Question

An ionic compound has a unit cell consisting of A ions at the corners of a cube and B ions on the centres of the faces of the cube. The empirical formula for this compound would be:

• (A) $AB$
• (B) $A_{2}B$
• (C) ${AB}_3$
• (D) $A_{3}B$

Answer 1

The Correct Option is C

Explanation:
Since $A$ is present at the 8 corners, number of $A$ ions per unit cell $=\frac{1}{8}\times 8=1$Since $B$ is present at the centre of 6 faces, number of $B$ per unit cell $=\frac{1}{2}\times 6=3$$\therefore$ The ratio of $A$ and $B$ is $1:3$, so the formula of the compound is $A{B}_3$.Hence, the correct option is (C).