The solubilities of carbonates decrease down the magnesium group due to a decrease in

Solution :
As we move down the group, the lattice energies of carbonates remain approximately the same. However the hydration energies of the metal cation decreases from $$B{e^{ + + }}\,{\text{to}}\,B{a^{ + + }}$$  , hence the solubilities of carbonates of the alkaline earth metal decrease down the group mainly due to decreasing hydration energies of the cations from Be‘ to $$B{e^{ + + }}\,{\text{to}}\,B{a^{ + + }}$$.