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Question

Predict the general formula for the given unit cell.

A
XYWZ
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B
X2Y2W2Z
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C
X3Y3W2Z
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D
X3Y2W2Z
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Solution

The correct option is D X3Y2W2Z
Contribution of a corner particle is =18
Contribution of a face centre particle is =12
Contribution of a edge centre particle is =14
Contribution of a body centre particle is =1

In the given unit cell,
Atom Z is present only at the body centre
Thus,
No. of Z atom per unit cell =1

Atom X occupies 8 corners of the cube and 4 face centres of the cube.

No. of X atoms per unit cell =18×8+12×4=3
Atom Y occupies 8 edge centres of the unit cell.

No. of Y atoms per unit cell =14×8=2

Atom W occupies 2 face centre and 4 edge centres.

No. of W atoms per unit cell =14×4+12×2=2

Hence, the formula of unit cell is
X3Y2W2Z

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