Question

A compound contains two types of atoms $X$ and $Y$. Its crystal structure is cubic lattice with $X$ atoms at the corner of the unit cells and $Y$ atoms at the face centre. The simplest formula of the compound is

• A. $XY$
• B. $X_{2}Y$
• C. $X{Y}_2$
• D. $X{Y}_3$

Answer 1

The correct option is D $X{Y}_3$

An atom at the corner of a unit cell is shared by eight unit cells. So, Each atom contributes $\frac{1}{8}$ to the unit cell.
An atom at the face is a shared by two unit cells, contributes $\frac{1}{2}$ to the unit cell.

Atoms	Location	Number of atoms
X	Corner	$8\times \frac{1}{8}=1$
Y	Face centre	$6\times \frac{1}{2}=3$

Thus, the simplest formula is $X{Y}_3$