The complex \([ \text{Co(H}_2\text{O)}_6 ]^{3+}\) consists of a \(\text{Co}^{3+}\) ion, which has a \(d^6\) electronic configuration. In an octahedral field created by the water ligands, the splitting of the \(d\)-orbitals leads to the \(t_{2g}\) and \(e_g\) orbitals. As cobalt in this state is in a low-spin configuration (due to the relatively strong ligand field of water), all six electrons pair up in the \(t_{2g}\) set, resulting in no unpaired electrons. \[ \text{at } (0,0) \, t_{2g}: \quad (0,-0.3); \, (1.2,-0.3); \, (0.2,-0.3) \text{ circle (0.05); } \, (0.6,-0.3) \text{ circle (0.05); } \, (1.0,-0.3) \text{ circle (0.05);} \] \[ \text{at } (2,0) \, e_g: \quad (2.2,-0.3); \, (3.2,-0.3); \, (2.2,-0.3) \text{ circle (0.05); } \, (2.6,-0.3) \text{ circle (0.05);} \] Thus, there are no unpaired electrons in \([ \text{Co(H}_2\text{O)}_6 ]^{3+}\).
