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So Potassium 40 decays in such a way that roughly 89% of it becomes Calcium 40 and 11% of it becomes Argon 40. When they list these figures are they implying that after 1 half-life, of the 50% of the material that decayed to daughter products, 89% of that 50% is Calcium 40 and 11% is Argon 40?

Furthermore, does this mean that those will be the proportions of the daughter products in any given number of half lives? Is the partitioning of the decay probability to 89% Calcium and 11% Argon only observed at half-life intervals? Or is this constant throughout the decay chain, such as in between half-lives as well? It should be constant (89% and 11%) throughout? Right? I had recently read some confusing literature on the subject and began to doubt my own understanding.

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Potassium 40 has a half life of 1,300,000,000 years, which means that within that time half of the 11 percent which you refer to will have decayed to form Argon 40. Potassium 40 has two modes of decay, which is unusual for a radioactive isotope. Only 11 percent of it becomes argon 40, the remaining 89 percent decays by a different mode and becomes Calcium 40. but there is no need for you to worry about Calcium 40, it is the 11 percent of K40 which becomes Argon 40 which is useful in dating ancient rocks. Fortunately geologists don't have to wait until it has completed one full half life for it to be useful. By assessing the amount of Argon which has accumulated within the material since it was ejected by volcanoes in pristine condition and had no Argon at all in it, geologists can get a rough idea of the age of the rocks. The potassium/argon method is very tricky to carry out and error can easily creep in.

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