In a face centered lattice of X and Y, X atoms are present at the corners while Y atoms are at face centres.
(a) What is the formula of the compound ?
(b) What would be the formula of the compound if (i) one of the X atoms is missing from a corner in each unit cell
(ii) one of the X atoms at from a corner is replaced by Z atom. (also monovalent) ?

Answer

(a) `XY_(3)` (b) `X_(7)Y_(24)` (c) `X_(7)Y_(24)Z`

Explanation

(a) Number of X atoms in the unit cell `=8xx1//8=1`
Number of Y atoms in the unit cell `=6xx1//2=3`
Formula of the compound `=XY_(3)`.
(b) (i) IF one atom of X is missing, number of X atoms in the unit cell = 7/8
Number of Y atoms in the unit cell = 3
Formula of the compound = `X_(7//8)Y_(3)=X_(7)Y_(24)`
(ii)Number of X atoms in the unit cell = 7/8
Number Z atoms in the unit cell = 1/8
Number of Y atoms in the unit cell = 3
Formula of the compound `=X_(7//8)Y_(3)Z_(1//8) or X_(7)Y_(24)Z`.