Question

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

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

Answer 1

The correct option is C $A{B}_3$

Given, $A$ ion lies in the corner of the cube.
Therefore the number of $A$ ions per unit cell
$=\frac{1}{8}\times 8=1$
$B$ ions lies in the face centeres.
Therefore number of $B$ ions per unit cell $=\frac{1}{2}\times 6=3$
Therefore the empirical formula would be $=A{B}_3.$