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Question:

CaO and NaCl have the same crystal structure and approximately the same ionic radii. If U is the lattice energy of NaCl, the approximate lattice energy of CaO is:

4U

U

2U

U/2

Solution:

Lattice energy = −q₁q₂/r²
Where q₁ and q₂ are charges on ions and r is the distance between them.
Since inter-ionic distances in CaO and NaCl are similar, (larger cation has smaller anion and vice-versa) therefore r is almost the same.
Therefore, lattice energy depends only on the charge. Since the magnitude of charge on Na⁺ and Cl⁻ ions is unity and that on Ca²⁺ and O²⁻ ions is 2 each, therefore, the lattice energy of CaO is four times the lattice energy of NaCl i.e. 4U.
Hence, option D is correct.