# Carbon dating formula example

This discovery is in contrast to the carbon dating results for the Turin Shroud that was supposed to have wrapped Jesus’ body.Carbon dating has shown that the cloth was made between 12 AD.Although it may be seen as outdated, many labs still use Libby's half-life in order to stay consistent in publications and calculations within the laboratory.From the discovery of Carbon-14 to radiocarbon dating of fossils, we can see what an essential role Carbon has played and continues to play in our lives today.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.It's just a little section of the surface of the Earth. And that carbon-14 that you did have at you're death is going to decay via beta decay-- and we learned about this-- back into nitrogen-14. So it'll decay back into nitrogen-14, and in beta decay you emit an electron and an electron anti-neutrino. But essentially what you have happening here is you have one of the neutrons is turning into a proton and emitting this stuff in the process. So I just said while you're living you have kind of straight-up carbon-14. What it's essentially saying is any given carbon-14 atom has a 50% chance of decaying into nitrogen-14 in 5,730 years. So carbon by definition has six protons, but the typical isotope, the most common isotope of carbon is carbon-12. And then that carbon dioxide gets absorbed into the rest of the atmosphere, into our oceans. When people talk about carbon fixation, they're really talking about using mainly light energy from the sun to take gaseous carbon and turn it into actual kind of organic tissue. But what's interesting is that a small fraction of carbon-14 forms, and then this carbon-14 can then also combine with oxygen to form carbon dioxide.

The equation relating rate constant to half-life for first order kinetics is $k = \dfrac \label$ so the rate constant is then $k = \dfrac = 1.21 \times 10^ \text^ \label$ and Equation $$\ref$$ can be rewritten as $N_t= N_o e^ \label$ or $t = \left(\dfrac \right) t_ = 8267 \ln \dfrac = 19035 \log_ \dfrac \;\;\; (\text) \label$ The sample is assumed to have originally had the same (rate of decay) of d/min.g (where d = disintegration).Radiocarbon dating (usually referred to simply as carbon-14 dating) is a radiometric dating method.It uses the naturally occurring radioisotope carbon-14 (14C) to estimate the age of carbon-bearing materials up to about 58,000 to 62,000 years old. Carbon-14 has a relatively short half-life of 5,730 years, meaning that the fraction of carbon-14 in a sample is halved over the course of 5,730 years due to radioactive decay to nitrogen-14.Once an organism is decoupled from these cycles (i.e., death), then the carbon-14 decays until essentially gone.The half-life of a radioactive isotope (usually denoted by $$t_$$) is a more familiar concept than $$k$$ for radioactivity, so although Equation $$\ref$$ is expressed in terms of $$k$$, it is more usual to quote the value of $$t_$$.