# Consider the bcc unit cells of the solids 1 and 2 with the position of atoms as shown below. The radius of atoms 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?Option 1)45%Option 2)75%Option 3)90%Option 4)65%

Answers (1)

length of body diagonal = $\sqrt{3}a=r+r+2(2r)$

= $\sqrt{3}a=6r$

= $a=2\sqrt{3}r$

$Packing\; fraction=\frac{volume\; of \; particles}{volume\;of\; unit\; cell}$

$=\frac{\frac{4}{3}\pi r^{3}+\frac{4}{3}\pi (2r)^{3}}{a^{3}}$

$=\frac{\frac{4}{3}\pi r^{3}+\frac{4}{3}\pi (2r)^{3}}{\left (2\sqrt{3}r \right )^{3}}$

= 91.27%=90%

Option 1)

45%

Option 2)

75%

Option 3)

90%

Option 4)

65%

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