Explanation:

The solubility of a compound in water depends on the nature of the compound and the interactions between its ions and water molecules. In the case of sulphates, the solubility generally increases with the increase in the atomic number of the cation. This trend can be explained by considering the charge-to-size ratio of the cations.

Magnesium Sulphate (MgSO4):
Magnesium sulphate (MgSO4) is a soluble salt in water. It is commonly known as Epsom salt. The solubility of MgSO4 in water is relatively high.

Barium Sulphate (BaSO4):
Barium sulphate (BaSO4) is an insoluble salt in water. It is commonly used as a contrast agent in medical imaging. The solubility of BaSO4 in water is extremely low.

Calcium Sulphate (CaSO4):
Calcium sulphate (CaSO4) is a sparingly soluble salt in water. It is commonly known as gypsum. The solubility of CaSO4 in water is relatively low.

Beryllium Sulphate (BeSO4):
Beryllium sulphate (BeSO4) is a very soluble salt in water. The solubility of BeSO4 in water is higher compared to the other sulphates mentioned.

Explanation:
The solubility of a salt in water is determined by the hydration energy of the ions and the lattice energy of the solid. The hydration energy is the energy released when water molecules surround and interact with the ions, stabilizing them in solution. The lattice energy is the energy required to break apart the crystal lattice of the solid.

In the case of sulphates, the solubility generally increases with the increase in the atomic number of the cation. This is because as we move down the periodic table, the size of the cations increases while the charge remains the same. As a result, the charge-to-size ratio decreases, making it easier for the water molecules to surround and stabilize the ions in solution.

Beryllium sulphate (BeSO4) has the highest solubility among the given options because beryllium ions are relatively small and highly charged. The small size of the beryllium ion allows for strong interactions with water molecules, while the high charge density of the ion enhances the attractive forces between the ion and water molecules, resulting in a higher solubility in water.