Question

In a face centered cubic lattice, atoms A are at the corner points and atoms B at the face centered points. If atom B is missing from one of the face centered points, the formula of the ionic compound is:

• A. $A{B}_2$
• B. $A_5{B}_2$
• C. $A_2{B}_3$
• D. $A_2{B}_5$

Answer 1

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

If in a face centered cubic lattice, atoms A are at the corner points.

Therefore, the contribution of A $=8\times \frac{1}{8}=1$

If B is at the face centered points, then contribution of B $=6\times \frac{1}{2}=3$

If one B is missing from one face, then its contribution decreases to $\frac{5}{2}$ per lattice, then the formula will be $A_2{B}_5$.