Give the formulas for the following:
$(i)$ Average speed of molecules $(u_{av})$
$(ii)$ Most probable speed $(u_{mp})$
$(iii)$ Root mean square speed $(u_{rms})$

(N/A) The formulas for the speeds of gas molecules based on the kinetic molecular theory are as follows:
$(i)$ Average speed $(u_{av}) = \sqrt{\frac{8RT}{\pi M}}$
$(ii)$ Most probable speed $(u_{mp}) = \sqrt{\frac{2RT}{M}}$
$(iii)$ Root mean square speed $(u_{rms}) = \sqrt{\frac{3RT}{M}}$
Where $R$ is the universal gas constant,$T$ is the absolute temperature,and $M$ is the molar mass of the gas.