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Question

The silver metal crystallizes with a face-centred cubic lattice. The edge length of the unit cell is 4.08 oA. Calculate the percentage of empty space in the FCC structure?

A
52%
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B
74%
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C
26%
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D
31%
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Solution

The correct option is C 26%
For Face centered cubic (fcc) :
The atoms along the face diagonals are in contact with each other.
Here,
2×a=4ra=22×r
where, r is the radius of sphere.

Zeff for fcc=4
So,

The total volume occupied by sphere V=4×43×πr3
Volume of the cube=a3=(22r)3
Packing efficiency (P.F)=4×43×πr3(22r)3×100%P.F=π×10032%=74.174%

The percentage of empty space in the unit cell is,
% of Empty space =10074=26

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