Question

In a face centered cubic arrangement of $A$ and $B$ atoms whose $A$ atoms are at the corner of the unit cell and $B$ atoms at the face centers. One of the $B$ atoms missing from one of the face in unit cell. The simplest formula of compound is:

• A. $A{B}_3$
• B. $A_8{B}_5$
• C. $A_2{B}_5$
• D. $A{B}_{\frac{2}{5}}$

Answer 1

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

Atoms at the corner contribute $\frac{1}{8}$ to the unit cell.
Atoms at the faces contribute $\frac{1}{2}$ to the unit cell
Number of atoms of $A=8\times \frac{1}{8}=1$
Number of atoms of $B=5\times \frac{1}{2}=\frac{5}{2}$
So, the formula will be $A{B}_{\frac{5}{2}}$
Simplest formula will be $A_2{B}_5$.