The correct option is A KCl>MgO
As the charge on the ions (cations and anions) increase, the lattice energy increases, and it decreases when the size of the ions (cations and anions) increases.
a) Size: K+>Mg2+
Charge: +1<+2
Size: Cl−>O2−
Charge: −1<2−
Thus, the lattice energy of MgO is greater than KCl.
b) Size: Al3+<Mg2+
Charge: +3>+2
Size: N3−>O2−
Charge: −3>−2
Here, the charge factor dominates and hence the lattice energy of AlN is greater than MgO.
c) Size: Ca2+<Ba2+
Charge: +2=+2
Size: O2−=O2−
Charge: −2=−2
The lattice energy of CaO is greater than BaO.
d) Size: Mg2+<Ca2+
Charge: +2=+2
Size: CO2−3=CO2−3
Charge: −2=−2
The lattice energy of MgCO3 is greater than the CaCO3.