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Q.
At what temperature will the oxygen molecules have the same rms as $H_2$ at $300\, K$?
Kinetic Theory
Solution:
$V _{rms }=\sqrt{\frac{3 RT }{ M }}$
$T \propto M \left(\therefore v _{ ms }\right.$ and $R$ are constant $)$
$\frac{ T _{ O _{2}}}{ T _{ H _{2}}}=\frac{ M _{ O _{2}}}{ M _{ H _{2}}}=\frac{32}{2}=16$
$T _{ O _{2}}=16 \times 300=4800\, K$