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.Exactly the same treatment can be applied to radioactive decay.From the equation above, taking logarithms of both sides we see that lt = -ln(N/N.Note that that the domain of F is the interval from zero to 1, which corresponds to the interval of time from zero to infinity.The ratio of C-14 to C-12 in the atmosphere's carbon dioxide molecules is about 1.3×10, and this value is assumed constant for the main part of archaeological history since the formation of the earth's atmosphere.Knowing the level of activity of a sample of organic material enables us to deduce how much C-14 there is in the material at present.
The steps are the same as in the case of photon survival.Since we also know the ratio of C-14 to C-12 originally, we can find the time that has passed since carbon exchange ceased, that is, since the organic material "died".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.Plotting t against F with a value of l=1 gives the graph on the right. The equivalent thickness for the medium in radiation attenuation is known as "half-value thickness".
Similarly, in a population which grows exponentially with time there is the concept of "doubling time".
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.