[UPSC CSE 2013] Statistical Physics (Q290, 10M)

The coefficient of viscosity of helium at 27^\circ\mathrm{C} is 2 \times 10^{-5}\ \mathrm{kg\,m^{-1}\,s^{-1}}. Calculate \begin{qroman}\item the average speed and \item the diameter of a helium molecule,\end{qroman} if it is assumed that the gas obeys Maxwell-Boltzmann distribution. Given Boltzmann constant k_{\mathrm B} = 1.38 \times 10^{-23}\ \mathrm{J\,K^{-1}} and mass of helium atom = 6.67 \times 10^{-27}\ \mathrm{kg}.