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Consider a cube 1 of body-centered cubic unit cell of edge Length ·a·. Now atom at the body center can viewed to be lying on the corner of another cube 2. Find the volume common to cube 1 and cube 2.

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$\frac{a^{3}}{27}$

$\frac{a^{3}}{64}$

$\frac{a^{3}}{2 \sqrt{2}}$

$\frac{a^{3}}{8}$

answer is D.

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Detailed Solution

Common volume is $\frac{1}{8} th$ the total volume.

Given edge length of cube $= a$

The common volume is a cube of edge length $(a / 2)$

So, common volume $= {(\frac{a}{2})}^{3} = \frac{a^{3}}{8}$

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