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).

• A. The empirical formula of the compound is $M X$
• 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 $0.414$

Answer 1

Answer: (A), (C)

Contribution of $M=\frac{1}{2} \times 2=1$
Contribution of $X=\frac{1}{4} \times 4=1$
Formula $=M X$
Distance between $M$ and $X=\sqrt{\frac{a^{2}}{4}+\frac{a^{2}}{2}}$
$=\sqrt{\frac{3}{4}} a=\frac{\sqrt{3}}{2} a$
$=0.866 \,a$
Both cation and anion have same co-ordination number, i.e., $8$ .
Assuming, anions are in contact, the ratio of ionic radii of cation $M$ to anion $X$ is $0.732$, the minimum radius ratio for a cubical void.