This chemistry question involves key chemical concepts and calculations. The detailed solution below walks through each step, from identifying the reaction type to computing the final answer.
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Step 1: Identify the given information and the crystal structure. The compound XY has an NaCl structure. The radius of the cation X^+ (r_c) is 100 \, pm. We need to find the radius of the anion Y^- (r_a). Step 2: Recall the radius ratio rule for the NaCl structure. The NaCl structure is characterized by a coordination number of 6 for both the cation and the anion. This means the cation occupies octahedral voids. For stable octahedral coordination, the radius ratio (r_c)/(r_a) must be in the range 0.414 (r_c)/(r_a) < 0.732. Step 3: Calculate the possible range for r_a using the radius ratio limits. Using the lower limit of the radius ratio (0.414): (r_c)/(r_a) 0.414 100 \, pmr_a 0.414 r_a 100 \, pm0.414 r_a 241.545 \, pm Using the upper limit of the radius ratio (0.732): (r_c)/(r_a) < 0.732 100 \, pmr_a < 0.732 r_a > 100 \, pm0.732 r_a > 136.612 \, pm Thus, for the NaCl structure to be stable, the radius of the anion r_a must be in the range 136.612 \, pm < r_a 241.545 \, pm. Step 4: Evaluate the given options. (a) 275.1 \, pm: This value is greater than 241.545 \, pm, so it is outside the valid range. (b) 322.5 \, pm: This value is greater than 241.545 \, pm, so it is outside the valid range. (c) 241.5 \, pm: This value is within the valid range (136.612 \, pm < 241.5 \, pm 241.545 \, pm). This corresponds to the maximum possible anion radius for which the cation can still maintain stable octahedral coordination (i.e., the cation just touches all six anions). (d) 165.7 \, pm: This value is within the valid range (136.612 \, pm < 165.7 \, pm 241.545 \, pm). When multiple options fall within the valid range, the question often refers to a limiting condition. In this case, the value 241.5 \, pm represents the upper limit for the anion radius to maintain the NaCl structure (octahedral coordination) with a cation radius of 100 \, pm. If the anion were larger than this, the radius ratio would fall below 0.414, and the coordination number would likely decrease, leading to a different crystal structure. The value 241.5 \, pm is obtained directly from the lower limit of the radius ratio: r_a = 100 \, pm0.414 ≈ 241.545 \, pm Rounding to one decimal place gives 241.5 \, pm. The final answer is c) 241.5 \, pm.