Question

A compound formed by elements $A$ and $B$ crystallizes in the cubic arrangement in which $A$ atoms are at the corners of a cube and $B$ atoms are at the face centers. What is the formula of compound?

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

Answer 1

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

A atoms are at the corners of a cube. There are 8 corners and each contributes one eigth to the unit cell. Total number of A atoms per unit cell $=8\times \frac{1}{8}=1$

B atoms are at the face centers. There are six face centers and each contributes one half to the unit cell. Total number of B atoms per unit cell $=6\times \frac{1}{2}=3$

The formula of the compound $=A{B}_3$