JEE Advanced · Chemistry · 15. Solid State

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 $MX$ .
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 $0.414$

Verified Solution

Answer & Solution

Correct Answer

(C) The ratio of $M - X$ bond length to the cubic unit cell edge length is $0.866$

Step-by-step Solution

Detailed explanation

M_{2 \times \frac{1}{2}} X_{4 \times \frac{1}{4}} = MX

d^{2} = {(\frac{a}{\sqrt{2}})}^{2} + {(\frac{a}{2})}^{2}

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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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).

Step-by-step Solution

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).