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The stability of the following alkali metal chlorides follows the order:
(A) \[LiCl{\text{ }} > {\text{ }}KCl{\text{ }} > {\text{ }}NaCl{\text{ }} > {\text{ }}CsCl\]
(B) \[CsCl{\text{ }} > {\text{ }}KCl{\text{ }} > {\text{ }}NaCl{\text{ }} > {\text{ }}LiCl\]
(C) \[NaCl{\text{ }} > {\text{ }}KCl{\text{ }} > {\text{ }}LiCl{\text{ }} > {\text{ }}CsCl\]
(D) \[KCl{\text{ }} > {\text{ }}CsCl{\text{ }} > {\text{ }}NaCl{\text{ }} > {\text{ }}LiCl\]

Answer
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Hint: As we go down the group in case of alkali metals, size of the cations increases due to which the attractive force between cation and anion decreases. This affects stability of the compound.

Complete step-by-step solution:
Stability of alkali metal chloride depends directly on the lattice energy. Lattice energy is the amount of energy released when an ionic solid is formed from its ionic constituents. This is an exothermic process. Lattice energy is inversely proportional to size of alkali metals and thereby decreases down the group. This accounts for the stability of alkali chlorides.
As we go down the group, size of the alkali metals increases and lattice energy decreases as the force of attraction decreases in higher alkali metals. Therefore, the stability of alkali metals decreases down the group i.e. from lithium to caesium.
But there comes an exception that potassium chloride being more stable than sodium chloride. The reason behind this is that the atomic size of potassium and chlorine is almost similar. This results in strong bonding between them making it more stable.

Hence, the correct option is (A).

Note: Another method to find the order is to consider the electronegativity difference. Alkali metal chlorides with higher electronegativity differences are unstable and less electronegativity differences are more stable.