Question

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

• A. $A_2B_2$
• B. $AB_3$
• C. $AB$
• D. $A_3B$

Answer 1

Answer: (B)

$AB_3$

Answer 2

A-atoms are present at the corners of a cube. So, the number of A-atoms per unit cell $=8\times\frac{1}{8}=1$
Similarly, 5-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 formula of compound is $A B3.$