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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It depends on the type of radioactive dating being used, but essentially (to my understanding) is that it comes down to measuring the ratio of parent isotopes to daughter isotopes. In the case of carbon dating the carbon-14 is coming from the sun and being absorbed by living cells. But of course the amount of carbon-14 I get could be very different from the amount you get. To control for this you can measure the ratio of carbon-14 to nitrogen-14 in the sample.
Likewise, for longer-term dating, you can use uranium and measure the ratio of lead to uranium to control for different amounts of sample.
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