Percentage of free space in a body centred cubic unit cell is

30%

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32%

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34%

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28%

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Solution

The correct option is B 32%
Packing fraction $= \frac{v o l u m e o c c u p i e d b y a t o m s i n a u n i t c e l l}{v o l u m e o f t h e u n i t c e l l}$
For bcc,
Packing fraction $= \frac{2 \times \frac{4}{3} π r^{3}}{{(\frac{4 r}{\sqrt{3}})}^{3}} = \frac{\sqrt{3} π}{8} = 0.68$
Volume occupied $= 68 %$
Volume vacant $= 100 - 68 = 32 %$

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