Math in carbon dating

So the rate at which this happens, so the rate of carbon-14 decay, is essentially half disappears, half gone, in roughly 5,730 years. Even better, maybe you dig a little deeper, and you find another bone. And you say, wow, you know this thing right over here has 1/4 the carbon-14 that I would expect to find in something living. Well, if it only has 1/4 the carbon-14 it must have gone through two half lives.

what range of C^14 to C^12 ratio would the scientist expect to find in the animal remains?

Im not really sure how to go about solving this problem, any help would be apprecaited.

What I want to do in this video is kind of introduce you to the idea of, one, how carbon-14 comes about, and how it gets into all living things. They can also be alpha particles, which is the same thing as a helium nucleus. And they're going to come in, and they're going to bump into things in our atmosphere, and they're actually going to form neutrons. And we'll show a neutron with a lowercase n, and a 1 for its mass number. And what's interesting about this is this is constantly being formed in our atmosphere, not in huge quantities, but in reasonable quantities. Because as soon as you die and you get buried under the ground, there's no way for the carbon-14 to become part of your tissue anymore because you're not eating anything with new carbon-14.

And then either later in this video or in future videos we'll talk about how it's actually used to date things, how we use it actually figure out that that bone is 12,000 years old, or that person died 18,000 years ago, whatever it might be. So let me just draw the surface of the Earth like that. So then you have the Earth's atmosphere right over here. And 78%, the most abundant element in our atmosphere is nitrogen. And we don't write anything, because it has no protons down here. And what's interesting here is once you die, you're not going to get any new carbon-14. You can't just say all the carbon-14's on the left are going to decay and all the carbon-14's on the right aren't going to decay in that 5,730 years.

Carbon dating has given archeologists a more accurate method by which they can determine the age of ancient artifacts.

Libby invented carbon dating for which he received the Nobel Prize in chemistry in 1960.Archaeologists use the exponential, radioactive decay of carbon 14 to estimate the death dates of organic material.The stable form of carbon is carbon 12 and the radioactive isotope carbon 14 decays over time into nitrogen 14 and other particles.When an organism dies it ceases to replenish carbon in its tissues and the decay of carbon 14 to nitrogen 14 changes the ratio of carbon 12 to carbon 14.Experts can compare the ratio of carbon 12 to carbon 14 in dead material to the ratio when the organism was alive to estimate the date of its death.000$ years: $\displaystyle m(12000) = m_0 e^ = 10^e^ \approx 2.34 \times 10^$ I think you can now do the ,000$ year case (just change the value of $t$).

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