QJEEM16Ch56e0: JEE Main 2016 Chemistry - Class 11 JEEM16Ch56e0 Solution: Initially, the root mean square (rms) velocity of N 2 molecules …

Root mean square (rms) velocity of N₂ molecule (u) = $\sqrt {{{3RT} \over M}}$ .

For N₂ molecule, molecular mass, M = 28. Therefore,

$u = \sqrt {{{3RT} \over {28}}}$ ..... (1)

When the temperature becomes doubled, that is, 2T. Let the new root mean square (rms) velocity of N-atom be u'. For N-atom, the molecular mass, M = 14. Therefore,

$u' = \sqrt {{{3RT} \over {14}}}$ ....... (2)

On dividing Eq. (1) by Eq. (2), we get

${u \over {u'}} = \sqrt {{1 \over 4}}$

$= {1 \over 2} \Rightarrow u' = 2u$