Question

In a face centered lattice of X and Y, 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 X atoms is missing from a corner in each unit cell?

• A. $X_7{Y}_{24}$
• B. $X_{24}{Y}_{24}$
• C. $X{Y}_{24}$
• D. $X_{24}{Y}_7$

Answer 1

The correct option is A $X_7{Y}_{24}$

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 $\frac{1}{8}$.
After the removal of 1 corner X atoms,
$\text{No. of X atom per unit cell}=7\times \frac{1}{8}=\frac{7}{8}$

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.
$\text{No. of Y atom per unit cell}=6\times \frac{1}{2}=3$

So, the number of atoms present or the formula of the compound is
$X_{\frac{7}{8}}{Y}_3$ or $X_7{Y}_{24}$