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Fossils are generally found in sedimentary rock not igneous rock.
Sedimentary rocks can be dated using radioactive carbon, but because carbon decays relatively quickly, this only works for rocks younger than about 50 thousand years.
But, again, exptrapolation of the discordia back to the two points where it intersects the Concordia, would give two ages - t* representing the possible metamorphic event and t and solve for t . This argument tells when the elements were formed that make up the Earth, but does not really give us the age of the Earth. Thus, our best estimate of the age of the Earth is 4.55 billion years.
Nd ratios on several minerals with a mass spectrometer and then from the slope determine the age of the rock. If a magma cools quickly on the surface of the Earth, some of the Ar may be trapped.
After the passage of two half-lives only 0.25 gram will remain, and after 3 half lives only 0.125 will remain etc.
To see how we actually use this information to date rocks, consider the following: Usually, we know the amount, N, of an isotope present today, and the amount of a daughter element produced by decay, D*.
Radioactive atoms are inherently unstable; over time, radioactive "parent atoms" decay into stable "daughter atoms." When molten rock cools, forming what are called igneous rocks, radioactive atoms are trapped inside. By measuring the quantity of unstable atoms left in a rock and comparing it to the quantity of stable daughter atoms in the rock, scientists can estimate the amount of time that has passed since that rock formed.Another possible scenario involves U leakage, again possibly as a result of a metamorphic event.U leakage would cause discordant points to plot above the cocordia. Lunar rocks also lie on the Geochron, at least suggesting that the moon formed at the same time as meteorites. Pb separated from continents and thus from average crust also plots on the Geochron, and thus suggests that the Earth formed at the same time as the meteorites and moon.U would have been stable in the crystallographic site, but the site is now occupied by by Pb.An event like metamorphism could heat the crystal to the point where Pb will become mobile.