The question:

>> One fellow disagrees with the general consensus that it's around 4.5 billion years. Part of the evidence relates to the half-life of potassium-40. He want to know how we can base our estimates of the Earths' age partially on this evidence, when we, and I paraphrase here, "don't REALLY know the half-life of this isotope is X number of years".
My question is how DO we know what the half life of Potassium 40 is, and could it be incorrect, thus throwing off our age estimates?

I’ll give it a shot. Warning - Exceedingly lengthy but thorough! And it takes the mixing and matching from several different disciplines to get there. The dating of things older than recent history probably begins with tree rings. Since we know exactly how old a living tree is by it’s rings, then we can start there. You can date back up to about 20,000-50,000 years in some temperate forests with tree rings thanks to Andrew Ellicott Douglass who first formulated a method for dendrochronology in the early 1900s. This method is done by using thick and thin rings on a living tree with ones on other dead ones, but not so ancient that you can’t overlap some of the thick and thin rings with the living one. You can then overlap more and more felled trees in the same forest. The assumption is that in the big rain years all of the trees in the same forest will have thick rings. Though a thick one on one tree might be thinner on another, so it’s relative to each tree’s growth rate. Then, in drought years, all of them will be thin.. Since a sort of morse code develops with patterns of drought and rain over decades and centuries, you can take data that overlaps from tree to log to log pretty far back. www.mnsu.edu/emuseum/inf..._andrew.html

Around the same time, discoveries were being made in radioactivity by Becquerel, Curie, Rutherford, Roentgen and others. These guys were finding out things like radioisotopes, or emitters were charged particles and that they would veer when coming in contact with a magnetic field meaning they were particles and not waves like x-rays, that they would make air become an electrical conductor leading to the geiger counter, and in 1911 Charles Wilson had invented the cloud chamber which would allow a person to actually see the trails of the radioactive particles.
www.rsc.org/images/essay...m18-17763.pdf
During this early miasma of discoveries, Frederick Soddy and Ernest Rutherford 1903 came up with the Law of Radioactivity. It seems that all radioactive isotopes, called parents, decay at the same rate into their particular daughter elements. (whatever they decay into). So, all you have to do is establish a rate for whatever element you find, and it continues decaying at this same rate either forever, or until all of its atoms have decayed. Since one can analyze the percentages of parent and daughter elements in a rock or any sample, and the rate of decay of that parent element is always the same according to the law of radioactivity, one can determine the age of that object. The way that is done is finding the percentages of the parent and daughter element in the clump of matter in question. If it’s 100% parent element, it is 0 time. If it is down to 50% parent and 50% daughter, then it is the term they coined - one half life old. Every element has its own amount of time that it takes for half of it to decay. Some elements have half lives of less than a millionth of second. So, with the Law of Radioactivity, you can say, since there is this amount of parent and this amount of daughter in this sample, it must have decayed for this long. But, what people have difficulty believing, is that we seem to have some elements with half lives much older than our current understanding of the earth’s age or even the age of the universe! 10s of billions of years! Like Rubidium-87, 40 billion years! How could we know that?

Well, remember the tree rings? We can be relatively sure of the age of some pieces of wood that go back to 20,000 years old. In 1949 Willard Libby invented the radiocarbon dating method that would use the percentage of parent element C-14 and daughter N-14 from a sample and be able to determine the age of the sample. It was assumed that rate of C-14 and N-14 decay and creation by cosmic rays colliding with Nitrogen in the Atmosphere remained constant throughout time. At least as long as the atmosphere had been able to sustain life. Then, one could calibrate the law of radioactivity by looking for a tree ring sample that had exactly half C-14 and half N-14. It was found that that the tree ring exactly 5,730 years old was one half life. Then, a tree ring exactly 11,460 years was two half lives old. So, the Law of Radioactivity was proven pretty solidly, not that it wasn’t already.

And now to the age of the earth. All you have to do is find the oldest rocks by using elements that have long half lives, and they have. But, of course with plate tectonics and an active mantle, the fact that the crust continues to recycle as it plummets back into the earth about a centimeter per year in most places, perhaps it is older than the oldest rocks. Some have therefore done the double-checking with moon samples and they mostly agree on 4-5 billion year range. I don’t know how anyone could argue such strong scientific methodologies and grueling cross-referenced data collection.