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In a solid having rock salt structure, i...

In a solid having rock salt structure, if all the atoms touching one body diagonal plane are removed (except at body centre), then the formula of the left unit cell is

A

`A_(3.5)B_(2.5)`

B

`A_(7)B_(3)`

C

`A_(5)B_(3)`

D

`A_(3)B_(5)`

Text Solution

Verified by Experts

The correct Answer is:
A
a.
`NaCl` (rock salt)-type structure is `fcc` type.
`( :. Z_(eff) = 4) [Z_(eff)(Na^(o+)) = 4, Z_(eff)(Cl^(Θ)) = 4]`
In `NaCl` structure anion `(Cl^(Θ))` (here `B^(Θ)`) are present at corners and face centre while cations `(Na^(o+))` (here `A^(o+))` are present in all `OV_(s)` (present at body centre and edge centre).
`:.` Number of `B^(Θ)` ions removed
`= 4 xx (1)/(8)` (corner share) `+ 2 xx (1)/(2)` (face centre share)
`= (1)/(2) + 1 = 3//2`
Number of `A^(o+)` ions removed `= 2 xx (1)/(4)` (edge centre share)
`= (1)/(2)`
`:.` Number of `B^(Θ)` ions left `= 4 - (3)/(2) = (5)/(2) = 2.5`
Number of `A^(o+)` ions left `= 4 - (1)/(2) = (7)/(2) = 3.5`
Thus, formula is: `A_(3.5)B_(2.5)`
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