Here we would like to figure out why we do not seem to have any molecular hydrogen in the Martian atmosphere. Although this can get very complicated quickly IRL, we can simplify things by asking a couple of questions, one at a time. We will examine just molecular hydrogen as a diatomic ideal gas. The molar mass of molecular hydrogen is about 2 x 10-3 kg/mol. The mass of Mars is about 6.4 x 1023 kg, and the mean radius of Mars is about 3.39 x 106 m. a) First, we would like to see if Martian gravity has what it takes to hold molecular hydrogen. Calculate the mean escape velocity at the surface of Mars. b) Then, we would like to see if Mars is too hot to hold molecular hydrogen. Calculate the rms speed of molecular hydrogen at an average Martian atmospheric temperature of 210 K. Is molecular hydrogen expected to escape at this speed c) Perhaps if we wanted to be really sure we did not miss anything, we can examine another scenario. The Martian upper atmosphere (thermosphere and up) is hotter (but it may FEEL cold because it is so rarified). Let us repeat our rms speed calculation for molecular hydrogen at 400 K instead, which can be typical near the “edge of outer space.” Try this at about 200 km above the surface of Mars. Under these conditions, can molecular hydrogen escape Martian gravity there?
Here we would like to figure out why we do not seem to have any molecular hydrogen in the Martian atmosphere. Although this can get very complicated quickly IRL, we can simplify things by asking a couple of questions, one at a time. We will examine just molecular hydrogen as a diatomic ideal gas. The molar mass of molecular hydrogen is about 2 x 10-3 kg/mol. The mass of Mars is about 6.4 x 1023 kg, and the mean radius of Mars is about 3.39 x 106 m.
a) First, we would like to see if Martian gravity has what it takes to hold molecular hydrogen. Calculate the mean escape velocity at the surface of Mars.
b) Then, we would like to see if Mars is too hot to hold molecular hydrogen. Calculate the rms speed of molecular hydrogen at an average Martian atmospheric temperature of 210 K. Is molecular hydrogen expected to escape at this speed
c) Perhaps if we wanted to be really sure we did not miss anything, we can examine another scenario. The Martian upper atmosphere (thermosphere and up) is hotter (but it may FEEL cold because it is so rarified). Let us repeat our rms speed calculation for molecular hydrogen at 400 K instead, which can be typical near the “edge of outer space.” Try this at about 200 km above the surface of Mars. Under these conditions, can molecular hydrogen escape Martian gravity there?
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