Question

In a cube of any crystal, $A$-atoms are placed at every corners and B-atoms are placed at every centre of face. The formula of compound is:

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

Answer 1

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

${}^{\prime }{A}^{\prime }$ atoms are placed at '8' corners of the cube. Thus, number of ${}^{\prime }{A}^{\prime }$ atoms per unit cell = $8\times \frac{1}{8}=1$
${}^{\prime }{B}^{\prime }$ atoms are at the face centre of six faces. Thus, number of ${}^{\prime }{B}^{\prime }$ atoms per unit cell = $6\times \frac{1}{2}=3$
The formula is $A{B}_3$