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The cubic unit cell structure of a compound containing cation M and anion X is shown below. When compared to the anion, the cation has smaller ionic radius. Choose the correct statement(s).

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The empirical formula of the compound is MX.

The cation M and anion X have different coordination geometries.

The ratio of M-X bond length to the cubic unit cell edge length is 0.866.

The ratio of the ionic radii of cation M to anion X is 0.41

answer is A.

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Detailed Solution

$\begin{aligned} Z_{M} = 2 \times \frac{1}{2} = 1 \\ Z_{X} = 4 \times \frac{1}{4} = 1 \end{aligned}$

Empirical formula is MX.

$d^{2} = {(\frac{a}{\sqrt{2}})}^{2} + {(\frac{a}{2})}^{2} \frac{d^{2}}{a^{2}} = \frac{3}{4} \frac{d}{a} = \frac{\sqrt{3}}{2} = 0.866$

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