A crystalline solid is made of X, Y and Z elements. Atoms of X form fcc packing , atoms of Y occupy octahedral voids while atoms of Z occupy tetrahedral voids. What will be the simplest formula of solid if atoms along one body diagonal are removed ?

Options

A. `X_(5)Y_(4)Z_(8)`
B. XYZ
C. `X_(8)Y_(4)Z_(5)`
D. `X_(2)YZ`

Answer

A

Explanation

Number of atoms of X (at packing site, i.e., at corners and face-centres)
`8xx(1)/(8)+6xx(1)/(2)=4`
Number of atoms of Y=4
Number of atoms of Z=8
Along one body diagonal there will be two X atoms , one Y atoms and two Z atoms are found and are removed.
Number of aotms of X will be `=4-(1)/(8)xx2=(15)/(4)`
Number of atoms of Y will be 4-1=3
Number of atoms of Z will be =8-2=6
`X:Y:Z`
`(15)/(4):3:6`
`5:4:8`
`therefore` Simplest formula will be `X_(5)Y_(4)Z_(8)`.