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A unit cell consists of a cube in which ...

A unit cell consists of a cube in which anions (B) are present at each corner and cations (A) at centre of the alternate faces of the unit cell. What is the simplest formula of the compound ?

Text Solution

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The correct Answer is:
`A_(3)B_(2)`
Contribution made by anion (B) at one corner = 1/8
Condtribution made by anions (B) at eight corners `=1//8xx8=1`
Since cations (A) are present at the centres of all alternate faces only, this means that only three face centres of the cubic unit cell have cation (A).
Contribution made by cation (A) at one face = 1/2
Contribution made by cations (B) at three faces `=3xx1//2=3//2`
`therefore` formula of the compound : `A_((3//2))B or A_(3)B_(2)`.
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