I was in History class the other day and I asked how people are able to get “accurate” dates for how old certain objects are. He said something along the lines of there are certain elements in materials and they decay overtime, half life this so we know roughly how long ago it was made.
I’m a mathematics major and am proficient in physics. I understand the concept of exponential decay and half-life’s. My questions is how do we know how much of a material we are measuring there initially was? To me, without knowing that, we could say that something was made whenever we want it to be made. Clearly I’m missing something but I can’t quite figure it out.
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That depends! If you’re asking about specifically carbon dating, that’s what this answer will be, but history is all about corroborating between as many sources as possible.
Carbon-14 is an unstable isotope of carbon in our atmosphere. It forms when cosmic rays from space interact with carbon in our atmosphere. This maintains a steady ratio of C-14 to other isotopes of carbon, where it forms as fast as it decays. When carbon is taken from the atmosphere, such as by plants, the C-14 will decay but no more is being created, so we can measure how much C-14 remains when compared to other carbon isotopes. This tells us how long it has been since that carbon was in the atmosphere.
While the C-14 balance in the atmosphere is a decent starting point, it *does* change over time. We can also study how much C-14 can be expected at different ages based on carbon samples of a known age, to further improve our estimates.
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