Calculate the packing sufficiency of a metal crystal for simple lattice.
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The particles touch each other along the edge.Thus the edge length or side of the cube 'a' and the radius of each particles, r are related as :
a=2ra=2r
The volume of the cubic unit cell =a3=(2r)3=8r3a3=(2r)3=8r3
Since a simple cubic unit cell contains only 1 atom.The volume of the occupied space =4343πr3πr3
Packing efficiency =Volume of one atomVolume of cubic unit cellVolume of one atomVolume of cubic unit cell×100×100
43πr3×1008r3⇒43πr3×1008r3
π6⇒π6×100×100
52.4%
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