Q. The root mean square speed of hydrogen molecules at 300 $K$ is $1930\ m/s.$ Then the root mean square speed of oxygen molecules at $900\ K$ will be
A) $1930\sqrt{3}\ m/s$
B) $836\ m/s$
C) $63\ m/s$
D) $\frac{1930}{\sqrt{3}}m/s$
Explanation
(b) $V_{rms} = \sqrt{\frac{3RT}{M}} \Rightarrow \frac{\left( V_{rms} \right)_{O_{2}}}{\left( V_{rms} \right)_{H_{2}}} = \sqrt{\frac{T_{O_{2}}}{T_{H_{2}}} \times \frac{M_{H_{2}}}{M_{O_{2}}}}$
$\Rightarrow \frac{\left( V_{rms} \right)_{O_{2}}}{\left( V_{rms} \right)_{H_{2}}} = \sqrt{\frac{900}{300} \times \frac{2}{32}} = \frac{\sqrt{3}}{4}$
$\Rightarrow \left( v_{rms} \right)_{O_{2}} = 836m/s$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.