Discussion
A compound formed by element X and Y crystallizes in cubic structure in which atoms of ‘X’ are at the corners while that of ‘Y’ are at the face centre. The formula of the compound is :
Answer: C
The formula is XY3.
Count the atoms belonging to one unit cell. A corner atom is shared by eight cells and a face-centre atom by two:
\[ \begin{aligned} \mathrm{X} &= 8 \times \tfrac{1}{8} = 1 \\ \mathrm{Y} &= 6 \times \tfrac{1}{2} = 3 \end{aligned} \]
One X to three Y gives XY3, as in the Cu3Au type of ordered alloy.
X8Y6 counts the positions without sharing them among neighbouring cells. X3Y and 3XY reverse or misplace the factor of three, which belongs to the face-centred Y atoms.
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