eli5 / How do we know the half life of (or even that it is radioactive) Bismuth-209 when it is literally longer than the age of the universe by several orders of magnitude
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You can calculate the half-life of a substance by measuring the rate at which it decays. Bismuth-209 decays by releasing alpha particles, which is a Helium nucleus – two neutrons and two protons.
In 2003 scientists at Institut d’Astrophysique Spatiale in France took a sample of Bismuth-209 and connected it to a very sensitive detector, and measured how many alpha particles it released over the course of 5 days. If you know the mass you started with, you know how many atoms you had, and if you know how many alpha particles were released, you know how many of those atoms underwent decay. You can extrapolate from that to know how long it would take for half of the atoms in the sample to decay, and that’s your half-life.
In the case of the Bismuth-209 experiment, they had something like 128 alpha particles, total, from 100 grams of the substance. Considering that’s like 3×10^23 atoms, and only 128 of them underwent decay in 5 days, that’s an extremely tiny fraction of the sample. Hence it having a half life of 10^19 years.
Lets forget about elements or radiation or half lives. Those aren’t at all important to this discussion. Let me explain
I have a big plate of cookies on the table during a party, its a 1000 cookies though, huge plate. Occasionally someone will take a cookie, but not too often. I see that every 15 minutes, 1 cookie gets taken. If I know that I lose 1 cookie every 15 minutes, how long would it take for 500 of the 1000 cookies to get taken? Its easy math 15 minutes x 500 cookies = 7500 minutes
Now thats a long time, but it wasn’t hard to figure out. My party isn’t going to last 7500 minutes but, if I stuck around for 7500 minutes and left the plate out, it would be spot on, after 7500 minutes, I’d have only 500 cookies left.
WeDriftEternal’s answer is fantastic. To put it back into atomic halflife terms:
You don’t need to measure or observe a whole half-life to figure out what the half-life is. We just measure how long it takes for a small fraction of a sample to decay, and then use that to work out how long it would take for 50% to decay (which is what half-life means).
So like: “In one week of observation, 1% of the sample decayed, so it would take 50 weeks for 50% to decay. The half life is 50 weeks.”***
Or in the case of bismuth, it’s more like: “In one week of observation, 0.000000000000000001% of the sample decayed, so it would take 50000000000000000 weeks for 50% to decay.”
The key is that we have very sensitive detectors that can measure even a few atoms decaying. Even a very small sample of material has trillions of atoms. So even for something with a very slow decay rate like bismuth-209, you can watch it and see how long it takes for like 10 atoms out of 100 trillion atoms to decay, and then just extrapolate to how long it would take for 50 trillion of those 100 trillion to decay, and that’s the half-life.
***This is not how the actual math goes – it’s not actually linear like this. That was an ELI5 simplification. The point is from a small fraction decaying you can work out how long it would take any larger portion to decay. Thanks to Way2Foxy for calling this out!
Some good answers here. But it’s worth noting two things—
1. We don’t KNOW (like we do with shorter life things and can see the entire decay curve). We measure a small part of that curve and make the (reasonable) assumption that it will curve like everything we DO know about.
2. The two most cited articles in Metrologie (the premiere measurement journal) are both about the high level of uncertainty in the very rare times we’ve measured them. We do make a lot of assumptions and have little data for these age-of-universe decays. As opposed to, say, carbon dating which is much better demonstrated.
A half life is the rate of decay. You can measure that rate by counting the decays and knowing the number of atoms you have. Since the number of atoms can be very high. Like 10^20 or more. There can be a good number of decays to measure even if the half life is very long. Also you are free to measure for a long time to get good statistics.
How do you know the speed of an object in km/h if you don’t measure for an hour? Simple, you measur3 the distance traveled in 1 second and calculate the km/h. Same for radioactive decay. You measure for a short time and using math you can calculate half-life, even though you didn’t measure for that long.
The ‘half-life’ is just the way we like to record the number. It isn’t some fundemental trait, but just a way of *measuring* a fundemantal trait.
i.e. Half-life is just one convenient way to write down the decay rate, but we can scale it however we like.
We could instead record the ‘99%-life’, which would be the time taken for 99% of the material to remain. Or we could record the ‘99.999%’ life.
Half-life is just a more useful way to think about it. Perhaps if everything took eons to decay (or everything decayed very fast), we’d have measured it differently, but we have to deal with a wide array of ways things change, and conceptually ‘half’ is very easy, and I think that is why we went with ‘half-life’.
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So, in a way, your question is kind of like “How can we measure the size of germs in meters, when they are so much smaller than a meter?”
or “How can we measure the size of a planet in meters, when the are so much larger than a meter?”
It is just a difference in measurement.
Something can be millions of a meter (or millions of meters) in size.
Similarly, we can measure a millionth of a half-life, or millions of half-lives (ok well millions of half-lives may be a bit too much in practical terms because it scales so fast, but in principle that isn’t a problem.).
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(It is a little bit more than a difference in measurement, since half-life is on a log-scale, and meters are on a linear scale, but fundementally I think that isn’t a big deal.)
Not very radioactive, is it?
The half-life is how long it takes for half of a sample to decay. In half the half-life, one-quarter will have decayed. This can be extended to where an experiment of say a dozen years length will have some really tiny fraction of the sample has decayed. You might think that there comes a limit to where the sample size at the beginning is too small for the decay to be measured, Avogadro’s Number is a really, really, REALLY big lever, though, and bismuth is not rare. So it isn’t that difficult actually to get enough bismuth together such that over a chemistry department’s lifespan you’d be able to measure some decays.
If you measure how fast a car travels for 1 mile, you can easily calculate how long it will take to drive 1 million miles if it keeps that same speed. Same kind of thing
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