Question

A compound of $A$ and $B$ crystallizes in a cubic lattice in which the $A$ atoms occupy the lattice points at the corners of the cube. The $B$ atoms occupy the centre of each fcc of the cube. The probable formula of the compound is:

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

Answer 1

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

$A$ atoms occupy the lattice points at the corners of the cube.
There are 8 corners in a unit cell, each contributing one eight to the unit cell.
Number of 'A' atoms in one unit cell $=8\times \frac{1}{8}=1$
The $B$ atoms occupy the centre of each fcc of the cube.
There are 6 face centres in a unit cell, each contributing one half to the unit cell.
Number of $B$ atoms in one unit cell $=6\times \frac{1}{2}=3$
The formula of the compound is $A{B}_3$