The atmosphere is pretty dynamic, lots of convection, so the time frame for total homogenization is on the order of years to decades. Some regions are better-mixed than others, but even trace contaminants end up in remote regions pretty quickly, as we have found with the distribution of trace contaminants like PCBs and tritium (the stuff gets everywhere in almost no time at all).
We take in about 1 gram of air with each breath. This compares to a total mass of something about 10^23 grams for the entire atmosphere (estimated at 5×10^19 kg, I just looked it up), so we breath in about 1/10^23 ths of the existing air. this is about the same as the number of atoms in a liter of air (which is about the same as a breath in volume) so the odds are pretty good that at least 1 atom (likely 10-100) also came out of Julius Caesar’s lungs on his last exhale, assuming a typical volume (not just a tiny gasp but even then, it only changes the odds by a factor or ten or so and we are in that range of uncertainty already with the estimates we are using).
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