I do not know the answer to this. The density is 10^19 atoms/cc. Mean inter atomic distance = 5 x 10^-7 cm. The random walk distance for atoms starting at the base of the atmosphere is actually quite long, and although collisions take a fraction of a second at these densities, it takes n^2 = (10^13)^2 = 10^26 steps to travel 50 kilometers. Multiplying by the collision time per atom of 5 x 10^-7/ 2 km/sec = 2 x 10^-12 sec and you get 10^26 x 10^-12 = 10^14 seconds or 3 million years. This would be an OVERESTIMATE because the diffusion rate will exponentiate as the density of the atmosphere diminishes. My best wild guess would be something like a few thousand years.