The color of transition metal ions is due to the d-d transitions in the metal’s d-orbitals, which are affected by the oxidation state and the ligand environment.
- Option (1) Ti\(^{4+}\), V\(^{3+}\): Ti\(^{4+}\) is colorless due to the absence of d-electrons, while V\(^{3+}\) has color due to d-d transitions, so they are not the same color.
- Option (2) Cr\(^{2+}\), Cu\(^{2+}\): Both Cr\(^{2+}\) and Cu\(^{2+}\) ions have similar electronic configurations and show characteristic colors due to their d-d transitions, making them the same color.
- Option (3) Cr\(^{3+}\), Ni\(^{2+}\): Cr\(^{3+}\) is typically green in color, while Ni\(^{2+}\) has a different characteristic color (usually blue-green), so they are not the same color.
- Option (4) Mn\(^{3+}\), Fe\(^{2+}\): Mn\(^{3+}\) is usually purple, while Fe\(^{2+}\) is pale green, so these ions are not the same color.
Thus, the correct answer is Cr\(^{2+}\), Cu\(^{2+}\) (option 2).