Answer
The temperature ratio is $=0.011$ at which two gas will produce the same root mean square velocity.
Work Step by Step
Let the temperature of $He(g)$ is $=T_1$
And the temperature of $UF_6(g)$ is $=T_2$
So the root mean square velocity of $He(g)$ is $=\sqrt {3RT_1/4×10^{-3})}$
And root mean square velocity of $UF_6(g)$ is $=\sqrt {(3RT_2/352.02×10^{-3})}$
Therefore,
$\sqrt {(3RT_1/4×10^{-3})}=\sqrt {(3RT_2/352.02×10^{-3})}$
or, $T_1/T_2=4/352.02=0.011$
So the temperature ratio is $=0.011$ at which two gas will produce the same root mean square velocity.
