Imagine that there is a brief radiation leak at a nuclear power plant. The radioactive gas molecules have an average speed of 360 m/s and a mean free path (i.e., an average distance between collisions) of 3 × 10−3 m. The root mean square step length, projected in any one direction (e.g., in the x direction) is 1.73 × 10−3 m. Suppose that this leak happens to occur when the air is perfectly still, with no turbulence or other mixing at all. What is the characteristic radius of the radioactive cloud after 1 minute, 1 hour, and 1 day?
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