Question

In a face centerd lattice of X and Y, X atoms are present at the corners while Y atoms are at the face centers. If two X atoms are removed from the corners, the formula of the compound would be:

• A. $X_{4}Y$
• B. $X_3{Y}_4$
• C. $X{Y}_4$
• D. $X_2{Y}_4$

Answer 1

The correct option is C $X{Y}_4$

In a cube, there are 8 corners and 6 faces.
X occupies the corner and Y occupies the faces.
Corner atoms contribute $\frac{1}{8}$ to the unit cells.
Face centre atoms contribute $\frac{1}{2}$ to the unit cells.
As two of the X atoms are missing,
Number of X per unit cell: $6\times \frac{1}{8}=\frac{3}{4}$
Number of Y per unit cell: $6\times \frac{1}{2}=3$
so, $X_{3/4}{Y}_3$
or $X_3{Y}_{12}$ i.e $X{Y}_4$.