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

D

Explanation

For fcc, number of `X` atoms `= 4//"unit cell"`
Number of `TVs = 8Z`
Number of `OVs = 4Y`
Number of atoms removed along one body diagonal `= 2X ("corner")` and `2Z("TVs")` are `1Y` (OV at body centre)
`:.` Number of `X` atoms left `= 4 - (2 xx 1/8) = 15/4`
Number of `Y` atoms left `= 4 - (1 xx 1) = 3`
Number of `Z` atoms left `= 8 - (2 xx 1) = 6`
The simplest formula `= X_(15/4)Y_(3)Z_(6) rArr X_(15)Y_(12)Z_(24)`
`rArr X_(5)Y_(4)Z_(8)`