Question

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

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

Answer 1

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

Each of the 8 corner atoms of a cube is shared by 8 such cubes so that each corner atom contribution to one cube will be 1/8.
After the removal of 2 corner X atoms, number of X present in the cell from the remaining 6 corner X atoms = $6\times \frac{1}{8}=\frac{3}{4}$
Each atom at the face centre is shared by two unit cell so that each face centred atom contributes half of it to each cube.
Number of face centred Y atoms present in the cell= $6\times \frac{1}{2}=3$
so , the number of atoms present or the formula of the compound =$X_{\frac{3}{4}}{Y}_3$ or $X_3{Y}_{12}$ or $X{Y}_4$