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A compound formed by elements X and Y crystallizes in a cubic structure in which the X atoms are at the corners of a cube and the Y atoms are at the face-centers. The formula of the compound is :-
A
$X_3Y$
B
$XY$
C
$XY_2$
D
$XY_3$
Detailed Solution
A corner atom is shared by 8 unit cells, so it contributes $\dfrac{1}{8}$ to one cell. A face-centre atom is shared by 2 unit cells, so it contributes $\dfrac{1}{2}$.
X atoms at 8 corners: $8 \times \dfrac{1}{8} = 1$ X atom per unit cell
Y atoms at 6 face centres: $6 \times \dfrac{1}{2} = 3$ Y atoms per unit cell
Ratio X : Y = 1 : 3
So the formula of the compound is $XY_3$.
X atoms at 8 corners: $8 \times \dfrac{1}{8} = 1$ X atom per unit cell
Y atoms at 6 face centres: $6 \times \dfrac{1}{2} = 3$ Y atoms per unit cell
Ratio X : Y = 1 : 3
So the formula of the compound is $XY_3$.