In a solid `AB` having the `NaCl` structure, A atom occupies the corners of the cubic unit cell. If all the face-centred atoms along one of the axes are removed, then the resultant stoichiometry of the solid is

Options

A. `AB_(2)`
B. `A_(2)B`
C. `A_(4)B_(2)`
D. `A_(2)B_(4)`

Explanation

AB has NaCl-type structure (fcc systems)
`therefore" "`Number of A atoms
`8 xx ("coner") 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 ("corner") xx (1)/(4)` (per edge centre share ) + 1 (body centre )
i.e., `O_(h)` Void = 1 + 3 = 4, unit cell
Number of A atoms removed (face-centred atom of one axis)
= ` 2 ("faces") xx (1)/(2) `(per face centre share) = 1/unit cell
Number of A atoms left = 4 – 1 = 3/unit cell.
Formula = `A_(3) B_(4)`