Compute the mean molecular speed \bar{v} in the light gas hydrogen (H _{2}) and the heavy gas radon (Rn), both at room temperature 293 K. (Use the longest-lived radon isotope, which has a mass of 222 u.) Compare the results.

Strategy The mean speed is given by Equation (9.17) as

\bar{v}=\frac{4}{\sqrt{2 \pi}} \sqrt{\frac{k T}{m}} (9.17)

With the temperatures the same, we need to use the appropriate molecular masses to complete the computation. The lighter mass (hydrogen) will have the higher average speed.