Fraction of total volume occupied by atoms in a simple cube... | CHEMISTRY - CLOSE-PACKED STRUCTURES | SolveeIt

Question

Fraction of total volume occupied by atoms in a simple cube is

$\frac{\mathbf{\pi}}{\mathbf{2}}$

$\frac{\sqrt{3}\pi}{8}$

$\frac{\sqrt{2}\pi}{6}$

$\frac{\pi}{6}$

Answer

$\frac{\pi}{6}$

Explanation

Solution

In a simple cubic system, number of atoms a = 2r

$\therefore$ Packing fraction

$= \frac{\text{Volume occupied by one atom}}{\text{Volume of unit cell}} = \frac{\frac{4}{3}\pi r^{3}}{a^{3}} = \frac{\frac{4}{3}\pi r^{3}}{(2r)^{3}} = \frac{\pi}{6}$

Question: Fraction of total volume occupied by atoms in a simple cube is...

Solution