Question

A compound formed by the elements X, Y crystlallizes in a cubic structure . Atoms of element X occupy all the corners and half the face centres of the cube. Atoms of element Y are present at the remaining face centres and body centre.
The simplest formula for the compound is:

• A. $X{Y}_2$
• B. $X_3{Y}_2$
• C. $X{Y}_4$
• D. $XY$

Answer 1

The correct option is D $XY$

In a cubical unit cell:

$\text{Contribution for a corner particle is}=\frac{1}{8}$
$\text{Contribution for a face centre particle is}=\frac{1}{2}$
$\text{Contribution for a body centre particle is}=1$

Now for X :

$\text{Total X atoms in a unit cell}=(8\times \frac{1}{8})+(3\times \frac{1}{2})=\frac{5}{2}$
For Y :

$\text{Total Y atoms in a unit cell}=(3\times \frac{1}{2})+1=\frac{5}{2}$

Formula for the compound:
$X_{\frac{5}{2}}{Y}_{\frac{5}{2}}\text{Simplest formula :}XY$