Question

In two vessels of same volume atomic hydrogen and helium at pressure $1$ atm and $2$ atm are filled. If 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. ${\overline{v}}_H=\frac{{\overline{v}}_{He}}{2}$

Answer 1

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

The average speed is given by
$\overline{v}=\sqrt{\frac{8kT}{\pi M}}=1.6\sqrt{\frac{kT}{M}}$
here $(M{)}_{\text{atomic helium}}=1.0$ gm,
$(M{)}_{\text{atomic helium}}=4.0$ gm,
so, ${\overline{v}}_H$ atomic $=2{\overline{v}}_{He}$ atomic