Concept: Lattice energy is the energy required to completely separate one mole of a solid ionic compound into gaseous ionic constituents. According to Born-Landé equation, lattice energy is directly proportional to the product of the charges of the ions and inversely proportional to the sum of their ionic radii. Higher the charge and smaller the ionic radii, higher will be the lattice energy.

Why (B) is correct: All the given compounds are alkali metal fluorides (KF, NaF, CsF, RbF). In all these compounds, the anion is F\u207b, which has a constant charge and size. The cations are K\u207a, Na\u207a, Cs\u207a, and Rb\u207a. All these cations have a +1 charge. Therefore, the lattice energy will primarily depend on the size of the cation. As we move down a group in the periodic table, the ionic radius increases. So, the order of ionic radii for the cations is Na\u207a < K\u207a < Rb\u207a < Cs\u207a. Since lattice energy is inversely proportional to the sum of ionic radii, the compound with the smallest cation will have the highest lattice energy. Na\u207a is the smallest cation among the given options. Therefore, NaF will have the highest lattice energy.

Option Analysis:

• A) KF: K\u207a is larger than Na\u207a, so KF will have lower lattice energy than NaF.
• B) NaF: Na\u207a is the smallest cation among the given options, leading to the highest lattice energy.
• C) CsF: Cs\u207a is the largest cation among the given options, leading to the lowest lattice energy.
• D) RbF: Rb\u207a is larger than K\u207a and Na\u207a, so RbF will have lower lattice energy than NaF and KF.

Correct Answer: (B)