Question

A crystal is made of particles X and Y. X forms fcc packing and Y occupies all the octahedral voids. If all the particles along one body diagonal are removed, then the formula of the crystal would be :

• A. $X_4{Y}_3$
• B. $X_5{Y}_4$
• C. $X_4{Y}_5$
• D. none of the above

Answer 1

The correct option is B $X_5{Y}_4$

In fcc, total $4$ octahedral voids are present.

So, it contains $4Y$ and $4X$ atoms but all the particles along one body diagonal are removed, then
Number of $Y$ atoms $=4-1=3$
Number of $X$ atoms $=4-\frac{1}{4}=\frac{15}{4}$
Compound is $X_{15/4}{Y}_3=X_5{Y}_4$.