Two bulbs A and B of equal capacity are filled with He and ${\mathrm{SO}}_2$ respectively at same temperature and pressure. Calculate ratio of ${\mu }_{rms}$ for He and ${\mathrm{SO}}_2$.

u_rms is the root-mean-square (rms) velocity, it is the square root of the mean square velocity. The rms velocity is directly proportional to the square root of temperature and inversely proportional to the square root of the molar mass.

Expression of u_rms is:

${\mu }_{rms}=\sqrt{\frac{3RT}{M}}$

In the given question, temperature is same and R is the universal gas constant. Therefore, the value of u_rms depends on the molar mass of the given gases.

$\frac{{\mu }_{rms\left(He\right)}}{{\mu }_{rms\left(S{O}_2\right)}}=\sqrt{\frac{M_{S{O}_2}}{M_{He}}}=\sqrt{\frac{64}{4}}=4$