The relation between root mean square speed ( v _ rms ) and most … - Vidyadip

MCQ

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
$v _{ rms }=\sqrt{\frac{2}{3}} v _{ p }$
✓
$v _{ rms }=\sqrt{\frac{3}{2}} v _{ p }$
C
$v _{ rms }= v _{ p }$
D
$v _{ rms }=\sqrt{\frac{1}{3}} v _{ p }$

✓

Answer

Correct option: 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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