Question

In a face-centred lattice of $X$ and $Y,X$atoms are present at the corners while $Y$ atoms are at face-centres. Then the formula of the compound if two atoms of $X$ are missing from the corners would be:

• A. $X_2{Y}_4$
• B. $X_{4}Y$
• C. $X{Y}_4$
• D. $X_3{Y}_4$

Answer 1

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

$\text{Calculating the contribution of X atoms:}$

Each atom $\left(X\right)$ at the corner of the unit cell contributes $\frac{1}{8}$ to the unit cell.

There are $8$ corners in a unit cell. It is given that two corner atoms $\left(X\right)$ are missing from the unit cell.

Therefore, the contribution of the corner atoms $\left(X\right)$ to the unit cell $=6\times \frac{1}{8}=\frac{2}{4}$

$\text{Calculating the contribution of}Y\text{atoms:}$

Each atom $\left(Y\right)$ at the face-centres of the unit cell contributes $\frac{1}{2}$ to the unit cell.

There are 6 face-centres in a unit cell. So, there are a total of 6 face-centred atoms $\left(Y\right)$ in the unit cell.

Therefore, the contribution of the face-centred atoms $\left(Y\right)$ to the unit cell $=6\times \frac{1}{2}=3$

$\text{Determining the formula of the compound:}$

The ratio of number of atoms in the unit cell

$X:Y=\frac{3}{4}:3$

$=1:4$

Therefore, the formula of the compound is $X{Y}_4.$

So, option (c) is the correct answer.