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Calculate the efficiency of packing in case of a metal crystals for : simple cubic

$\begin{array}{1 1}52.4\%\\62.4\%\\68\%\\54\%\end{array} $

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Packing efficiency in simple cubic laattice :
In a simple cubic lattice the atoms are located only on the corners of the cube
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 :
The volume of the cubic unit cell =$a^3=(2r)^3=8r^3$
Since a simple cubic unit cell contains only 1 atom.
The volume of the occupied space =$\large\frac{4}{3}$$\pi r^3$
$\therefore$ Packing efficiency =$\large\frac{\text{Volume of one atom}}{\text{Volume of cubic unit cell}}$$\times 100$
$\Rightarrow \large\frac{\Large\frac{4}{3}\pi r^3\normalsize \times 100}{8r^3}$
$\Rightarrow \large\frac{\pi}{6}$$\times 100$
$\Rightarrow 52.4\%$
answered Jul 30, 2014 by sreemathi.v
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