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I understand that after the 4th half life, there will be $\frac{1}{16} = 0.0625$ of the original substance left but I'm not sure how to find the half life according to this graph (since it's not linear, I can't simply find the half life using the fourth). And what does the "pulses per second" have to do with radioactivity? I assume it's just a way to measure radioactivity?

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  • $\begingroup$ ...what is this from? I wouldn't be surprised if "reactivity" was a result of translation error, they likely intended "activity". "Reactivity" would have application to fission and such, but not to decay. $\endgroup$ Commented Jan 2, 2023 at 2:21
  • $\begingroup$ It's from a high school (o level) reference book. $\endgroup$ Commented Jan 2, 2023 at 4:14

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As you mentioned, after 4 half-lives, you only have 1/16th of the original.

Since 4 half-lives correspond to 22,800 years, the half life is 1/4th of that. The graph cannot be linear, as it's an exponential decay, which is why the concept of half-life is used.

The pulse per second is just the number of times per second that the detector detects an ionizing particle. It will depend on how active your source is, how close to your detector it is, and if there's any shielding in between. If your detector is at a constant distance to your source, then it will just depend on how active your source is. (As Christopher mentioned in the comment above, 'Activity' is the right terminology)

See wikipedia for more information on counts per second.

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