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{8 RT }{\pi M }} $
$v _{ H }=\sqrt{\frac{8 RT }{\pi 1}} $
$v _{ He }=\sqrt{\frac{8 RT }{4 \pi}}=\frac{1}{2} v _{ H }$
i.e.$v _{ H }=2 v _{ He }$