Question

Two vessles having equal volume contain molecular hydrogen at one atmosphere and helium at two atmosphere respectively. If both samples are at the same temperature the r.m.s velocity of hydrogen molecules is

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

Answer 1

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

Given $V_{RMS}=\sqrt{\frac{3RT}{M}}$

i.e. Ratio of RMS velocities $=\sqrt{\frac{T{M}_{helium}}{T{M}_{hydrogen}}}$

Both the temperatures are equal.

Ratio of RMS velocities = $\sqrt{\frac{4}{1}}=2$

Hence RMS velocity of hydrogen would be twice as much as the RMS for helium.