Question

A compound alloy of gold and copper crystallizes in a cubic lattice in which the gold atoms occupy the corners of a cube, and the copper atoms occupy the centers of each of the faces of the cube. The formula of this compound is:

• A. $AuCu$
• B. $AuC{u}_2$
• C. $AuC{u}_3$
• D. $A{u}_{3}Cu$

Answer 1

The correct option is C $AuC{u}_3$

Given, gold atoms $\left(Au\right)$ occupies the corners of the cube and the copper atoms $\left(Cu\right)$ occupies the face centers.
Thus, the number of $Au$ atoms per unit cell $=8\times \frac{1}{8}=1$ and the number of $Cu$ atoms per unit cell$=6\times \frac{1}{2}=3.$ The formula of the compound is $AuC{u}_3$.

Therefore, the correct answer is (C).