The rms speed of the molecules of a diatomic gas is v. When the temperature is doubled, the molecules dissociate into two atoms. The new root mean square speed of the atom is :

\(\sqrt{2}\) v v 2v 4v

2v

vrms = \(\sqrt{\frac{3RT}{M}}\) According to question : T will become 2T and M will become M/2. So, the value of vrms will increase by \(\sqrt{4}\) = 2 times i.e. new rms velocity will be 2v.