The r.m.s. speed of gas molecules is given by

$A$ container is divided into two equal halves by a diathermic partition. Two different ideal gases are filled in the left $(L)$ and right $(R)$ parts. The $rms$ speed of the molecules in the $L$ part is equal to the average speed of the molecules in the $R$ part. Find the ratio of the mass of a molecule in the $L$ part to the mass of a molecule in the $R$ part.

If the root mean square (rms) speed of nitrogen molecules at room temperature is $100 \ m \ s^{-1}$, then the rms speed of Helium molecules at the same temperature is

What will be the effect on the root mean square velocity of oxygen molecules if the temperature is doubled and oxygen molecule dissociates into atomic oxygen?

If the r.m.s. velocity of hydrogen molecules is $4$ times that of an oxygen molecule at $47^{\circ} C$,the temperature of the hydrogen molecules is (Molecular weight of Hydrogen and Oxygen are $2$ and $32$ respectively). (in $^{\circ} C$)

Nitrogen gas is at $300^{\circ} C$ temperature. The temperature (in $K$) at which the $rms$ speed of a $H_{2}$ molecule would be equal to the $rms$ speed of a nitrogen molecule is........ (Molar mass of $N_{2}$ gas = $28 \ g/mol$,Molar mass of $H_{2}$ gas = $2 \ g/mol$)