Question

In a ccp lattice of $X$ and $Y$, $X$ atoms are present at the corners while $Y$ atoms at the face centres. Then the formula of the compound, if one of the $X$ atoms from a corner is replaced by $Z$ atoms (having same valency), would be?

• A. $X_7{Y}_{24}{Z}_2$
• B. $X_7{Y}_{24}Z$
• C. $X_{24}{Y}_{7}Z$
• D. $X{Y}_{3}Z$

Answer 1

The correct option is B $X_7{Y}_{24}Z$

The number of $X$ atoms present per unit cell$=8\times \frac{1}{8}=1$
The number of $Y$ atoms present per unit cell$=6\times \frac{1}{2}=3$
The formula before removing the $X$ atom$=X{Y}_3$
The formula after removing one of the X atom from the corner$=X_{1-\frac{1}{8}}{Y}_3{Z}_{\frac{1}{8}}\Rightarrow X_7{Y}_{24}Z$