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

Options

A. `A_(3.5)B_(2.5)`
B. `A_(7)B_(3)`
C. `A_(5)B_(3)`
D. `A_(3)B_(5)`

Answer

A

Explanation

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)`