How to do carbon dating math

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In the previous article, we saw that light attenuation obeys an exponential law.

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.

We'll denote the magnitude of the rate of decay of the Carbon 14 nuclei as R. In a similar way, dating charcoal found at Stonehenge gives ages of approximately 3798 ±275 years, and, when used on some of the oldest archaeological artefacts in the Americas, the technique gives ages of approximately 25,000 years, corresponding to a time of significantly lower sea levels and supporting the theory that the very first humans in the "New World" crossed the Bering Straits by foot from Siberia into Alaska.

This magnitude is equal to the rate that beta particles are detected. Incidentally, other "larger time scale" radio-dating techniques exist, apart from Libby's radiocarbon method.

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.

He graduated in 1977 with a BSc Honours in Applied Physics from the University of Lancaster, and obtained an MSc in Medical Physics from the University of Leeds in 1987.

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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.

The steps are the same as in the case of photon survival.

On average, how much time will pass before a radioactive atom decays?

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