In which of the following pairs, both the ions are coloured in an aqueous solution?

\(Ni^{2+}, Ti^{3+}\)

The correct answer is option 2. \(Ni^{2+}, Ti^{3+}\).

Transition metal ions often exhibit colors due to the presence of partially filled d-orbitals. When light falls on these ions, it can be absorbed by electrons transitioning between these d-orbitals. The energy difference between the d orbitals corresponds to different wavelengths of light, which leads to the observation of colors.

Now, let's break down the explanation for each ion in the given pair:

1. \(Ni^{2+}\):

Nickel in the +2 oxidation state (\(Ni^{2+}\)) has a \(d^8\) electronic configuration. This means it has a partially filled d orbital, making it prone to absorbing certain wavelengths of light. As a result, \(Ni^{2+}\) ions often form intensely colored complexes in aqueous solution due to the transitions of electrons between these partially filled d orbitals.

2. \(Ti^{3+}\):

Titanium in the +3 oxidation state (\(Ti^{3+}\)) has a \(d^1\) electronic configuration. This means it has a partially filled d orbital, making it prone to absorbing certain wavelengths of light. As a result, \(Ti^{3+}\) ions often form intensely colored complexes in aqueous solution due to the transitions of electrons between these partially filled d orbitals.

Therefore, in the given pair \(Ni^{2+}\) and \(Ti^{3+}\), can form colored complexes due to the presence of partially filled d orbitals, thus making option 2 the correct choice.