If the average thermal speed vrms must be at least 6 times smaller than the escape speed vesc for a certain type of molecule to be stable in a planet’s atmosphere,

Question

determine whether molecular oxygen (O2) would be stable near Mars’s surface. Mars has a mass of 6.4x1023 kg and a radius of 3,400 km. The average temperature on Mars is T= -81°F.

Answer 1

You have to compare 6v_rms for oxygen gas and v_esc for Mars.

v(escape) = sqrt(2GM/R) from 1/2 mv² = GMm/R or E_K = U_G (M is mass of Mars, R is radius)

v(rms) = sqrt(3RT/M_O2) Be careful here as the R = 8.314 J/mole K and M_i must be in kg/mole, not g/mole and T in Kelvin!

Good luck!