lf it has enough kinetic energy, a molecule at the surface of the Earth can \"es

Question

lf 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 13.6. Using the principle of conservation of energy, show that the minimum kinetic energy needed for "escape" is where m0gRE, where m0 is the mass of the molecule, g is the free-fall acceleration at the surface, and Ht is the radius of the Earth. Calculate the temperature for which the minimum escape kinetic energy is ten times the average kinetic energy of an oxygen molecule.

Explanation / Answer

by applying conservation on Energy we have K.E lost = P.E gained hence 0.5mv^2=GMm/Re minimum energy required= GMm/Re=m*g*Re (since g=GM/Re*Re) for k.E = 3/2 kT = 0.1*m*g*Re k is boltzmann constant the rest is just mathematics

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