The temperature at which the $r.m.s.$ velocity of hydrogen molecules is $4.5$ times that of an oxygen molecule at $47^{\circ} C$ is (Molecular weight of hydrogen and oxygen molecules are $2$ and $32$ respectively). (in $^{\circ} C$)

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

The temperature of an ideal gas is increased from $200 \ K$ to $800 \ K$. If the r.m.s. speed of the gas at $200 \ K$ is $v_0$,then the r.m.s. speed of the gas at $800 \ K$ will be:

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.

Two gases $A$ and $B$ are contained in two separate, but otherwise identical containers. Gas $A$ consists of monatomic molecules, each with atomic mass of $4 \ u$, whereas Gas $B$ consists of rigid diatomic molecules, each with atomic mass of $20 \ u$. If gas $A$ is kept at $27^{\circ} C$, at what temperature should gas $B$ be kept so that both have the same rms speed (in $^{\circ} C$)?

Consider a mixture of gas molecules of types $A, B$,and $C$ having masses $m_{A} < m_{B} < m_{C}$. The ratio of their root mean square speeds at normal temperature and pressure is: