Question

In a face centerd lattice of $X$ and $Y,X$ atoms are present at the corners while $Y$ atoms are at face centers. Then, the formula of the compound would be if one of the $X$ atoms is missing from a corner in each unit cell:

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

Answer 1

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

$\text{The atoms at the corner contribute}\frac{1}{8}\text{to the unit cell}$
$\text{Number of X atom per unit cell}=7\times \frac{1}{8}=\frac{7}{8},\text{since one corner atom is missing}$
$\text{The atoms at the face contribute}\frac{1}{2}\text{to the unit cell}$
$\text{Number of Y atom per unit cell}=6\times \frac{1}{2}=3$
$\therefore \text{Formula of the compound}=X_{\frac{7}{8}}{Y}_3\text{or}{X}_7{Y}_{24}$