In a solid `AB` having the `NaCl` structure, `A` atom occupies 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

Options

A. `AB_(2)`
B. `A_(2)B`
C. `A_(4)B_(3)`
D. `A_(3)B_(4)`

Answer

D

Explanation

In one `NaCl` type unit cell of solid, `A^(+)` are present at corners and face centers and `B^(-)` are present at edge centers and body center. Thus, a unit cell will contain `4A^(+)` and `4B^(-)` ions. In this unit two face centered ions `A^(+)` lies along one axis and are removed.
Contribution of two face centered `A^(+)` ions `= 2xx(1)/(2)=1`
In the resultant unit cell,
`therefore` Number of `A^(+)` ions present per unit cell `= 4`
`therefore` Number of `A^(+)` ions present per unit cell `= 4-1=3`
`therefore` Stoichiometry `= A_(3)B_(4)`.
Hence, (D) is the correct answer.