Question

A compound of $A$ and $B$ crystallizes in a cubic lattice in which A atoms occupy the lattice points at the corners of the cube and two atoms of $B$ occupy the center of each of the cube faces. What is the formula of this compound ?

• A. $A{B}_3$
• B. $A{B}_4$
• C. $A{B}_2$
• D. $A{B}_6$

Answer 1

The correct option is D $A{B}_6$

In a cube there are 8 corners and 6 faces.
$A$ occupies all corners and $2B$ atoms occupy each one opposite pair of faces.
Corner atoms contribute $\frac{1}{8}$ to the unit cells.
Face center atoms contribute $\frac{1}{2}$ to the unit cells.
Number of $A$ atoms = $8\times \frac{1}{8}=1$
Number of $B$ atoms = $12\times \frac{1}{2}=6$

Formula of the compound will be $=A{B}_6$