Question

In two vessels of same volume, atomic hydrogen and helium at pressure 1 atm and 2 atm are filled. If the temperature of both the samples is same, then average speed of hydrogen atom ${\overline{v}}_H$ will be related to helium ${\overline{v}}_{He}$ as :

• A. ${\overline{v}}_H$ = $\sqrt{2{\overline{v}}_{He}}$
• B. ${\overline{v}}_H$ = ${\overline{v}}_{He}$
• C. ${\overline{v}}_H$ = $2{\overline{v}}_{He}$
• D. $v_H=v_{He}/2$

Answer 1

The correct option is C ${\overline{v}}_H$ = $2{\overline{v}}_{He}$

Average speed is given by:

$v_{avg}=\sqrt{\frac{8RT}{\pi M}}$

$v_H=\sqrt{\frac{8RT}{\pi 1}}$

$v_{He}=\sqrt{\frac{8RT}{4\pi }}=\frac{1}{2}{v}_H$

i.e.

$v_H=2v_{He}$