Light gases like $H_2$ and $He$ are found in negligible amounts in the atmosphere. Why?

Uranium has two isotopes of masses $235$ and $238$ units. If both of them are present in uranium hexafluoride gas, find the percentage ratio of the difference in rms velocities of the two isotopes to the rms velocity of the heavier isotope.

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:

The density of hydrogen gas at standard atmospheric pressure $(P = 1.01 \times 10^{5} \ Pa)$ is $0.09 \ kg/m^{3}$. Find the root mean square velocity $(v_{rms})$ and the average kinetic energy of $1 \ mole$ of the gas.

If $c$ is the $rms$ speed of molecules in a gas and $v$ is the speed of sound waves in the gas,show that $\frac{c}{v}$ is constant and independent of temperature for all diatomic gases.

The temperature of an ideal gas is increased from $120 \ K$ to $480 \ K.$ If at $120 \ K,$ the root mean square velocity of the gas molecules is $v,$ at $480 \ K$ it becomes