Atom X occupies the F.C.C lattice sites as well as alternate tetrahedral voids of the same lattice. The packing efficiency in percentage of the resultant solid is closed to Y, the value of $\frac{Y}{17}$ is____________

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answer is 2.

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Detailed Solution

X = corner + F.C.C + alternate tetrahedral voids $= 8 \times \frac{1}{8} + 6 \times \frac{1}{2} + 8 \times \frac{1}{2}$

$r_{+} + r_{-} = \frac{\sqrt{3} a}{4}$

$r_{+} = \frac{\sqrt{3} a}{8}$

$a = \frac{8 r_{x}}{\sqrt{3}} = 8$

Potential energy $= \frac{8 \times \frac{4}{3} π r^{3}}{a^{3}} \times 100 = \frac{8 \times \frac{4}{3} \times π r^{3}}{{(\frac{8 r^{3}}{\sqrt{3}})}^{3}} \times 100 = 34$

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