Which one of the following ions is colourless in its aqueous solution?

Zn²⁺

The answer is (4), Zn2+.

The ions \(Ti^{3+}, Cu^{2+},\text{ and } Ni^{2+}\) all have unpaired electrons in their d-orbitals, which can absorb light and give them a characteristic color. The ion \(Zn^{2+}\), on the other hand, has a completely filled d-orbital, so it is colorless.

The color of an ion is due to the d-d transitions of the electrons in the d-orbital. When light is absorbed, it causes an electron to move from one energy level to another. The difference in energy between the two energy levels is equal to the energy of the light that is absorbed.

In the case of \(Zn^{2+}\), the d-orbital is completely filled, so there are no energy levels available for the electrons to move between. This means that \(Zn^{2+}\) cannot absorb light and exhibit color.

The other ions do have unpaired electrons in the d-orbital, so they can absorb light and exhibit color.

Here is a table of the colors of the ions in aqueous solution: