Step 1: Ti\(^{2+}\) has the electron configuration [Ar] 3d\(^2\), with two electrons in the 3d orbitals. In the presence of ligands (e.g., in salts), the d-orbitals split into lower-energy t\(_{2g}\) and higher-energy e\(_{g}\) levels due to crystal field splitting. Electrons can transition between these levels (d-d transitions), absorbing visible light and causing the salts to appear coloured.
Step 2: For the divalent cation of the transition metal with atomic number 25 (Mn), the Mn\(^{2+}\) ion has the configuration [Ar] 3d\(^5\). This half-filled d\(^5\) configuration also allows d-d transitions in the ligand field, leading to absorption of visible light and coloured salts (e.g., pale pink in MnSO\(_{4}\)).