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In a solid 'AB' having the NaCl structur...

In a solid 'AB' having the `NaCl` structure, 'A' atoms occupy the corners of the cubic unit cell. If all the face centered atoms along one of the axes are removed, then the resultant stoichiometry of the solid is :

A

`AB_(2)`

B

`A_(2)b`

C

`A_(4)B_(3)`

D

`A_(3)B_(4)`

Text Solution

Verified by Experts

The correct Answer is:
D
`AB` has `NaCl`- type structure (fcc systems).
`:.` Number of `A` atoms
`= 8 ("corner") xx (1)/(8) ("per corner share") + 6 ("faces")`
`xx (1)/(2) ("per face centre share")`
`= 1 + 3 = 4//"unit cell"`
Number of `B` atoms
`= 12 ("edge") xx 1/4 ("per edge centre share")`
`+1 ("body centre")`
`= 1+3=4//"unit cell"`
Number of A atoms removed (face centred tom of one axis)
`= 2("faces") xx 1/2 ("per edge centre share")`
`= 1//"unit cell"`
Number of A atoms left `= 4 -1 = 3//"unit cell"`.
Formula `= A_(3)B_(4)`
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