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Let's take the example of carbon-14.After 5730 years, the activity of a particular sample would have reduced to half. After 11460 years, the activity would have reduced to 1/4th its value. And after 17190 years, the activity would have reduced to 1/8th it's original value. If this trend continued, won't the activity, at some point of time, reduce to 0? (I mean, won't it get so close to zero that we can scientifically assume it as zero?)

I ask this question, as my textbook says, "The activity of a radioactive isotope never reduces to zero.".

Always curious, Ramana

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When you see an exponential trend line for radioactive decay, eg number of unstable nuclei left against time, it is just a trend line which is close to the actual data points if the number of unstable nuclei is very large.
Put another way the statistical fluctuations of the actual number of unstable nuclei from the trend line are small.
So in theory the number should never become zero.
Even though the exponential might predict that you can have 0.734 nuclei that can never happen.
When one gets down to small numbers of unstable nuclei the statistical fluctuations have to be considered.

So starting from 8 unstable nuclei all you know is that the prediction is that on average after one half life there should be 4 unstable nuclei but in fact there is a finite probability that after one half life there are still 8 (or 7 or 6 or 5 or 3 or 2 or 1 or zero) unstable nuclei.

As the number of unstable nuclei decreases the probability of having no unstable nuclei after one half life increases.

Left with one unstable nucleus you can be reasonably certain that it will decay and leave you with no unstable nuclei.

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