Nitrogen gas is at $300^{\circ} C$ temperature. The temperature (in $K$) at which the $rms$ speed of a $H _{2}$, molecule would be equal to the $rms$ speed of a nitrogen molecule, is........
(Molar mass of $N _{2}$ gas $28\, g$ )
A$45$
B$41$
C$38$
D$49$
JEE MAIN 2020, Medium
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B$41$
b $V _{ rms }=\sqrt{\frac{3 RT }{ M }}$
$V _{ N _{2}}= V _{ H _{2}}$
$\sqrt{\frac{3 RT _{ N _{2}}}{ M _{ N _{2}}}}=\sqrt{\frac{3 RT _{ H _{2}}}{ M _{ H _{2}}}}$
$\frac{573}{28}=\frac{ T _{ H _{2}}}{2} \Rightarrow T _{ H _{2}}=40.928$
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