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
Correct Answer: B
Solution :
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 \[{{\overline{v}}_{He}}=\frac{1}{2}{{\overline{v}}_{H}}\]
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