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Question

# Atoms X,Y,Z crystallize in a cubic lattice where atom X occupies the corners of the cube and atom Y occupies the end-centred positions and Z occupies the body centre positions What will be the simplest formula of the unit cell if one of the face diagonals containing end centre atom is removed?

A
X3Y2Z4
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B
X3Z4
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C
XY2Z3
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D
None of the above.
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Solution

## The correct option is A X3Y2Z4In a cubical unit cell: Contribution for a corner particle is =18 Contribution for a end particle is =12 Contribution for a body centre particle is =1 When one of the face diagonals containing end centre atom is removed: 1 end centred atom is removed. 2 corner atoms are removed. For X: Since 2 corner atoms are removed , Total X atoms in a unit cell=(6×18)=34 For Y: Since 1 end centred atom is removed , Total Y atoms in a unit cell=(1×12)=12 For Z : No atoms removed. Total Z atoms in a unit cell=1 Formula for the compound: X34Y12Z1Simplest formula : X3Y2Z4

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