Question

$A_x{B}_y$ forms a crystal in which $A$ occupies the corner as well as the face centeres and $B$ occupies the edge centers of the cube. Then $x$ and $y$ are respectively:

• A. $4,3$
• B. $4,4$
• C. $3,3$
• D. $3,4$

Answer 1

The correct option is A $4,3$

In a crystal lattice,
atoms in the corner contribute $\frac{1}{8}$ to the unit cell.
Atoms in the faces contribute $\frac{1}{2}$ to the unit cell
Atoms in the edge centers contribute $\frac{1}{4}$ to the unit cell
Effective number of $A$ atoms per unit cell =$\frac{1}{8}\times 8+\frac{1}{2}\times 6=4$
Effective number of B atoms per unit cell $=\frac{1}{4}\times 12=3$
So the compound is $A_4{B}_3$.
Hence $x=4,y=3$