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I was reading radioactivity where I find that half life of a radioactive material is less than mean life due the presence of $\log2$ in the numerator:

$$ t_{1/2} = \frac{0.693}{\lambda} $$

But how what does it mean that the mean life is greater than the half life and why it need to be so?

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  • $\begingroup$ How strong is your calculus? Are you familiar with $e$, the natural logarithm, and the magic ways they interact with the kinds of integrals that go into computing an average? $\endgroup$
    – rob ♦
    Commented Mar 18, 2022 at 4:36
  • $\begingroup$ Possible duplicates here and here. $\endgroup$
    – joseph h
    Commented Mar 18, 2022 at 4:46
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    $\begingroup$ Does this answer your question? Link between average lifespan and half time in radioactivity $\endgroup$
    – rfl
    Commented Mar 18, 2022 at 5:10
  • $\begingroup$ Does this answer your question? What is the mean life of a radioactive substance? $\endgroup$
    – anna v
    Commented Mar 18, 2022 at 5:10
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    $\begingroup$ TLDR: Half of the atoms in a sample will decay in less time than the half-life. The other half will take longer. Half of the other half will take more than twice as long. A few of the other half will take a lot longer. Those outliers—the ones that take a lot longer to decay—raise the mean lifetime. $\endgroup$
    – Solomon Slow
    Commented Mar 18, 2022 at 13:28

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