Question

X,Y atoms crystallize in a cubic lattice . X atoms are present at the corners while Y atoms are at face centers. What would be the simplest formula of the compound if one of the Y atoms is missing from a face centre in each unit cell?

• A. $X_3{Y}_4$
• B. $X_4{Y}_3$
• C. $X_2{Y}_5$
• D. $X_5{Y}_2$

Answer 1

The correct option is C $X_2{Y}_5$

Each of the 8 corner atoms of a cube is shared by 8 such cubes so that each corner atom contribution to one cube will be $\frac{1}{8}$.
$\text{No. of X atoms per unit cell}=8\times \frac{1}{8}=1$
Each atom at the face centre is shared by two unit cell so that each face centred atom contributes half of it to each cube.
$\text{No. of Y atom per unit cell}=6\times \frac{1}{2}=3$
After removal of one Y atom:

$\text{No. of Y atom per unit cell}=5\times \frac{1}{2}=\frac{5}{2}$
So, the number of atoms present or the formula of the compound is
$X_1{Y}_{\frac{5}{2}}$ or $X_2{Y}_5$