Question

A compound of $'A'$ and $'B'$ crystallises in a cubic lattice in which the $'A'$ atoms occupy the lattice points at the corners of the cube. The $'B'$ atoms occupy the centre of each face of the cube. The probable empirical formula of the compound is

• A. $AB$
• B. $AB_3$
• C. $AB_2$
• D. $A_3B$

Answer 1

Answer: (B)

$AB_3$

Answer 2

A occupies corners, thus number of $A$ atoms per unit cell $=8 \times \frac{1}{8}=1$ $B$ occupies face centres, thus number of $B$ atoms per unit cell $=6 \times \frac{1}{2}=3$ $\therefore$ The empirical formula of the compound is $A B_{3} .$