Question

Two vessels $A$ and $B$ of equal volumes are at two atmosphere and four atmosphere pressure respectively. If $A$ has hydrogen and $B$ has helium and at same temperature, then the rms speed of the hydrogen molecules is

• A. equal to that of the helium molecules
• B. twice that of the helium molecules
• C. half that of the helium molecules
• D. $\sqrt{2}$ times that of the helium molecules

Answer 1

The correct option is D $\sqrt{2}$ times that of the helium molecules

Root-mean-square of the velocity of a gas is $V_{rms}=\sqrt{\frac{3RT}{M}}$
Where $M$ is molecular weight of the gas

Here,
$\frac{(V_{rms}{)}_{H_2}}{(V_{rms}{)}_{He}}=\sqrt{\frac{M_{H_e}}{M_{H_2}}}=\sqrt{\frac{4}{2}}=\sqrt{2}$