The relation between root mean square speed $\left( v _{ rms }\right)$ and most probable speed $\left( v _{ p }\right)$ for the molar mass $M$ of oxygen gas molecule at the temperature of $300\, K$ will be
A$v _{ rms }=\sqrt{\frac{2}{3}} v _{ p }$
B$v _{ rms }=\sqrt{\frac{3}{2}} v _{ p }$
C$v _{ rms }= v _{ p }$
D$v _{ rms }=\sqrt{\frac{1}{3}} v _{ p }$
JEE MAIN 2022, Medium
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B$v _{ rms }=\sqrt{\frac{3}{2}} v _{ p }$
b $v _{ rms }=\sqrt{\frac{3 RT }{ M }} \text { and } v _{ mp }=\sqrt{\frac{2 RT }{ M }}$
Thus $v _{ rms }=\sqrt{\frac{3}{2}} v _{ mp }$
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