(I'll repost one of my comments in a similar thread, with a few minor changes.)

If you have only one xenon atom in a box, to have a 50% chance that to see that it decayed you should wait a "1.8 x 10^22 years—or about a trillion times the age of the Universe".

If you have two atoms in a box, you must wait approximately half of the time to have a 50% chance to see the decay. (It's not exactly one half, there are some technical details here, but one half is a good approximation.)

They have 2 tons of xenon. I'm not sure if 1 ton = 1000kg or 907 kg, but it doesn't change the result too much. I'm also not sure about the isotope of Xenon they are using, so I'll use 131 as the atom mass, but it doesn't change the result too much. With 2 tons you have 2 x 907 * 1000 / 131 x 6.02x10^23 = 8E28 xenon atoms, so you expect to have a few decays per hour (if I did the calculations correctly).

I'm not sure if they can detect the 100% of the decays and the noise level, so it probably takes a longer time to detect a good signal.

>If you have two atoms in a box, you must wait approximately half of the time to have a 50% chance to see the decay. (It's not exactly one half, there are some technical details here, but one half is a good approximation.)

Really? As far as I know radioactive decay is mostly believed to be a Poisson process (or rather the time it takes for a single atom is believed to be exponentially distributed), in which case the time it will take is exactly one half, on average.

Are the two of you using the same answer to the question "Does a X% chance of 2 events (in given interval) contribute X% or 2X% to the chance of seeing one event?"? That is, do you mean [time for a 50% chance of seeing ≥1 decay] or [time to see, on average, 0.5 decays].

In my case I'm talking about the (average) time until the first decay.

If you put two atoms A and B in an box and wait 1/2 of the half life, then the probability that the atom A survives is 1/sqrt(2). The probability that the atom B survives is also 1/sqrt(2). So (assuming independence) the probability that both survive is exactly 1/2. So you are right!

(I'd prefer to say that it's a property of the exponentially distribution, not the Poisson process.)

Poisson distribution is the limit of having infinite particles around.

It is, although the only difference is that the rate of this particular process changes after the first decay. Which makes it more of a continuous time Markov process, but the general idea is similar.

The decay in question is from xenon-124, so they're probably using a natural isotope mix which will also contain those quasi-stable ones.

Wikipedia says that the natural abundance of Xenon-124 is 0.095% = 1/1000. Adding that correction I get a few decays per day that is more similar to the data reported in other commit that is 126 events in 177 days.

Edit: I think I'm missing a ln_e(2) in the calculation, but it's only a 30% more or 30% less. It's not a huge change in the result.

article says “1,300 kilograms (2,866 pounds) of xenon isotope”

not sure if that was intentional..

The other article didn't have the exact number, so I used the number of Wikipedia that says something like 3.6 tons in total and 2tons inside the measurement part (or something like that).

Dredging up memories from high school chem: not actually impossible odds. Half-life means the time it takes for half of the atoms out of a given quantity to decay. There are 6.02E23 atoms per mole, and about 8 moles per kg for xenon. So with a large enough quality of xenon-124, some decay event should happen within a reasonable timeframe. Of course it’s still a tremendous technical feat to actually setup and detect such an event.

I think the article just did a poor job of portraying the rarity of the event. This article links to a Gizmodo article[1] which does a better job of explaining that they had 3.2 tonnes xenon-124 and many occurrences:

> After 214 days of observing (177 days of usable data), the researchers’ analysis revealed approximately 126 two-neutrino double electron capture events.

[1] https://gizmodo.com/dark-matter-detector-makes-incredible-ne...

Indeed, larger samples will observe higher rarity events/outcomes.

It's probability, not rule I think.