# How to do carbon dating math

$$ So either the answer is that ridiculously big number (9.17e7) or 30,476 years, being calculated with the equation I provided and the first equation in your answer, respectively. Okay now that you know a little bit more information, you can try to find out how much carbon is in element.

But the question is, when does an atom or nucleus decide to decay? So it could either be beta decay, which would release electrons from the neutrons and turn them into protons. And normally when we have any small amount of any element, we really have huge amounts of atoms of that element. That's 6.02 times 10 to the 23rd carbon-12 atoms. This is more than we can, than my head can really grasp around how large of a number this is. Carbon-14 dating can be used on objects ranging from a few hundred years old to 50,000 years old. Libby and others (University of Chicago) devised a method of estimating the age of organic material based on the decay rate of carbon-14.This change in the amount of 14C relative to the amount of 12C makes it possible to estimate the time at which the organism lived.A fossil found in an archaeological dig was found to contain 20% of the original amount of 14C. I do not get the $-0.693$ value, but perhaps my answer will help anyway.Carbon-14 is produced in the atmosphere when neutrons from cosmic radiation react with nitrogen atoms: C ratio of 0.795 times that found in plants living today. Solution The half-life of carbon-14 is known to be 5720 years. Radioactive decay is a first order rate process, which means the reaction proceeds according to the following equation: is the quantity of radioactive material at time zero, X is the amount remaining after time t, and k is the first order rate constant, which is a characteristic of the isotope undergoing decay.

The method of carbon dating makes use of the fact that all living organisms contain two isotopes of carbon, carbon-12, denoted 12C (a stable isotope), and carbon-14, denoted 14C (a radioactive isotope).

And we saw that they're good if we are trying to figure out how much of a compound we have left after one half-life, or two half-lives, or three half-lives.

We can just take 1/2 of the compound at every period.

If we take the natural log of both sides, what do we get? So the natural log, 0.875 divided by minus 1.2 times 10 to the minus 4, is equal to the amount of time it would take us to get from 400 grams to 350. So if you have 0.875, and we want to take the natural log of it, and divide it by minus 1.-- So divided by 1.2e 4 negative, 10 to the negative 4. Oh, I'll just divide it by this, and then just take the negative of that. So this is equal to 1,112 years to get from 400 to 350 grams of my substance.

The natural log of e to anything, the natural log of e to the a is just a. And I want to know how long-- so I want to know a certain amount of time-- does it take for me to get to 350 grams of c-14? [PHONE RINGS] My cell phone is ringing, let me turn that off. This might seem a little complicated, but if there's one thing you just have to do, is you just have to remember this formula.

So let's do that in this video, just so that all of these variables can become a little bit more concrete.