Calculate packing efficiency in simple cubic lattice

The length or side of the cube be ‘a’, and the radius of each particle be ‘r’. a=2r Volume of cube =a3 [latex](2r^{3}) = 8r^{3}[/latex] In the simple cube, each unit cell has only one sphere, The volume of sphere = [latex]\frac{4}{3}\pi r^{3}[/latex] Packing efficiency is given by [latex]Packing efficiency = \frac{Volume of a sphere}{Volume if a cube}*100[/latex] [latex]Packing efficiency = \frac{\frac{4}{3}\pi r^{3}}{8r^{3}}*100[/latex] = 52.4%

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