First slide

Crystal lattices and unit cells

Question

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).

Difficult

A

The empirical formula of the compound is MX.
B

The cation M and anion X have different coordination geometries.
C

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

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

Solution

1) $\begin{aligned} Z_{M} = 2 \times \frac{1}{2} = 1 \\ Z_{X} = 4 \times \frac{1}{4} = 1 \end{aligned}$
$∴$ Empirical formula is M
2) Coordinate numbers of both M and X is 8.
3) Bond length of M – X bond
$= AB = \sqrt{3} \cdot \frac{a}{2} = 0.866 a$
4) $r_{M} : r_{X} = (\sqrt{3} - 1) : 1 = 0.732 : 1.000$

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