Q10 of 50 Page 1

Calculate the packing efficiency of a metal crystal for a simple cubic lattice.


Diagram of a simple cubic lattice.


As we can see, in a simple cubic lattice the atoms are located only on the corners of the cube. The particles touch each other along the edge.


Let the edge length or side of the cube be 'a' and the radius of each particles, ‘r’. They are related as:-


a=2r


We know, volume of the cubic unit cell =


a3 = (2r)3 =8r3 . [As a = 2r]


Also we know, that a simple cubic unit cell contains only 1 atom so the volume of the occupied =


∴ Packing efficiency =


= = = 52.4%


So, the packing efficiency of a metal crystal for a simple cubic lattice is 52.4%


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