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## Summary:

- How to calculate half life

## Main Question or Discussion Point

How did they calculate the half life of xenon 124 to be longer than the age of the universe if they only observed one decay??? Is there some way to estimate half life???

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- #1

- 97

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## Summary:

- How to calculate half life

How did they calculate the half life of xenon 124 to be longer than the age of the universe if they only observed one decay??? Is there some way to estimate half life???

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- #4

Vanadium 50

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If you have a box of 100 atoms and 5 of them decay in a year, what is the half-life?

If you have a box of 1000000 atoms and 5 of them decay in a year, what is the half-life?

If you have a box of 10

- #5

fresh_42

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- #6

DrClaude

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They use natural xenon, 2 tonnes of it, with an abundance of 1 kg

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In addition to what was already said, where does this come from? According to the article (https://www.nature.com/articles/s41586-019-1124-4), this is not just based on one event.if they only observed one decay

If I understand correctly, it is just the natural abundance in the detector. You only get ~ 0.1% Xenon 124, but then you take a ton of Xenon.that they get enough isotopes, especially if they are created synthetically.

- #8

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There is only one isotope of relevance, 124-Xe. The issue is getting enough nuclei of that isotope.get enough isotopes

For the future, you should remember to include a reference to the original paper when you have a particular issue that you want to discuss. In this case, the appropriate reference would have been the Nature paper.

The paper quotes a measured number of events of ##N_0 = 126\pm 29## over 177.7 days of data taking. They have an isotopic abundance of about ##10^{-3}## and the efficiency is almost one. This means that they have

$$

N = 10^{-3} \frac{M N_A}{m}

$$

124-Xe atoms, where ##M## is the total xenon mass, ##N_A## the Avogadro number, and ##m## the molar mass of xenon (ca 131 g/mol), leading to ##N \simeq 5\cdot 10^{24}##. The estimate of the half-life is therefore (solving from the expression in #2)

$$

T \simeq \frac{N t \ln 2}{N_0} \simeq 10^{12} T_{\rm univ},

$$

where ##T_{\rm univ}## is the age of the Universe.

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fresh_42

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I had encountered another element recently with an equally absurd half time and it wasn't natural, or extremely rare. Unfortunately I have forgotten which one. I only remember that I asked myself the same question, and a high number of isotopes didn't seem to provide a solution. The only other possibility was an extremely long observation time, but it made me wonder, whether there are other methods, maybe theoretical calculations.There is only one isotope of relevance, 124-Xe. The issue is getting enough nuclei of that isotope.

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mfb

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Every isotope with a measured lifetime larger than 10

There are theoretical calculations for a lot of unmeasured lifetimes, of course, and theoretical calculations are not limited to naturally occurring isotopes. Long-living isotopes typically exist in nature, however. They might live too long for us to detect the decay but we won't suddenly find an isotope that lives so long but doesn't occur in nature.

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