Consider the particles in the Earth's atmosphere under equilibrium conditions in the presence of the Earth's gravitationl

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Consider the particles in the Earth's atmosphere under equilibrium conditions in the presence of the Earth's gravitationl field. Assume a horizontally stratified (x, y plane) atmosphere with constant temperature T and consider a constant value

for the acceleration due to gravity. Derive an expression for the number density nα(z) as a function of height z, for the type α species, in terms of the number density nα(z0) at a base level z0 and of the scale height Hα = kT /mαg. How is the expression for nα(z) modified, when T and g vary with height?

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