The ratio of root mean square velocity of hydrogen at $50 \, K$ to that of nitrogen at $500 \, K$ is closest to

Helium diffuses four times faster than which of the following?

If the $RMS$ speed of nitrogen at a certain temperature is $3000 \ ms^{-1}$,the approximate kinetic energy of one mole of nitrogen at that temperature in $kJ$ is (assume nitrogen as ideal gas)

Match the following (where $U_{rms}$ = root mean square speed,$U_{av}$ = average speed,$U_{mp}$ = most probable speed)

List-$I$	List-$II$
$(a)$ $U_{rms} / U_{av}$	$(i)$ $1.22$
$(b)$ $U_{av} / U_{mp}$	$(ii)$ $1.13$
$(c)$ $U_{rms} / U_{mp}$	$(iii)$ $1.08$

At what temperature will the root mean square speed of ozone $(O_3)$ be equal to the root mean square speed of oxygen $(O_2)$ at $27\,^oC$?

At $T(K)$,the root mean square (rms) velocity of argon (molar mass $40 \ g \ mol^{-1}$) is $20 \ ms^{-1}$. The average kinetic energy of the same gas at $T(K)$ (in $J \ mol^{-1}$) is: