The 84 elements found on Earth occur as 339 isotopes. Only 269 of these are stable, and the other 70 are radioactive. An additional 1650 radioactive isotopes have been created in nuclear reactors and in particle accelerators.
The following is a table of all 29 known radioactive isotopes that have a half-life of one million years or more, and that are not being continually produced by natural nuclear reactions. It has been sorted in order of half-life. For each isotope, the table shows whether it is one of the ones found on Earth.
|Plutonium 244||82||by extreme effort|
The thing to notice is that this list falls naturally into two halves. Short-lived radioactives are suspiciously absent from the Earth. If we had carried this list all the way down to 1,000 year half-lives, the block of no's would be 37 long instead of 10 long.
The most obvious explanation for the above is that all these elements were present when the Earth was formed, but by now the short-lived ones have decayed away. This explanation is compatible with the age scientists accept for the Earth.
Of course, nothing about this list really proves that the Earth is old. But the list is exactly what we would expect if the Earth is old, and it is a very puzzling list if the Earth is young.
Radioactives with half-lives shorter than one million years are also produced: for example, Carbon 14 (half life 5730 years).
Uranium 235's half life is 704 million years, so 4.55 billion years is just a bit over six half-lives. It's reasonable for Uranium 235 to still be around in small quantities after that amount of time. And, in fact, it makes up about one percent of the Uranium now on Earth. The amounts of Uranium 235 and Uranium 238 would have been about equal, 4.55 billion years ago.
Samarium 146's half life is 103 million years, so 4.55 billion years is 44 half lives. This means that Samarium 146 could be 200 billion times rarer than Uranium 235, but could be a thousand times commoner than Plutonium 244. I predict that if anyone tries very very hard to find Samarium 146, they will succeed. Curium 247, at almost 300 half lives, is completely out of the question.
In short, the cutoff point in the list is consistent with 4.55 billion years.
The Age Of The Earth, pages 80 and 376-387. However, I have used a more recent measurement of Samarium 146's half life: see WebElements and Brookhaven National Labs.
Detection of Plutonium-244 in Nature, Hoffman et al, Nature 234,132-134 (19 November 1971)