The fraction of total volume occupied by the atoms in a simple cubic is (a) dfracπ4√(2) (b) (π)/(6) (c) (π)/(4

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Q.The fraction of total volume occupied by the atoms in a simple cubic is

(a)

\dfrac{\pi}{4\sqrt{2}}

(b)

\dfrac{\pi}{6}

(c)

\dfrac{\pi}{4}

(d)

\dfrac{\pi}{3\sqrt{2}}

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Step 1. For a simple cubic cell, $a = 2r$ , so the sphere volume is $\tfrac{4}{3}\pi r^3 = \tfrac{4}{3}\pi(a/2)^3 = \tfrac{\pi a^3}{6}$ .

Step 2. With exactly 1 sphere per simple-cubic cell, the total occupied volume is $\tfrac{\pi a^3}{6}$ , and the cell's own volume is $a^3$ . …

Q.The fraction of total volume occupied by the atoms in a simple cubic is