Imagine a planet whose diameter and mass are one half of those of the earth. The day's temperature of this planet reaches up to 800K. (Escape velocity on the surface of the earth is 11.2 km / sec

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Imagine a planet whose diameter and mass are one half of those of the earth. The day's temperature of this planet reaches up to 800K. (Escape velocity on the surface of the earth is $11.2 km / sec, k = 1.38 \times 1 0^{- 23} J / K$ . Consider that the molecules possess average kinetic energy. Among the following, choose the wrong statement

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The planet has half the mass and half the radius of the earth, so its escape velocity is $v_{e} = \frac{2 G ( M /2 )}{R /2} = \frac{2 GM}{R} = 11.2 km/s$ , the same as the earth's.

At 800 K the rms speed of oxygen molecules is $v_{r m s} = \frac{3 k T}{m} \approx \frac{3 \times 1.38 \times 1 0 ^{- 23} \times 800}{32 \times 1.66 \times 1 0 ^{- 27}} \approx 0.8 km/s$ , far below 11.2 km/s; nitrogen and argon molecules are comparable or heavier, so none of these gases can escape.

Hence statement (1) - that oxygen molecules escape from the planet - is the wrong statement.

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