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.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.In the case of the Dead Sea scrolls, important questions required answers. Did they really date from around the time of Christ? Using Libby's radiocarbon dating technique, the scrolls have been dated, using the linen coverings the scrolls were wrapped in.One scroll, the Book of Isaiah, has been dated at 1917BC ±275 years, certainly long before the time of Christ.Current research involves a theoretical description of X-ray beam spectra.Radiocarbon dating (also referred to as carbon dating or carbon-14 dating) is a method for determining the age of an object containing organic material by using the properties of radiocarbon, a radioactive isotope of carbon.This question can be answered using a little bit of calculus. Once we have an expression for t, a "definite integral" will give us the mean value of t (this is how "mean value" is defined).
To show this, we needed to make one critical assumption: that for a thin enough slice of matter, the proportion of light getting through the slice was proportional to the thickness of the slice.
Here isotopes with longer half lives are used, which enables dating of geological formations and rocks. For example, in lava form, molten lead and Uranium-238 (standard isotope) are constantly mixed in a certain ratio of their natural abundance.
Once solidified, the lead is "locked" in place and since the uranium decays to lead, the lead-to-uranium ratio increases with time.
Again, we find a "chance" process being described by an exponential decay law.
We can easily find an expression for the chance that a radioactive atom will "survive" (be an original element atom) to at least a time t.