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Question

Chemistry Question on States of matter

Root mean square velocity of a gas molecule is proportional to

A

m1/2m^{1/2}

B

m0m^0

C

m−1/2m^{-1/2}

D

m

Answer

m−1/2m^{-1/2}

Explanation

Solution

Root mean square speed is given by the expression
         Urms=3RTM                 [becuseM=mN]\, \, \, \, \, \, \, \, \, U_{rms}=\sqrt{\frac{3RT}{M}}\, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, [becuse M=mN]
         Urms1m    ⇒Urms∝(m)−1/2\, \, \, \, \, \, \, \, \, U_{rms}\sqrt{\frac{1}{m}}\, \, \, \, \Rightarrow U_{rms} \propto (m)^{-1/2}