Physics - Heat & Thermo Question with Solution | TestHub

The RMS velocity of a gas is given by, $v_{RMS}=\sqrt{\frac{3RT}{M}}$

When ${\mathrm{O}}_2$ dissociates into $\mathrm{O}$ its molecular mass becomes $\frac{M}{2}$. Therefore,

Ratio of RMS speed, $\frac{v_1}{v_2}=\sqrt{\frac{T_1}{T_2}\times \frac{M_2}{M_1}}$$\Rightarrow \frac{v_1}{v_2}=\sqrt{\frac{T}{2T}\times \frac{M/2}{M}}$$\Rightarrow \frac{v_2}{v_1}=2$