Q.Which of the following gases will have least rms speed at a given temperature?

Definition and formula. The root mean square speed, $v_{rms}=\sqrt{\overline{v^2}}$, is the square root of the average of the squared speeds of every molecule in a gas sample. From the kinetic-theory temperature result $kT=\tfrac13m\overline{v^2}$,

where $M$ is the molar mass and $R$ the universal gas constant.

Dependence on temperature and mass. $v_{rms}\propto\sqrt T$ and $v_{rms}\propto1/\sqrt M$: heating a gas always raises its $v_{rms}$, and at any fixed temperature, lighter molecules (hydrogen, helium) always have a higher $v_{rms}$ than heavier ones (oxygen, nitrogen, carbon dioxide). …