Why mean life of radioactive element is slightly greater than halflife..?

Asked Mar 18 '22 at 04:30

Active Mar 18 '22 at 05:28

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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?

edited Mar 18 '22 at 05:28

Qmechanic

201,751

asked Mar 18 '22 at 04:30

Muhammad Akbar

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? – rob Mar 18 '22 at 04:36
Possible duplicates here and here. – joseph h Mar 18 '22 at 04:46
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Does this answer your question? Link between average lifespan and half time in radioactivity – rfl Mar 18 '22 at 05:10
Does this answer your question? What is the mean life of a radioactive substance? – anna v Mar 18 '22 at 05:10
I do not think that the answer has already been given. They mainly consists of proving that the relationship between half-life and transformation constant without an explanation in words. If anything this answer has within it the explanation. I would like to be given the opportunity to write a short answer to this question. – Farcher Mar 18 '22 at 07:58
See also What is the probability distribution for the detection times of radioactive emissions from a radioactive sample? – Roger V. Mar 18 '22 at 07:59
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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. – Solomon Slow Mar 18 '22 at 13:28

Why mean life of radioactive element is slightly greater than halflife..?

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