The silver metal crystallizes with a face-centred cubic lattice. The edge length of the unit cell is 4.08oA. 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 C26% For Face centered cubic (fcc) :
The atoms along the face diagonals are in contact with each other.
Here, √2×a=4ra=2√2×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=(2√2r)3 Packing efficiency (P.F)=4×43×πr3(2√2r)3×100%P.F=π×1003√2%=74.1≈74%
The percentage of empty space in the unit cell is, % of Empty space =100−74=26