Question

In a crystalline solid, atoms of X form fcc packing and the atoms of Y occupy all the octahedral voids. If all the atoms along one body diagonal are removed ,then the simplest formula of the crystalline solid will be:

• A. $XY$
• B. $X_4{Y}_3$
• C. $X_5{Y}_4$
• D. $X_4{Y}_5$

Answer 1

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

in fcc packing (at corners and face centres of cubic unit cell) $\text{Number of atoms of X}=8\times \frac{1}{8}+6\times \frac{1}{2}=4$
No of octahedral voids = Number of atoms in FCC = 4
$\text{Number of atoms of Y}=4$
Along one body diagonal, there are two corner atoms and one body centre atom.
So, there are two X atoms and one Y atom.

$\text{Number of effective atoms of X after removal}=4-(2\times \frac{1}{8})=\frac{15}{4}$
$\text{Number of effective atoms of Y after removal}=4-1=3$
$X:Y=\frac{15}{4}:3$
$\therefore \text{Simplest formula}=X_5{Y}_4$