What relationship must exist between a certain molecule's average speed, v, in a planetary atmosphere and the escape velocity, V_esc, from the planet's surface for this particular molecular species to be retained by the planet? A)v should not exceed V_esc. B)v must be less than about 6 × V_esc. C)v must be less than about 1/6 V_esc. D)v should not exceed 2 × V_esc.

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Quizplus · Accepted Answer

For a molecule to be retained by a planet, its average speed must be significantly less than the planet's escape velocity. The rule of thumb is that the molecule's average speed should be less than about 1/6 of the escape velocity. This ensures that only a small fraction of the molecules in the high-speed tail of the Maxwell-Boltzmann distribution have enough speed to escape the planet's gravitational pull.

What Relationship Must Exist Between a Certain Molecule's Average Speed