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_(3)`
D. `A_(3)B_(4)`

Answer

D

Explanation

Face centred atoms along one of the axis=3
Face centred atoms along the corners=2
No. of atoms at centre of face=1
`therefore` Contribution of `A^(-)` ion is=
`=(1)/(8)xx6xx5xx(1)/(2)=3.25cong3.0`
`therefore` Formula of compound `=A_(3)B_(4)`
(i) Effective number of `A^(-)` or `Cl^(-)` (normally) `=(8xx(1)/(8))+(6xx(1)/(2))=4`
From corners from faces (all face centred)
E.N. of `A^(-)` after removing atoms along.
one axes `=(8xx(1)/(8))+(4xx(1)/(2))=3`
(ii) E.N. of `B^(+)` or `Na^(+)=(12xx(1)/(4))+1=4`,
From edge centres from body centre
`therefore` Formula is `A_(3)B_(4)`. Hence (D) is correct option.