Explain the following: (a) The ionic radii of \(\mathrm{Ca}^{2+}, \mathrm{Mn}^{2+}\) and \(\mathrm{Zn}^{2+}\) decrease regularly. (b) The ionic radius of \(\mathrm{Ni}^{2+}\) is smaller than that of \(\mathrm{Cu}^{2+}\) in presence of octahedral crystal-field environment of halide ions. (c) \(\mathrm{Co}^{3+}\) preferably adopts octahedral geometry under the effect of strong field ligands. (d) \(\mathrm{Mn}_{2} \mathrm{O}_{4}\) exists in normal spinel structure while \(\mathrm{Fe}_{2} \mathrm{O}_{1}\) exists in inverse spinel structure.

a) The ionic radii of \(\mathrm{Ca}^{2+}\), \(\mathrm{Mn}^{2+}\) decrease due to increased effective nuclear charge moving left to right across a period. b) \(\mathrm{Ni}^{2+}\) has a smaller ionic radius than \(\mathrm{Cu}^{2+}\) in octahedral crystal field due to greater effective nuclear charge. c) \(\mathrm{Co}^{3+}\) prefers octahedral geometry due to the large d-orbital splitting caused by strong field ligands. d) \(\mathrm{Mn}_{2} \mathrm{O}_{4}\) exists in normal spinel structure (divalent ions in octahedral sites), while \(\mathrm{Fe}_{3} \mathrm{O}_{4}\) exists in inverse spinel structure (half of the divalent ions are in tetrahedral sites and the other half along with all of the trivalent ions are in octahedral sites).