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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 X3Y2Z12
In 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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