A CCP of n spheres of radius r, n spheres of radius 0.414 r and 2n spheres of radius 0.225r are introduced in the octahedral and tetrahedral void respectively. Therefore, packing fraction of the lattice

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0.81

0.79

0.68

0.74

answer is B.

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Detailed Solution

$PF = \frac{4 \times \frac{4}{3} π r^{3} + 4 \times \frac{4}{3} π \times (0.414 r)^{3} + 8 \times \frac{4}{3} π \times (0.225 r)^{3}}{(2 \sqrt{2} r)^{3}}$

$PF = \frac{π}{3 \sqrt{2}} [1 + (0.414)^{3} + 2 \times (0.225)^{3}$

$= \frac{π}{3 \sqrt{2}} (1 + 0.070958 + 0.022781) or P.F = 0.80961 .$

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