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Property of the alkaline earth metals that increases with their atomic number is
A. Electronegativity
B. Solubility of their hydroxides in water
C. Solubility of their sulphates in water
D. Ionisation energy

Answer
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Hint: The elements Beryllium, Magnesium, Calcium, Strontium, Barium, and Radium form group 2 of the periodic table. These metals are alkaline and exist on earth hence are called alkaline earth metals.

Complete Step by Step Answer:
Group-2 includes Beryllium, Magnesium, Calcium, Strontium, Barium, and Radium. These elements are the alkaline earth metals as they are alkaline and exist in the earth.

We have to find out which of the following properties of the alkaline earth metals increase with their atomic number.
A. electronegativity
Electronegativity is the ability of an atom to attract an electron pair towards itself in a chemical bond.
We know that down the group, atomic size increases due to the addition of electrons to new subshells.
So, with the increase in atomic size, it becomes difficult for the metal atom to attract the electron pair towards itself.
So, electronegativity decreases.
So, A is incorrect.
Lattice energy is the energy required to break an ionic compound into isolated constituent gaseous cations and anions.
Hydration energy is the amount of energy released when a gaseous cation or anion is hydrated by water dipoles.
We can say that high lattice energy ensures a high molecular force of attraction due to which dissolution of constituent ions in water is not possible.
So, for the dissolution of a substance in water, hydration energy must be more than lattice energy.

B. solubility of their hydroxides in water
The lattice energy of hydroxides is insufficient due to the little size of the hydroxide ion.
So, the size of hydroxide ions does not have any effect on the lattice energy.
The lattice energy declines with the rise in metallic size from Beryllium to Barium. This leads to an increase in the solubility as the intermolecular force of attraction is not that high so dissolution happens easily.
So, the solubility of hydroxides increases from Beryllium to Barium.
So, B is correct.

C. solubility of their sulphates in water
The lattice energy of sulphates is nearly the same as the sulphate anion is huge as compared to the size of a cation.
So, the solubility depends only on the hydration energy.
Hydration energy increases with a rise in charge on the cation formed by the metal and a reduction in atomic size as a small-sized cation can be attached properly by a larger number of water molecules.
We know that down the group atomic size rises. So, the hydration energy decreases down the group.
So, C is incorrect.

D. ionisation energy
Down the group, with the increase in atomic size, the distance between the nucleus and the outer electrons increases. So, the electrons are no longer tightly bound to the nucleus. So, it is easier to remove an electron from the outermost shell.
So, ionisation energy decreases down the group.
So, D is incorrect.

Hence, the correct answer is option (D).

Note: It should be pointed out that the solubility of barium hydroxide is the highest. Hydration energy is reduced in the group because of an increase in size. The reason is that it is tough for the water dipoles to react with very big-sized cations. But the drop in lattice energy of the hydroxides counterbalances this drop in hydration energy.