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Question

Calculate the percentage of space occupied by the voids in body centred cubic unit cell.

A
54%
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B
32%
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C
68%
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D
26%
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Solution

The correct option is B 32%
For body centred cubic arrangement, Zeff=2


4r=3 a
where,
r is radius of atom
a is edge length of cube
Thus, a=4 r3
Volume of cell =a3
Volume of cell =(4 r3)3
Packing efficiency =Total volume occupied by sphereVolume of unit cell×100
Packing efficiency =Z×43πr3a3×100
=2×43πr3(4r3)3×100=3 π×1008=68%
Percentage of empty space =10068=32%

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