Question

A compound formed by elements $A$ and $B$ crystallises in the cubic structure where $A$ atoms are at the corners of a cube and $B$ atoms are at the face centres. The formula of the compound is

• A. $A_2{B}_2$
• B. $A{B}_3$
• C. $AB$
• D. $A_{3}B$

Answer 1

Answer: (B)

$A{B}_3$

$A$ atoms are at the corners of a cube.
So, the number of $A$ atoms per unit cell $=8\times \frac{1}{8}=1$
Similarly, $B$ atoms are present at face centres of a cube.
So, the number of $B$ atoms per unit cell $=6\times \frac{1}{2}=3$
Hence, the compound is $A{B}_3$.