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A crystalline compound formed by element...

A crystalline compound formed by elements A and B has facecentred cubic unit cell. The corners and the face-centred of the unit cell are occupied by A and B atoms, respectively. If one of the corner-atoms is found to be missing, then what would the formula of the compound be?

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Number of B atoms present in face-centre = `6xx1/2=3`.
In the unit cell, A atoms are present at the corners. One of the corner-atoms is found to be missing. Thus, number of A atoms present in the unit cell = `(8-1)xx1/8=7/8`.
Therefore, the ratio of A and B atoms in the unit cell = `7/8:3=7:24`.
Hence, the formula of the compound would be `A_(7)B_(24)`.
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