Question

{"given":"The problem provides the ionic radii for the cation and anion in the crystal lattice. The radius of the silver cation ($\\text{Ag}^+$) is $126\\text{ pm}$, and the radius of the iodide anion ($\\text{I}^-$) is $216\\text{ pm}$.","key_observation":"The coordination number of an ion in an ionic crystal can be predicted using the radius ratio rule. The radius ratio is defined as the ratio of the radius of the cation to the radius of the anion ($r_+ / r_-$).","formula_steps":[],"option_analysis":[{"label":"(A)","text":"$2$","verdict":"incorrect","explanation":"A coordination number of $2$ corresponds to a linear void (radius ratio $< 0.155$), which does not match the calculated ratio."},{"label":"(B)","text":"$4$","verdict":"incorrect","explanation":"A coordination number of $4$ corresponds to a tetrahedral void (radius ratio $0.225 - 0.414$), which does not match the calculated ratio."},{"label":"(C)","text":"$6$","verdict":"correct","explanation":"The radius ratio is $\\frac{r_+}{r_-} = \\frac{126}{216} \\approx 0.583$. This value lies in the range $0.414 \\le \\frac{r_+}{r_-} < 0.732$, which corresponds to an octahedral void and a coordination number of $6$."},{"label":"(D)","text":"$8$","verdict":"incorrect","explanation":"A coordination number of $8$ corresponds to a cubic void (radius ratio $0.732 - 1.000$), which does not match the calculated ratio."}],"answer":"(C)"}