14.1 (a) The temperature near the top of Saturn’s cloud layer is about 110K. T

Question

14.1 (a) The temperature near the top of Saturn’s cloud layer is about 110K. The temperature at the top of the earth’s troposphere, at an altitude of about 20km, is about 220K. Calculate the rms speed of hydrogen (H2) molecules in both these environments. Give your answers in m/s and as a fraction of the escape speed from the respective planet.

(b) Hydrogen gas is a rare element in the earth’s atmosphere. In the atmosphere of Saturn, by contrast, 96% of all molecules are H2. Explain why.

(c) Suppose an astronomer claims to have discovered an oxygen (O2) atmosphere on the Moon. How likely is this to be true? The Moon has a surface temperature of about 220K near its equator.

Explanation / Answer

vH2 for saturn = 1170m/s

vH2 for earth = 1655m/s

fracrion for saturn = 3.2%

fraction for earth = 14.7%

b)Ans: Basically, H is the most abundant element in the universe and all
planets formed with H as the primary atmospheric constituent. However, the
low escape velocity for the Earth and the high rms velocity for H at the
temperature prevailing on Earth allowed all the H to escape. The opposite
situation holds for Jupiter which has such a high escape velocity that it is has
been able to hold on to all of it’s primordial H.)

c)vrms of o2 = 413m/s

fraction = 17.2 % which is quite high so there cannot be an oxygen atmosphere

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