Discussion
A compound contains two types of atoms X and Y. It crystallizes in a cubic lattice with atom X at the corners of the unit cell and Y at the body centre. The simplest possible formula of this compound is :
Answer: C
The formula is XY.
An atom at a corner of a cubic unit cell is shared by eight cells, and an atom at the body centre belongs wholly to one cell:
\[ \begin{aligned} \mathrm{X} &= 8 \times \tfrac{1}{8} = 1 \\ \mathrm{Y} &= 1 \times 1 = 1 \end{aligned} \]
One X and one Y per cell gives XY, the arrangement of the cesium chloride structure.
X2Y and X4Y come from counting corner atoms as more than one-eighth each, and XY4 reverses the roles of the two atoms. The same counting with face centres (each shared by two cells) is what gives XY3 in a face-centred arrangement.
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