A crystal is made up of particals `X`, `Y`, and `Z`. `X` froms `fcc` packing. `Y` occupies all octahedral voids of `X` and `Z` occupies all tetrahedral voids of `X`. If all the particles along one body diagonal are removed. Then the fromula of the crystal would be

Options

A. `XYZ_(2)`
B. `X_(2)YZ_(2)`
C. `X_(8)Y_(4)Z_(5)`
D. `X_(5)Y_(4)Z_(8)`

Answer

4

Explanation

When all particle along one body diagonal are removed, these 2X particles from corner are removed, one Y particle removed & 2Z particle removed.
Hence new arrangement , X particle `=(1)/(8)xx6+(1)/(2)xx6=(15)/(4),Y` particles `=3,Z` particle`=6`
Hence formula `=X_(15//4)Y_(3)Z_(6)=X_(5//4)YZ_(2)=X_(5)Y_(4)Z_(8)`