# 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. What is the empirical formula for this compound?

$\begin{array}{1 1} AB_3 \\ A_3B \\ AB_2 \\ A_8B_6 \end{array}$

Answer: $AB_3$
Number of A ions per unit cell = $\large\frac{1}{8}$$\times 8 = 1 Number of B ions per unit cell = \large\frac{1}{2}$$\times 6 = 3$
$\Rightarrow$ the empirical formula is $AB_3$