-green is orange-red (wavelength $\approx 600\text{--}700\text{ nm}$).

Therefore, an aqueous solution of $\text{CuSO}_4$ absorbs light in the orange-red region.

Correct Answer: A