Q: Two vessels having equal volume contain molecular hydrogen at one atmosphere, and helium at two atmospheres respectively. What is the ratio of rms speeds of hydrogen molecule to that of helium molecule, if both the samples are at the same temperature

Sol: According to kinetic theory of gases,

$\large v_{rms} = \sqrt{\frac{3 R T}{M}}$

$\large \frac{v_H}{v_{He}} = \sqrt{\frac{M_{He}}{M_H}}$

$\large v_H = \sqrt{\frac{4}{2}} v_{He} = \sqrt{2} v_{He} $