Question

A substance $A_x{B}_y$ crystallizes in a face centred cubic (fcc) lattice in which atoms $A$ occupy each corner of the cube and atoms $B$ occupy the centres of each face of the cube. Identify the correct composition of the substance $A_x{B}_y$.

• A. $A{B}_3$
• B. $A_4{B}_3$
• C. $A_{3}B$
• D. Composition cannot be specified

Answer 1

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

Effective number of corner atoms $\left(A\right)=8\times \frac{1}{8}=1=x$
Effective number of face centred atoms $\left(B\right)=\frac{1}{2}\times 6=3=y$
Thus, the composition of the substance is $A{B}_3$.