Verified Solution • 2025–26 Session moderate

QJEEM22Ph3cab: JEE Main 2022 Physics - Class 11 JEEM22Ph3cab Solution: The relation between root mean square speed (v rms ) and most…

The relation between root mean square speed (vrms) and most probable sped (vp) for the molar mass M of oxygen gas molecule at the temperature of 300 K will be :

Multiple Choice Options

  • A vrms=23vp{v_{rms}} = \sqrt {{2 \over 3}} {v_p}
  • B vrms=32vp{v_{rms}} = \sqrt {{3 \over 2}} {v_p}
  • C vrms=vp{v_{rms}} = {v_p}
  • D vrms=13vp{v_{rms}} = \sqrt {{1 \over 3}} {v_p}

Step-by-Step Verified Solution

vrms=3RTM{v_{rms}} = \sqrt {{{3RT} \over M}}

vp=2RTM{v_p} = \sqrt {{{2RT} \over M}}

⇒vrms=32vp\Rightarrow {v_{rms}} = \sqrt {{3 \over 2}} {v_p}

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