Examples of velocities of atoms and molecules in a gas

• What is the average velocity of a particle of air?
  air is mostly Nitrogen gas molecules

  atomic mass of Nitrogen molecule = 28 mH = 4.68 x 10^-26 kg

  temperature of air = 20 ^oC = 293 ^oK

  v = (3 k T / m)^1/2 --> v = 509 m/s

• Why does Earth have an atmosphere?
  temperature is related to the average particle velocity but, in practice, there is a distribution of particle velocities so, in practice there are particles 3x, 4x, 5x, 6x, ... faster than the average velocity
  

  How fast must an air particle go to escape the Earth's gravity? (escape velocity for Earth = 11.2 km/s)

  Say the fastest Nitrogen molecules travel at (509) 6 = 3050 m/s = 3.1 km/s

  Therefore, Nitrogen molecules cannot escape the Earth (WHEW!)

  But, Hydrogen is 28x lighter than Nitrogen so they move at 16 km/s, which is faster than the escape velocity --> Hydrogen will escape into space

  Escape velocity for Moon is 1.4 km/s, so Nitrogen molecules can escape --> The Moon has no atmosphere