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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=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

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