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Question: The packing fraction of the element that crystallizes in simple cubic arrangement is -...

The packing fraction of the element that crystallizes in simple cubic arrangement is -

A

π4\frac{\pi}{4}

B

π6\frac{\pi}{6}

C

π3\frac{\pi}{3}

D

π2\frac{\pi}{2}

Answer

π6\frac{\pi}{6}

Explanation

Solution

P.F. = 43πr3×1a3\frac{\frac{4}{3}\pi r^{3} \times 1}{a^{3}}

= 43πr3(2r)3\frac{\frac{4}{3}\pi r^{3}}{(2r)^{3}} = π6\frac{\pi}{6}