Why hydrated copper sulphate is blue in colour?

The correct answer is: (3) d-d transition due to orbital splitting

The blue color of hydrated copper sulfate, \(CuSO_4·5H_2O\), is due to the d-d transition of the copper \((Cu^{2+})\) ions in the complex. When light interacts with the copper ions, certain wavelengths of light are absorbed while others are transmitted or reflected. The absorbed light corresponds to specific energy levels of the electrons in the d-orbitals of the copper ions. The energy difference between these electronic energy levels corresponds to the frequency of light in the red region of the visible spectrum. As a result, the transmitted or reflected light appears blue to our eyes.

The other options (1) and (2) are not accurate explanations for the blue color of hydrated copper sulfate. While sulfate ions \((SO_4^{2-})\) can absorb red light due to their electronic transitions, it is not the primary reason for the blue color of the compound. Additionally, while \(Cu^{2+}\) ions can absorb certain wavelengths of light due to their electronic transitions, it is the specific d-d transition in the copper ions that leads to the blue color.