However, now the "thin slice" is an interval of time, and the dependent variable is the number of radioactive atoms present, N(t). If we have a sample of atoms, and we consider a time interval short enough that the population of atoms hasn't changed significantly through decay, then the proportion of atoms decaying in our short time interval will be proportional to the length of the interval.
We end up with a solution known as the "Law of Radioactive Decay", which mathematically is merely the same solution that we saw in the case of light attenuation.
In this second article he describes the phenomenon of radioactive decay, which also obeys an exponential law, and explains how this information allows us to carbon-date artefacts such as the Dead Sea Scrolls.
In the previous article, we saw that light attenuation obeys an exponential law.
The process of carbon-14 dating was developed by William Libby, and is based on the fact that carbon-14 is constantly being made in the atmosphere.
It is incorporated into plants through photosynthesis, and then into animals when they consume plants.
Draw the log graph and deduce l (and hence half-life).
The experimental scatter should be obvious on the graph, and hence the value of a straight line graph can be pointed out.
Carbon has two stable, nonradioactive isotopes: carbon-12 (12C) and carbon-13 (13C).There are also trace amounts of the unstable radioisotope carbon-14 (14C) on Earth.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.We get an expression for the number of atoms remaining, N, as a proportion of the number of atoms N, where the quantity l, known as the "radioactive decay constant", depends on the particular radioactive substance.Again, we find a "chance" process being described by an exponential decay law.The following tools can generate any one of the values from the other three in the half-life formula for a substance undergoing decay to decrease by half.