A compound formed by elements X and Y crystallizes in the cubic structure where Y atoms are at the corner of the cube and X atoms are at the alternate edge centres. What is the formula of the compound?

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Solution

In the given compound; there must be 8 corners in a cube,

So, as the Y atoms are at corners, so each of the Y atom will contribute $\frac{1}{8}$ part towards a particular unit cell.

The no. of Y atoms per unit cell $= 8 \times \frac{1}{8} = 1$

Further, the X atoms are at the alternate faces so they will be available only at one of the opposite faces, so the contribution of each of the X-atoms will be $\frac{1}{2}$ towards the face center.

The no. of X-atoms $= 2 \times \frac{1}{2} = 1$

Hence, the formula of the compound will be "XY" .

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