Say that the only pressure differences in the atmosphere was due to the gravitational pull of the earth. That is, say pressure only changed as a function of height.
So we're assuming there's no wind, no differences in humidity, equal composition of air everywhere, the atmosphere is at the same temperature everywhere...etc.
I'm told that in any fluid, the particles are always in random motion, smashing into one another and smashing into whatever surface we insert into the fluid, and that's what causes pressure.
But, how "much" motion" is this "random motion" really?
In this hypothetical scenario, would an air particle from the top of Mount Everest ever make its way down to sea level?
Would air's random motion be mostly horizontally, or vertically? (I think vertically...but I'm not sure...)
Just for context, I'm asking this question because I'm struggling to understand pressure, and especially its relation to gravity.