Q. The ratio of average speed of an oxygen molecule to the rms speed of a nitrogen molecule at the same temperature is
A) $\left( \frac{3\pi}{7} \right)^{1/2}$
B) $\left( \frac{7}{3\pi} \right)^{1/2}$
C) $\left( \frac{3}{7\pi} \right)^{1/2}$
D) $\left( \frac{7\pi}{3} \right)^{1/2}$
Explanation
(b)
$u_{av} = \sqrt{\frac{8RT}{\pi M}}$ So, $u_{av(O_{2})} = \sqrt{\frac{8RT}{\pi \times 16}}$
$u_{rms} = \sqrt{\frac{3RT}{M}}$ so $u_{rms(N_{2})} = \sqrt{\frac{3RT}{14}}$
$\frac{\ u_{av(O_{2})}}{u_{rms(N_{2})}} = \sqrt{\frac{8 \times 14}{\pi \times 16 \times 3}} = \left( \sqrt{\frac{7}{3\pi}} \right)^{1/2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.