High above the stratosphere, the atmospheric temperature may reach 1091 k. however, spacecraft and astronauts do not burn up because the concentration of molecules is very low and molecular impacts on spaceships or astronauts transfer very little energy. what is the root-mean-square velocity, in m/s, of ozone molecules at that temperature

The root-mean-square (rms) velocity of a gas is given by:

where T is the temperature of the gas, R is the gas constant, and M_m is the molar mass of the gas. The molar mass of ozone is

while the temperature of the gas in this problem is T=1091 K. By using these data and the previous equation, we can calculate the rms velocity of the molecules of ozone: