# 1.10   Calculate the efficiency of packing in case of a metal crystal for               (i) simple cubic

(i) Simple cubic :-  In a simple cubic lattice the atoms are located only on the corners of the cube.

Thus, the side of the cube ‘a’, and the radius of each particle, r are related as:

a = 2r

Volume of cubic unit cell = $(2r)^3$ = $8r^3$

And Volume of 1 atom :

$=\frac{4}{3}\Pi r^3$

$Packing\ efficiency = \frac{Volume\ of\ one\ atom}{Volume\ of\ cubic\ unit\ cell}\times100 \%$

$= \frac{\frac{4}{3}\Pi r^3}{8\Pi r^3}\times100 \% = \frac{\Pi }{6}\times100\%$

$= 52.4\%$

Thus packing efficiency of simple cubic is $52.4\%$

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