Question

A compound has cubical unit cell in which X atoms are present at 4 corners , Y atoms are present at the remaining corners and only at those face center(s) which is/are not opposite to each other.
The formula for the compound will be:

• A. $X{Y}_4$
• B. $X{Y}_2$
• C. $X_{4}Y$
• D. $X_{2}Y$

Answer 1

The correct option is A $X{Y}_4$

In a cubical unit cell:

$\text{Contribution for a corner particle is}=\frac{1}{8}$
$\text{Contribution for a face centre particle is}=\frac{1}{2}$
X is present at 4 corners,
Y is present at 4 remaining corners and at 3 face centers.
For X :
$\text{Total X atoms in a unit cell}=4\times \frac{1}{8}=\frac{1}{2}$
For Y :
$\text{Total Y atoms in a unit cell}=(4\times \frac{1}{8})+(3\times \frac{1}{2})=2$
Formula of the compound is :
$X_{\frac{1}{2}}{Y}_2\Rightarrow X{Y}_4$