The rms speed of ${\mathrm{N}}_2$ molecules is $\mathrm{u}$. If the temperature is doubled and the nitrogen molecules dissociate into nitrogen atoms. Then what will be the new RMS speed?

RMS speed $=\sqrt{\frac{3\mathrm{RT}}{\mathrm{M}}}$, Inversely proportional to the molar mass and directly proportional to the temperature.

We can say that for the same mass of the gases rms speed is directly proportional to the number of moles of the gases.

$\frac{{\mathrm{u}}_1}{{\mathrm{u}}_2}=\sqrt{\frac{{\mathrm{n}}_1{\mathrm{T}}_1}{{\mathrm{n}}_2{\mathrm{T}}_2}}=\sqrt{\frac{\mathrm{n}\times \mathrm{T}}{2\mathrm{n}\times 2\mathrm{T}}}=\sqrt{\frac{1}{4}\mathrm{ }}=\frac{1}{2}$

$\therefore \mathrm{ }{\mathrm{u}}_2=2{\mathrm{u}}_1$

Therefore, in case the temperature is doubled and the nitrogen molecules dissociate into nitrogen atoms, the RMS speed becomes double.