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I understand that, overtime, Uranium decays into different elements until it finally reaches Lead, but how does that show the age of the Earth? I know it can be calculated by the amount of Lead in Uranium, but how do we know how long ago the Uranium was created?

I apologize if this is a dumb question, but if Uranium was created in a supernova, that must have been gone for several billion years to my knowledge, then isn't the time we are calculating how long it has been since that supernova rather than how long the Solar System has existed?

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The answer is covered in a little detail in this article on Uranium-Lead dating. It relies on the fact that certain minerals are formed with basically zero content of lead, but which do incorporate Uranium into their structures. The example given in the article are those based around zircon silicates, a refractory crystalline material that is formed at high temperatures early in the life of the Earth (or the solar system).

The basic assumption is that all the lead found in minerals such as this has arisen through radioactive decay; as such, then radiometric dating techniques give you the time since that mineral was formed. The most basic scheme look at the ratio of $^{238}$U to $^{206}$Pb, where the intermediary decays have a combined half-life of about 4.5 billion years. However, there is a double check using the ratio of $^{235}$U, which decays through a different series to $^{205}Pb$ with a half-life of 710 million years.

So basically, although there a complications and details,these ratios of isotopic abundances will give time that has elapsed since the mineral was formed and thus a lower limit ($>4.4$ billion years) to the age of the Earth.

The age of the solar system itself can come from looking at minerals found in meteorites using a similar technique - so-called lead-lead dating, which uses the ratio of abundances for radiogenic lead isotopes that are produced at different rates by different decay chains to that of $^{204}$Pb, which is not produce by radiactive decay. These give a time of 4.55 billion years between now and the formation of those meteorites.

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  • $\begingroup$ Quick question: Are there not a few dozen (more? less?) other decay chains that have been used to verify the uranium to lead chain as well? $\endgroup$ Jan 21, 2017 at 23:47
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The equation of radioactive decay (which looks like $N = N_0 \exp(-At)$ ) involves four things: decay speed (or activity) $A$, the initial concentration $N_0$, the final concentration $N$ and the time elapsed $t$.

Strictly speaking, to derive the time we have to know all of the other three parameters. And while the final concentration and the decay rate might be directly measured (assuming the constant activity), the initial concentration cannot be determined directly and should rely on modeling or some other indirect methods. So in a way, this is not a precise method of dating.

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