Question

In a face centered cubic lattice, atom (A) occupies the corner positions and atom (B) occupied the face centre positions. If one atom of (B) is missing from one of the face centered points, the formula of the compound is

• A. $A_2{B}_5$
• B. $A_2{B}_3$
• C. $A{B}_2$
• D. $A_{2}B$

Answer 1

The correct option is A $A_2{B}_5$

In a face centered cubic lattice, atom (A) occupies the corner positions. There are 8 corner positions and each position contributes one eighth to the unit cell. Hence, total number of (A) atoms per unit cell
$=\frac{1}{8}\times 8=1$
Atom (B) occupied the face centre positions. There are six face centre positions. One atom of (B) is missing from one of the face centered points. Thus, there are 5 face centre positions that are occupied with (B). Each such position contributes one half to the unit cell. Hence, total number of (B) atoms per unit cell.

$=\frac{1}{2}\times 5=2.5$

The formula of the compound is $A{B}_{2.5}$ or $A_2{B}_5$