Question

{"given":"A binary solid $(A^+ B^-)$ with a rock salt structure has an edge length $a = 400 \\text{ pm}$ and a cation radius $r_+ = 75 \\text{ pm}$.","key_observation":"In a rock salt (NaCl) structure, the anions form a face-centered cubic (fcc) lattice, and the cations occupy all the octahedral voids. The cations and anions touch each other along the edge of the unit cell. Therefore, the edge length $a$ is equal to twice the sum of the radii of the cation and the anion.","formula_steps":[],"option_analysis":[{"label":"(A)","text":"$100 \\text{ pm}$","verdict":"incorrect","explanation":"This value would correspond to an edge length of $350 \\text{ pm}$, which contradicts the given edge length of $400 \\text{ pm}$."},{"label":"(B)","text":"$125 \\text{ pm}$","verdict":"correct","explanation":"Using the relation for the rock salt structure, $a = 2(r_+ + r_-)$. Substituting the given values: $400 = 2(75 + r_-) \\implies 200 = 75 + r_- \\implies r_- = 125 \\text{ pm}$."},{"label":"(C)","text":"$250 \\text{ pm}$","verdict":"incorrect","explanation":"This value represents the diameter of the anion ($2r_-$), not the radius of the anion."},{"label":"(D)","text":"$325 \\text{ pm}$","verdict":"incorrect","explanation":"This value is obtained by incorrectly subtracting the cation radius from the edge length ($400 - 75$), which is not the correct geometric relationship."}],"answer":"(B)"}