On any planet,the presence of an atmosphere implies ($C_{rms}$ = root mean square velocity of molecules and $V_e$ = escape velocity):

Two molecules of a gas have speeds of $9 \times 10^{6} \ m/s$ and $1 \times 10^{6} \ m/s$ respectively. What is the root mean square speed of these molecules?

In a closed container,the same number of hydrogen $(H_2)$ and carbon dioxide $(CO_2)$ molecules are kept. If a small hole is made in the container,which gas will effuse out faster?

In two vessels of the same volume,atomic hydrogen and helium at pressures of $1\, atm$ and $2\, atm$ are filled,respectively. If the temperature of both samples is the same,then the average speed of hydrogen atoms $\langle C_H \rangle$ will be related to that of helium $\langle C_{He} \rangle$ as:

If the $rms$ speeds of helium and oxygen are equal,then the ratio of the temperatures of helium and oxygen is

The relation between root mean square speed $(v_{rms})$ and most probable speed $(v_{p})$ for the molar mass $M$ of oxygen gas molecule at the temperature of $300\, K$ is: