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 ${\bar{\nu }}_H$ will be related to helium ${\bar{v}}_{He}$ as

• A. $\bar{\nu }H=\sqrt{2}\bar{\nu }He$
• B. $\bar{\nu }H=\bar{\nu }He$
• C. ${\bar{\nu }}_H$ $=2\bar{\nu }He$
• D. ${\bar{\nu }}_H={\nu }_{He}/2$

Answer 1

Answer: (C)

Average speed is given by:
$v_{\text{avg }}=\sqrt{\frac{8RT}{\pi M}}$
$v_H=\sqrt{\frac{8RT}{\pi 1}}$
$v_{He}=\sqrt{\frac{8RT}{4\pi }}=\frac{1}{2}{v}_H$
i.e.$v_H=2v_{He}$