A compound XY has the NaCl structure. The radius of the cation X+ is 100 pm. What is the possible range for the radius of the anion Y-?

The compound XY has an NaCl structure.
The radius of the cation X$^+$ ($r_c$) is $100 \, \text{pm}$.
We need to find the radius of the anion Y$^-$ ($r_a$).

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 $\frac{r_c}{r_a}$ must be in the range $0.414 \le \frac{r_c}{r_a} < 0.732$.

Using the lower limit of the radius ratio (0.414):

Using the upper limit of the radius ratio (0.732):

Thus, for the NaCl structure to be stable, the radius of the anion $r_a$ must be in the range $136.612 \, \text{pm} < r_a \le 241.545 \, \text{pm}$.

• (a) $275.1 \, \text{pm}$: This value is greater than $241.545 \, \text{pm}$, so it is outside the valid range.
• (b) $322.5 \, \text{pm}$: This value is greater than $241.545 \, \text{pm}$, so it is outside the valid range.
• (c) $241.5 \, \text{pm}$: This value is within the valid range ($136.612 \, \text{pm} < 241.5 \, \text{pm} \le 241.545 \, \text{pm}$). 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) $165.7 \, \text{pm}$: This value is within the valid range ($136.612 \, \text{pm} < 165.7 \, \text{pm} \le 241.545 \, \text{pm}$).

When multiple options fall within the valid range, the question often refers to a limiting condition. In this case, the value $241.5 \, \text{pm}$ represents the upper limit for the anion radius to maintain the NaCl structure (octahedral coordination) with a cation radius of $100 \, \text{pm}$. 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 $241.5 \, \text{pm}$ is obtained directly from the lower limit of the radius ratio:

Rounding to one decimal place gives $241.5 \, \text{pm}$.

The final answer is $\boxed{\text{c) } 241.5 \, \text{pm}}$.