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The counts per second of a sample at 0, 5, 10, 15, 20, 25 and 30 minutes are 800, 566, 400, 283…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
The counts per second of a sample at 0, 5, 10, 15, 20, 25 and 30 minutes are 800, 566, 400, 283, 200, 141 and 100. Fit with curve_fit, using for the uncertainties. Find the half-life, and the time at which the count reaches 50.
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. Write the model, fit it, and get the half-life from . The time to reach 50 is the root of "model minus 50", for which brentq needs a bracket, for example from 0 to 200 minutes.
Check. The counts halve every 10 minutes: 800, 400 (at 10), 200 (at 20), 100 (at 30). So the half-life is 10 minutes, and the count 50 comes one half-life after 100, at 40 minutes.
Answer: (close to 800), per minute, half-life 9.99 minutes (that is 10 minutes), and the count is 50 at 40.0 minutes.
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