Minor nitpicks:
-I read “1 angstrom of uncertainty in 1 atom” as the location is normally distributed with mean <center> and SD 1 angstrom, or as uniformly distributed in solid sphere of radius 1 angstrom. Taken literally, though, “perturb one of the particles by 1 angstrom in a random direction” is distributed on the surface of the sphere (particle is known to be exactly 1 angstrom from <center>).
-The answer will absolutely depend on the temperature. (in a neighborhood of absolute zero, the final positions of the gas particles are very close to the initial positions.)
-The answer also might depend on the exact starting configuration. While I think most configurations would end up ~50/50 chance after 20 seconds, there are definitely configurations that would be stably strongly on one side.
Nothing conclusive below, but things that might help:
-Back-of-envelope calculation said the single uncertain particle has ~(10 million * sqrt(temp in K)) collisions /sec.
-If I’m using MSD right (big if!) then at STP, particles move from initial position only by about 5 cm in 20 seconds (cover massive distance, but the brownian motion cancels in expectation.)
-I think that at standard temp, this would be at roughly 1⁄50 standard pressure?
Minor nitpicks: -I read “1 angstrom of uncertainty in 1 atom” as the location is normally distributed with mean <center> and SD 1 angstrom, or as uniformly distributed in solid sphere of radius 1 angstrom. Taken literally, though, “perturb one of the particles by 1 angstrom in a random direction” is distributed on the surface of the sphere (particle is known to be exactly 1 angstrom from <center>). -The answer will absolutely depend on the temperature. (in a neighborhood of absolute zero, the final positions of the gas particles are very close to the initial positions.) -The answer also might depend on the exact starting configuration. While I think most configurations would end up ~50/50 chance after 20 seconds, there are definitely configurations that would be stably strongly on one side.
Nothing conclusive below, but things that might help: -Back-of-envelope calculation said the single uncertain particle has ~(10 million * sqrt(temp in K)) collisions /sec. -If I’m using MSD right (big if!) then at STP, particles move from initial position only by about 5 cm in 20 seconds (cover massive distance, but the brownian motion cancels in expectation.) -I think that at standard temp, this would be at roughly 1⁄50 standard pressure?