Question

Calculate packing fraction from the following figure to two decimal places. Multiply it by 100 and enter the value.

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Answer 1

We know that packing fraction is the amount of space occupied in a unit cell. So, here the unit cell will be the square and the circle inside occupies some space.

$P.F=\frac{Areaoccupiedbycircle}{Areaofsquare}$

= $\frac{\left(pi{}^{\ast }{r}^2\right)}{a^2}$

Notice that a = 2r

So, P.F = $\frac{\left(pi{}^{\ast }{r}^2\right)}{(2r{)}^2}$

= $\frac{\left(pi{}^{\ast }{r}^2\right)}{4r^2}$

= $\frac{pi}{4}$ = 0.78

0.78 ${}^{\ast }$ 100 = 78