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. $AB_{3}$
• B. $A_{4}B_{3}$
• C. $A_{3}B$
• D. Composition cannot be specified

Answer 1

Answer: (A)

Effective number of corner atom $\left(A\right)$
$=8\times \frac{1}{8}=1=X$
Effective number of face centred atom $\left(B\right)$
$=\frac{1}{2}\times 6=3=Y$
Thus, composition of substance $=AB_{3}$ .