The ability of a planet to retain particular gases in an atmosphere depends on the temperature that

Question:

The ability of a planet to retain particular gases in an atmosphere depends on the temperature that its atmosphere has (or would have) and the escape velocity for the planet. In general, if the average speed of a particular gas molecule exceeds 1/6 of the escape velocity, that gas will disappear from the atmosphere in about 108 years.

(a) Graph the average speed of H₂O, CO₂, O₂, CH₄, H₂, and He from 50 K to 1000 K. On the same graph show the points representing 1/6 of the escape velocity versus average temperature of the atmosphere for the planets in Table 13-5 below.

(b) Show that the escape speed v from a planet is given by

(c) Which of the six gases plotted probably would and would not currently be found in the atmospheres of the solar system bodies in the table? Explain each answer briefly.