Which has a minimum percent volume occupied by the spheres?

Simple cubic

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Body-centred cubic

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Hexagonal closed packed

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Cubic closed packed

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Solution

The correct option is C Simple cubic
The edge length or side of the cube, $a$ and the radius of each particle, $r$ are related as $a = 2 r$ .
The volume of the cubic unit cell $= a^{3} = (2 r)^{3} = 8 r^{3}$
A simple cubic unit cell contains only $1$ atom.
The volume of the occupied space $= \frac{4 π r^{3}}{3}$
$∴ Packing efficiency$ $= \frac{Volume of one atom}{Volume of cubic unit cell} \times 100 = 52.4 %$

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