In a crystalline solid,atoms of X from fcc packing and the atoms of Y occupy all octahedral voids.If the atoms along one body diagnal are removed then the simplest formula of the crystalline solid will be:

Options

A. XY
B. `X_(4)Y_(3)`
C. `X_(5)Y_(4)`
D. `X_(4)Y_(5)`

Answer

C

Explanation

Number of atoms of X in fcc packing (at corners and face centres of cubic unit cell) `=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 atoms and one Y atom.
Number of effective atoms of X after removal
`=4-2xx(1)/(8)=(15)/(4)`
Number of effective atoms of Y after removal `=4-1=3`
`X:Y=(15)/(4):3`
`=5:4`
`therefore` SImplest formula `=X_(5)Y_(4)`