Question

The fraction of total volume occupied by the atoms present in a simple cube is

• A. $\frac{\pi}{6}$
• B. $\frac{\pi}{3\sqrt{2}}$
• C. $\frac{\pi}{4\sqrt{2}}$
• D. $\frac{\pi}{4}$

Answer 1

Answer: (A)

$\frac{\pi}{6}$

Answer 2

The correct answer is A) $\frac{\pi}{6}$

For simple cube, $\, \, \, \, \, \, \, \, \, Radius(r)=\frac{a}{2}\, \, \, \, \, \, \, \, \, \, \, \, \,$[a = edge length)

The volume of the atom =$\frac{4}{3}\pi \Bigg(\frac{a}{2}\Bigg)^3$ Packing fraction$=\frac{Z\times\frac{1}{4}\pi r^3}{a^3}$

The volume of the sphere (atoms) in a unit cell. For simple cubic, Z = 1 atom Packing fraction $=\frac{\frac{4}{3}\pi\Bigg(\frac{a}{2}\Bigg)^3}{a^3}=\frac{\pi}{6}$

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