Question

In a face centred cubic lattice, atom A occupies the corner position and atom B occupies the face centre position. If one atom of B is missing from one of the face centred points, the formula of the compound is:

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

Answer 1

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

Contribution of A atoms (at the corner) $=8\times \frac{1}{8}=1$
Contribution of B atoms (at face centre) $=5\times \frac{1}{2}=\frac{5}{2}$
A : B
$1:\frac{5}{2}=2:5$