Even though radiation is generally something negative, sometimes it can be used for something positive as well. This page describes how certain radioactive elements can be used to tell the age of something.

If you know the half-life of a given radioactive element, you can in principle use the decay of that radionuclide as a clock to measuer a time interval. This clock, however, doesn't go 1, 2, 3, ... in fact it goes more like 1, 2, 4, 8, ... The decay of very long-lived nuclides, ofr example, can be used to measure the age of rocks, that is, the time that has elapsed since they were formed. Measurements for rocks from the Earth and the moon yield a consistent age of about 4.5 X 109 years.

The radionuclide 40K, for example, decays to a stable isotope 40Ar. The half-life of this decay is 1.25 X 109 years. By measuring the ratio of 40K, to 40Ar found in the rock in question, one can then calculate the age of that rock.

For measuring shorter time intervals, in the range of historical interest, radiocarbon dating has proved invaluable. The radionuclide 14C (with half-life of 5730 years) is produced at a constant rate in the upper atmosphere. This radiocarbon mixes with the carbon that is normally present in the atmosphere so that there is about one atom of 14Cfor every 1013 atoms of ordinary 12C. The atmospheric carbon exchanges with the carbon in every living thing on Earth, including humans, so that all living things contain a small fixed fraction of the 14C nuclide.

This exchange persists as long as the organism is alive. After the organism dies, the exchange with the atmosphere stops and the amount of radiocarbon trapped in the organism, since it is no longer being replensished, dwindles away with a half-life of 5730 years. By measuring the amount of radiocarbon per gram of organic matter, it is possible to measure the time that has elapsed since the organism died.

Now, we explain how to calculate this. Half-life refers to the amount of time in which only half the amount of the original substance is left. This follows an exponential decay. This is where we get the fomula

Where Nf is the final amount, Ni is the initial amount, t is the elapsed time, and tau is the half life.

So consider the following problem: If a weirdo named Brent usually has 4 grams of 14C and his dead brother only has 3.95 grams of 14C now, how long has Brent's brother been dead (assuming they both had the same when they were alive)?

So, Nf = 3.95, Ni = 4.00, and tau = 5730 years. So, let's solve:

and so his brother has been dead for 104 years.

tq-nuke@tjhsst.edu