Consider the bcc unit cell of the solids 1 and 2 with the position of atoms as shown below. The radius of atom B is twice that of atom A. The unit cell edge length is 50% more in solid 2 than in 1.What is the approximate packing efficiency in solid 2?

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answer is 90.

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Detailed Solution

Volume occupied by atoms in solid 2
$= \frac{4}{3} π r^{3} + \frac{4}{3} π {(2 r)}^{3} = 12 π r^{3}$
Relationship between edge length (a) and edge of atom(r)
$= 6 r = \sqrt{3} a \Rightarrow a = \frac{6 r}{\sqrt{3}} a = 2 \sqrt{3} r$
$P . E = \frac{4}{3} π r^{3} + \frac{4}{3} π {(2 r)}^{3}$
Packing efficiency= $= \frac{12 π r^{3}}{{(\frac{6 r}{\sqrt{3}})}^{3}} \times 100 = 90 %$

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