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A sample has 400 atoms, and each decays with the probability 0.05 per second…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A sample has 400 atoms, and each decays with the probability 0.05 per second. Repeat the whole 20-second simulation 2000 times, and find the mean and the spread of the number of atoms that are left. Compare them with the theory: each atom survives 20 seconds with the probability , so the number of survivors has the mean and the spread .
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. For each run, follow the 400 atoms for 20 seconds with rng.binomial. Collect the final counts of the 2000 runs.
Check. The probability to survive is , so the mean is and the spread is . The simulation gives 143.1 and 9.51. The relative spread is about 0.066, so the count of the survivors is uncertain by about 7 percent.
Answer: mean 143.1 (theory 143.4), spread 9.5 (theory 9.6), a relative spread of 6.6 percent. With a sample of 400 atoms, the number of survivors is not very sharp.
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