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Question:

The root mean square velocity of hydrogen molecule at 27°C is υH and that of oxygen at 402°C is υO, then

9vO=134vH

vO>vH

4vO=9vH

8vO=3vH

Solution:

The root mean square velocity of hydrogen molecule=vH=√(3RTH/MH)
The root mean square velocity of oxygen molecule=vO=√(3RTO/MO)
Hence,vO/vH=√(TO/TH * MH/MO)=√((402+273)(2)/(27+273)(32))=3/8
⇒8vO=3vH