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A particle makes a step of 2 mm to the left or to the right every 0.1 s…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A particle makes a step of 2 mm to the left or to the right every 0.1 s. For one dimension, the mean squared distance is , where is the diffusion coefficient. Simulate 4000 particles for 200 steps, fit a straight line to the mean squared distance against the time, and find . Compare with the theory: for steps of length every .
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Plan. The positions are in mm. The mean squared distance at each time is the mean over the particles. The slope of its graph against the time is .
Check. After steps, the mean squared distance is , and the time is s, so the slope is . Then . The simulation gives a slope of 41.5 and , which is within the scatter of 4000 walkers.
Answer: (the simulation gives 20.7, and the theory gives 20.0).
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