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I'd like to know when the formula [tex]N(t)=N_0e^{-\lambda t}[/tex] is not valid anymore. By that I mean... since [tex]N_0[/tex] is the number of atoms at time [tex]t=0[/tex] and [tex]N(t)[/tex] is the number of atoms at time "[tex]t[/tex]", we see that [tex]N(t)[/tex] depends of [tex]N_0[/tex]. Now my question is : how do you know how many atoms should we take in count? Say we have 2 balls of plutonium, separated by 3 meters. How do you apply the formula given above? Is it still valid? Do you have to take [tex]N_0[/tex] as the number of atoms in the 2 balls, or you can apply the formula for each ball?

To be more precise, what is the minimum density of radioactive elements we can consider to have a decent approximation using the formula?

What is the "error" of the formula?

I'm sorry if this makes a lot of questions and if they're not precise enough.

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# Radioactive decay questions

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