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Why is radioactive or Carbon 14 dating only accurate for 60,000 years? In theory, there should always be at least SOME Carbon 14 in everything that was living at any given time. This is because no matter how many times you multiply something by 2, there will always be an answer (as long as the number is real). So why only to 60,000? Also, there are records of things existing for upwards of 4.28 billion years old (link:https://www.livescience.com/57942-what-was-first-life-on-earth.html), if Carbon 14 dating is only accurate for 60,000 years, how do we know how old some of these microfossils are?

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There is no exact date beyond which carbon 14 decay is/is not useful. However, given that the half life of carbon 14 is 5730 years, then there really isn't much carbon 14 left in a sample that is 60,000 years old. The decay constant is $\lambda = \ln 2/t_{1/2}$, so the fraction of carbon left would be $\exp[-\lambda t]$, which, for $t=$60,000 years, would be $0.07$%.

Of course, these small traces probably could be found with modern techniques, but then you have to factor in systematic uncertainties associated with present-day contamination (the air contains carbon 14 !). Any small uncertainty in the contamination could easily be magnified into a huge age error in an old sample with a very small amount of carbon 14 present.

Your final question about age dating techniques is too broad for a Physics SE question. However, there are other radioactive dating techniques that can be used to find the ages of rocks and minerals, using isotopes with half-lives of many billions of years (Samarium/Neodymium dating is referred to in the article for which you provide a link).

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  • $\begingroup$ That link would be better pointing to en.wikipedia.org/wiki/Radiometric_dating#Modern_dating_methods $\endgroup$ – J.G. Apr 4 '18 at 15:55
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    $\begingroup$ exactly. This is why uranium isotopes were used to date the formation of the solar system $\endgroup$ – lurscher Apr 4 '18 at 16:01
  • $\begingroup$ Re, "The air contains carbon 14", well yes. That is why carbon dating works. $^{14}C$ is produced in Earth's atmosphere by the action of cosmic rays. It gets oxidized to CO2, and it eventually is absorbed by green plants, which then are consumed by other living things. The production and the decay of atmospheric $^{14}C$ are in equilibrium, so the ratio of $^{12}C$ to $^{14}C$ in all living organisms is pretty much a constant. When an organism dies though, its tissues stop exchanging carbon with the environment, and the ratio changes as the $^{14}C$ decays $\endgroup$ – Solomon Slow Apr 4 '18 at 17:58
  • $\begingroup$ @jameslarge Hence the exclamation mark. I think the point is that external Carbon 14 can contaminate a sample and it is rather difficult to stop that contamination occurring. $\endgroup$ – Rob Jeffries Apr 4 '18 at 18:11
  • $\begingroup$ Oops! I see that now. $\endgroup$ – Solomon Slow Apr 4 '18 at 18:36
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Also, there are records of things existing for upwards of 4.28 billion years old, if Carbon 14 dating is only accurate for 60,000 years, how do we know how old some of these microfossils are?

Don't use C14!

In the case of ~4by you typically use uranium/lead. The problem with this method is that both lead and uranium are still around, so if you want to measure the relative quantities of the two, you need to be sure to exclude any contamination.

It turns out we're lucky here: zircon crystals eject all lead while they form. So if you find a zircon today, any lead inside must have come from uranium. So you measure the two and there's your date. It's good to about 4.5 by +-0.1% That's super-good, but it does mean you need to find some zircons. Good thing they're relatively common.

I went to a great talk at UToronto where someone was explaining all of this. Then he pulled out a rock and passed it around. It was found in antarctica after falling from space and then slowly moving with the ice flows until it reached the ocean where someone picked it up. They dated it, and found that it formed within 10,000 years of the lighting-up of the sun.

It's that accurate.

There's a bunch of different decay chains you can use for different time periods. The trick is to find one where the resulting mixture isn't entirely dominated by one or the other today. After U-Pb, you move into potassium-argon, and so on through a bunch of methods until you get to C14, which is typically used only for the most recent sorts of objects.

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