|MadSci Network: Earth Sciences|
There is seldom "definitive proof" of anything in science. But what you often do get is a large number of strands of separate pieces of evidence all pointing in the same direction. A picture is built up that is totally compelling because it would require a huge co-incidence, a cosmic conspiracy, to provide any explanation that is significantly different. Much, but not all of the best evidence for the age of the earth comes from the decay of radioactive elements, in one way or another. Here are pointers to a couple of other Mad Scientist answers that deal with some of this evidence: David Barlow Andrew Karam (including good references) Here is some simple evidence that I will put before you: There are 81 stable elements, with, between them, just under 300 stable isotopes. Every one of these stable isotopes has been found on earth. Several radioactive isotopes are also found on earth. They fall into three categories: (1) Very long-lived isotopes, for example Uranium-235, Uranium-238, Thorium- 232, Potassium-40. (2) Short-lived isotopes that are produced via the decay of these long-lived isotopes, for example Uranium-234, Radium-226, Radon-222. (3) Short-lived isotopes of light elements that are produced in nuclear reactions between high energy particles from the sun and the atmosphere, for example Carbon-14, Hydrogen-3, Beryllium-10. There is no ongoing source of heavier elements, either stable or radioactive. It is currently believed that they were produced in a supernova, which also scattered them as the dust which formed part of the early solar system. So any of the isotopes of category (1) that are present on earth today are remnant fractions of what was present when the earth formed. Now any radioactive isotope decays with a fixed half-life. If it has a half life of 1 day, then at this time tomorrow only half of it will be left, only one quarter the next day, and so on. After 10 days there will only be one thousandth of the original amount, one millionth after 20 days, one billionth after 30 days, and after 50 days, you can forget it! Here are some category 1 isotopes that are abundantly present on earth: uranium-238 has a half-life of 4.51 billion years uranium-235 has a half-life of 0.71 billion years thorium-232 has a half-life of 14.1 billion years potassium-40 has a half-life of 1.28 billion years There are about 6 or 8 others, all with half-lives greater than that of U- 235. Here are some isotopes, potentially category 1, that are not found on earth. I mention mainly those that are the most stable isotope of their respective elements, because these would be the easiest to find if, indeed, they were present: plutonium-244 has a half-life of 80 million years uranium-236 has a half-life of 23.9 million years (and would be a product of any plutonium decay!) curium-247 has a half-life of 16 million years neptunium-237 has a half-life of 2.14 million years technetium-99 has a half-life of 0.212 million years There are about a dozen other radioactive isotopes known to have half-lives greater than 1 million years but less than 50 million years, which are not found naturally on Earth. All short-lived radioactive isotopes that are found naturally on earth clearly fall into categories (2) and (3). Radioactive isotopes can usually be identified by their radiation signature in amounts much less than you would need for chemical analysis. The absence of plutonium from the natural rocks of the earth indicates that the earth has been around for at least 30 half-lives of plutonium-244, which is 2.4 billion years. If its age were any less, we might have expected to detect the 1 part in 1 billion or more that would remain of any original plutonium that may have been present. The presence of uranium-235 at a level of just under 1% of all uranium indicates that the earth has been around for less than 20 half-lives, which is 14.2 billion years, in the absence of any other evidence. But the amount of its final decay product, lead-207, in natural lead limits the age to about 6 billion years maximum. If there had been U-235 decaying for longer than that, there would have to be a lot more lead-207 around. There is a lot of other evidence and more complicated analysis that makes geologists and geochemists very confident that the age of the earth is very close to 4.5 billion years. The figures in this answer were obtained from tables on pages B-253 & B-410 of the CRC Handbook of Chemistry & Physics, 56th Edition. Careful cross- checking between the two tables is needed because there are a few misprints in each of them.
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