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A compound of element A and B crystallis...

A compound of element A and B crystallises in the form of face-centered cubic lattice. The unit cell of the lattice contains A atom at each of its corner and a B atom at the centre of its each face. If a B atom from one of the faces is found missing, then what would be the formula of the compound?

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Since each corner atom of a cubic unit contributes `1//8^(th)` of its portion to the cell, for eight corners there is a total of `8xx1/8=1` atom per unit cell. Each face-centred atom contributes one-half of its portion to the cell. There are six faces per unit cell. If a B atom is found missing from one of the faces, then the total number of B atoms per unit cell `5xx1/2=5/2`.
So, the ratio of the number of A atoms to B atoms per unit cell:
`A:B=1:5/2=2:5`. This ratio corresponds to a formula of `A_(2)B_(5)`. Therefore, the formula of the compound would be `A_(2)B_(5)`.
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