Question

A compound formed by elements A and B crystallizes in the cubic structure where A atoms are at the corners of the cube and B atoms are at the face centres. The formula of the compound is:

• A. $A{B}_3$
• B. AB
• C. $A_{3}B$
• D. $A_2{B}_2$

Answer 1

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

A atoms are at the corners of the cube. There are 8 corners and each contributes one eight to the unit cell. Total number of A atoms $=8\times \frac{1}{8}=1$.
B atoms are at the face centres of the cube. There are 6 face centres and each contributes one half to the unit cell. Total number of B atoms $=6\times \frac{1}{2}=3$.
The formula of the compound is $A{B}_3$