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The more dice that are rolled and added together, the more the sum will tend to cluster around the average.

The law of large numbers just makes this intuition a bit more mathematically explicit, and extends it to any kind of random thing that’s repeated many times (one might even be tempted to say a talk about the half-life of an atom.

Most people would be weirded out if 75% heads of the coins came down heads.

This intuition has been taken by mathematicians and carried to its more difficult to understand, and convoluted, but logical extreme.

Carbon dating is thus not useful at all to most paleontologists.

It's mostly used by archaeologists, and, on occasion, anthropologists.

In fact, by the time you’re dealing with a mere one trillion atoms (a sample of atoms too small to see on a regular microscope), the chance that as much as 51% or as little as 49% of the atoms have decayed after one half-life (instead of 50%) is effectively zero. ), the standard deviation in this example is 500,000.

are radiometric dating methods reliable-35are radiometric dating methods reliable-83are radiometric dating methods reliable-88

Physicist: The predictability of large numbers of random events is called the “law of large numbers“.So, if a sample is 90% as radioactive as a pure sample, then 10% of it has already decayed.These measurements follow the same rules; if there’s a 10% chance that a particular atom has decayed, and there are a large number of them, then almost exactly 10% will have decayed.There simply isn't enough C-14 left in a fossil to use it for dating purposes after 50,000 years, which takes one back to the late Pleistocene, or the last Ice Age.While this is an important period, it's something only a handful of people have professional interest in; the majority of paleontologists don't deal with the Ice Age at all. This question is asked with the intention of understanding basically the decay constant of radiometric dating (although I know the above is not an entirely accurate representation).I do understand that radioisotope decay is modeled exponentially, and that a majority of this dating technique is centered in probability.If you were to see a 1% deviation in this situation, take a picture: you’d have just witnessed the least likely thing anyone has ever seen (ever), by a chasmous margin.Using this exact technique (waiting until exactly half of the sample has decayed and then marking that time as the half-life), won’t work for something like Carbon-14, the isotope most famously used for dating things, since Carbon-14 has a half-life of about 5,700 years. The amount of radiation a sample puts out is proportional to the number of particles that haven’t decayed.less than an hour, but there’s a good chance it’s been more.However, if you have trillions of trillions of atoms, which is what you’d expect from a sample of Awesomium-1 large enough to see, the law of large numbers kicks in.Now, say the isotope “Awesomium-1” has a half-life of exactly one hour.If you start with only 2 atoms, then after an hour there’s a 25% chance that both have decayed, a 25% chance that neither have decayed, and a 50% chance that one has decayed.So with just a few atoms, there’s not much you can say with certainty.If you leave for a while, lose track of time, and come back to find that neither atom has decayed, then you can’t say too much about how long it’s been.




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