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. Show your work. B) When, 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? D) So far, we really only used contact forces of collisions and the force of gravity. Are there any other forces (not necessarily fundamental ones) studied in class that can get molecular hydrogen into the upper atmosphere for us? The surrounding majority of Martian atmosphere is CO2 with a trace of N2 and Ar (all of which are more massive than molecular hydrogen). What fundamental quantity/quantities do we need to calculate its/their value? This is not a calculation question, this is a conceptual one. E) The rms speed is an energy-scaled average of an ensemble of particles, but particles can move slower and even much faster than the rms average. It turns out, if the escape speed is more than 10 times the rms speed of a molecule, the planet can sustain an atmosphere for “billions of years.” If we need more speed, is there hope that molecular hydrogen can escape Martian gravity still?
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. Show your work.
B) When, 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?
D) So far, we really only used contact forces of collisions and the force of gravity. Are there any other forces (not necessarily fundamental ones) studied in class that can get molecular hydrogen into the upper atmosphere for us? The surrounding majority of Martian atmosphere is CO2 with a trace of N2 and Ar (all of which are more massive than molecular hydrogen). What fundamental quantity/quantities do we need to calculate its/their value? This is not a calculation question, this is a conceptual one.
E) The rms speed is an energy-scaled average of an ensemble of particles, but particles can move slower and even much faster than the rms average. It turns out, if the escape speed is more than 10 times the rms speed of a molecule, the planet can sustain an atmosphere for “billions of years.” If we need more speed, is there hope that molecular hydrogen can escape Martian gravity still?
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