JEE Advanced · 2020 · 27 Sep 2020 · Paper 1 · 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).

1. (A)The empirical formula of the compound is MX.✓ Correct
2. (B)The cation M and anion X have different coordination geometries.
3. (C)The ratio of M-X bond length to the cubic unit cell edge length is 0.866.✓ Correct
4. (D)The ratio of the ionic radii of cation M to anion X is 0.414.

Answer: (A), (C)

Solution

(A) From the unit cell:

• $Z_M=2\times \frac{1}{2}=1$
• $Z_X=4\times \frac{1}{4}=1$

Empirical formula is MX. Correct.

(B) Both M and X have coordination number 8 (same coordination geometry). Incorrect.

(C) The M-X bond length is the body diagonal divided by 2: $\frac{\sqrt{3}a}{2}=0.866a$. Correct.

(D) For this structure (CsCl type), $r_M:r_X=(\sqrt{3}-1):1=0.732:1$, not 0.414. Incorrect.

JEE Advanced · 2020 · 27 Sep 2020 · Paper 1 · One or more correct options