In a crystalline solid, atoms of X form fcc packing and atoms of Y occupy all octahedral voids. If all the atoms along one body diagonal are removed, what is the simplest formula of the crystalline lattice solid?

Answer

`X_(5)Y_(4)`

Explanation

Number of atoms of X in fcc packing `=8xx(1)/(8)+6xx(1)/(2)=4`
Number of atoms of Y at octahedral voids = 4
Along one body diagonal, there are two X atoms and one Y atom.
Number of effective atoms of X after removal = `4-2xx(1)/(8)=(15)/(4)`
Number of effetive atoms of Y after removal = 4-1=3
`X:Y=(15)/(4):3=5:4`
Simplest formula of the solid `=X_(5)Y_(4)`.