Q. If mass of He is 4 times that of hydrogen, then mean velocity of He is

A) 2 times of H-mean value
B) $\frac{1}{2}$ times of H-mean value
C) 4 times of H-mean value
D) Same as H-mean value
Explanation

(b) Average speed or mean speed of gas molecules
$\overline{v} = \sqrt{\frac{8RT}{\pi M}}\ \ \ \ \ \ \ or\ \ \ \ \ \ \ \overline{v} \propto \frac{1}{\sqrt{M}}$
or $\frac{{\overline{v}}_{H}}{{\overline{v}}_{He}} = \sqrt{\frac{M_{He}}{M_{H}}}$
Here, $M_{He} = 4\ M_{H}$
$\therefore\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \frac{{\overline{v}}_{H}}{{\overline{v}}_{He}} = \sqrt{\frac{4}{1}} = 2\ \ \ \ \ \ \ \ or\ \ \ \ \ \ \ \ {\overline{v}}_{He} = \frac{1}{2}{\overline{v}}_{H}$

Dr. Abubacker
Reviewed by Dr. Abubacker

Physics Educator & NEET/JEE Specialist

Ph.D. in Physics with 19+ years of teaching experience.

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