Chemistry Question on Chemical bonding and molecular structure

Question

$CaO$ and $NaCl$ have the same crystal structure and approximately the same ionic radii. If $U$ is the lattice energy of $NaCl$ , the approximate lattice energy of $CaO$ is

Answer 1

Solution

Lattice energy $=-\frac{q_{1}q_{2}}{r^{2}}$ where $q_1$ and $q_2$ are charges on ions and r is the distance between them. Since interionic distances in CaO and NaCl are similar, (larger cation has smaller anion and vice versa) therefore, r is almost the same. Therefore, lattice energy depends only on charge. Since the magnitude of charge on $Na^+$ and $Cl^-$ ions is unity and that on $Ca^{2+}$ and $O^{2-}$ ions is 2 each, therefore, the lattice energy of CaO is four times the lattice energy of NaCl, i.e.,4U.