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).

Engineering

Chemistry

Eudiometry

Question

The ratio of the ionic radii of cation M to anion X is 0.414.

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

The empirical formula of the compound is MX.

The cation M and anion X have different coordination geometries.

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(A) $Z_{M} = 2 \times \frac{1}{2} = 1$

$Z_{X} = 4 \times \frac{1}{4} = 1$

$∴$ Empirical formula is MX

(B) Coordinate numbers of both M and X is 8.

$= AB = \sqrt{3} . \frac{a}{2} = 0 .866 ba$

(D) $r_{M} : r_{X} = (\sqrt{3} - 1) : 1 = 0 .732 : 1 .000$

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