Adopt a temperature of 300 K and a mean particle mass of 29 mh, and assume const

Question

Adopt a temperature of 300 K and a mean particle mass of 29 mh, and assume constant g. The scale height of the Earth's atmosphere is 8.8 km. If the atmosphere is isothermal, what fraction of the atmosphere lies below an altitude of 4.3 km? I'm assuming that the scale height formula H=kT/mg is to be used, but I can't seem to get the right answer.

Explanation / Answer

scale height = H = kT/Mg = 8.8km = 8800 m M = 29 m = 29 * (1.008*1.66e-27) = 48.525e-27 Kg k = 1.381e-23 ? = MP/kT P = P0 exp(-z/H) P0 = 1 atm = 1.013e5 Pa >>>> ? = MP/kT = (MP0/kT) exp(-z/H) >>>> ? = ((48.525e-27*1.013e5)/(1.381e-23*300)) exp(-z/8800) >>>> ? = 1.1865 exp(-z/8800) integrate from z=0 to z=4300meters: m = ??dV = ?(1.1865 exp(-z/8800)) (4?z^2) dz m = (14.91) * ?(exp(-z/8800)) (z^2) dz m = (14.91)*(-8800)*(e^(-z/8800))*(z*(z+17600)+154880000) m = (-20046325841536) - (-20321495040000) = 275169198464 m = 2.75

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