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A compound of A and B crystallizes in a cubic Lattice in which A atoms occupy the lattice points at the comers of a cube and two atoms of B occupy the center of each of the cube faces. Whet is the formula of this compound?

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${AB}_{3}$

${AB}_{4}$

${AB}_{2}$

${AB}_{6}$

answer is D.

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Detailed Solution

The formula of this compound ${AB}_{6}$

There are 6 faces and 8 corners in a cube. A fills all of the corners, while each opposite pair of faces is filled with two B atoms.

Corner atoms contribute $1 / 8$ to the unit cells

Face center atoms contribute $1 / 2$ to the unit cells.

Number of A atoms $\begin{aligned} = 8 \times \frac{1}{8} = 1 \end{aligned}$

Number of B atoms $= 12 \times \frac{1}{2} = 6$

Formula of the compound will be ${AB}_{6}$

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