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Question

# In a cubic lattice, atom X occupies the corners of the cube and atom Y occupies the end-centred positions and Z occupies the edge centres of the cube. What will be the simplest formula of the unit cell if one of the face diagonals containing end centre atom is removed?

A
X5Y6Z3
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B
X12Y4Z3
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C
X5Y5Z6
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D
X3Y2Z12
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Solution

## The correct option is D X3Y2Z12In a cubical unit cell: Contribution for a corner particle is =18 Contribution for a end particle is =12 Contribution for a edge centre particle is =14 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=(12×14)=3 Formula for the compound: X34Y12Z3Simplest formula : X3Y2Z12

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