Question

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

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

Answer 1

The correct option is A $\frac{\pi }{6}$

$P.F=\frac{Vol.occupiedbytheatominaunitcell}{Vol.ofunitcell}=\frac{\frac{4}{3}\pi r^3}{a^3}Forsimpleunita=2r=\frac{\frac{4}{3}\pi r^3}{8r^3}=\frac{4\pi }{24r}=\frac{\pi }{6}$