### Example of carbon dating equation

However it is possible, when dating very old rocks for instance, to use longer lived isotopes for dating on a longer time scale. In actually measuring these quantities, we take advantage of the fact that the rate of decay how many radioactive emissions occur per unit time is dependent on how many atoms there are in a sample this criteria leads to an exponential decay rate. Since physics can't predict exactly when a given atom will decay, we rely on statistical methods in dealing with radioactivity, and while this is an excellent method for a bazillion atoms, it fails when we don't have good sample sizes. The above calculations make several assumptions, such as that the level of 14 C in the atmosphere has remained constant over time. While 12C is the most abundant carbon isotope, there is a close to constant ratio of 12C to 14C in the environment, and hence in the molecules, cells, and tissues of living organisms. Carbon dating is based upon the decay of 14C, a radioactive isotope of carbon with a relatively long half-life years. Decay of radioactive isotopes Radioactive isotopes, such as 14C, decay exponentially. It's a semi-long story, so bear with me. If the amount of carbon 14 is halved every 5, years, it will not take very long to reach an amount that is too small to analyze. Calculating radiocarbon ages also requires the value of the half-life for 14 C, which for more than a decade after Libby's initial work was thought to be 5, years. The half-life of an isotope is defined as the amount of time it takes for there to be half the initial amount of the radioactive isotope present. The stable form of carbon is carbon 12 and the radioactive isotope carbon 14 decays over time into nitrogen 14 and other particles. On the other hand, if tons of half-lives have passed, there is almost none of the sample carbon 14 left, and it is really hard to measure accurately how much is left. During the lifetime of an organism, carbon is brought into the cell from the environment in the form of either carbon dioxide or carbon-based food molecules such as glucose; then used to build biologically important molecules such as sugars, proteins, fats, and nucleic acids. That's actually kind of cool. So, the fossil is 8, years old, meaning the living organism died 8, years ago. We can use a formula for carbon 14 dating to find the answer. Carbon Dating Carbon dating to determine the age of fossil remains In this section we will explore the use of carbon dating to determine the age of fossil remains. Simplifying this expression by canceling the N0 on both sides of the equation gives,. William Baker Answer Carbon 14 C14 is an isotope of carbon with 8 neutrons instead of the more common 6 neutrons. So, if you had a fossil that had 10 percent carbon compared to a living sample, then that fossil would be: When a date is quoted, the reader should be aware that if it is an uncalibrated date a term used for dates given in radiocarbon years it may differ substantially from the best estimate of the actual calendar date, both because it uses the wrong value for the half-life of 14 C, and because no correction calibration has been applied for the historical variation of 14 C in the atmosphere over time. Solving for the unknown, k, we take the natural logarithm of both sides,. A formula to calculate how old a sample is by carbon dating is: Other radioactive isotopes are also used to date fossils. Thus, we can write: Or in other words, if we have a box, and we don't know how old it is but we know it started with carbon 14 atoms, and we open it and find only 50 carbon 14 atoms and some other stuff, we could say, 'Aha!