(a) If it has enough kinetic energy, a molecule at the surface of the Earth can “escape the Earth’s gravitation,” in the sense that it can continue to move away from the Earth forever, as discussed in Section 13.7. Using the principle of conservation of energy, show that the minimum kinetic energy needed for “escape” is mgRE, where m is the mass of the molecule, g is the free-fall acceleration at the surface, and RE is the radius of the Earth.
(b) Calculate the temperature for which the minimum escape kinetic energy is ten times the average kinetic energy of an oxygen molecule.