Half-life

Radioactive decay is a spontaneous, “chancy” process. According to the current theories of particle physics, nothing causes a radioactive atom to decay at a particular time. It just happens at random, or by chance. Nevertheless, there is a certain probability that a radioactive atom will decay over any given period of time. For example, an atom of tritium (hydrogen-3) has a 50% chance of decaying during any 12-year period. So, if you have a large collection of tritium atoms, then 12 years from now you’ll have about half as many, because approximately 50% of the tritium will have decayed by then. And in 12 more years, about half of the remaining atoms will decay, so in 24 years you’ll have about a ¼ as many tritium atoms as you have today. And 36 years from now you’ll have ⅛ as many, and so on.

You may be wondering why physicists care about the time it takes for half of the atoms to decay, rather than the time it takes for all of them to decay. The reason is that the time it takes for all of them to decay depends on how many atoms there were to begin with. But the half-life is more or less the same regardless of how many atoms there are.

The average time it takes for half of a large collection of atoms (of any given isotope) to decay is called the half-life of that isotope. The half-life of tritium (hydrogen-3) is 12 years, as explained above. The half-lives of different isotopes vary dramatically. For example, uranium-238 has a half-life of about 4.5 billion years, lithium-8 has a half-life of about 1 second, and hydrogen-4 has a half-life less than a billionth of a trillionth (1/1022) of a second.

Radiometric Dating

Radioactive decay provides a way of estimating the ages of some objects. Estimating the age of an object based on the radioactive isotopes it contains is called radiometric dating. One of the most useful and important methods of radiometric dating involves carbon-14, a radioactive isotope of the element carbon. Most of the carbon on our planet is carbon-12, a stable (non-radioactive) isotope that has 6 protons and 6 neutrons. Carbon-14 has two extra neutrons, and decays into nitrogen-14 via beta minus decay.

The ages of old bones and other organic (carbon-based) remains can be estimated by measuring the proportion of carbon-14 to carbon-12 that they contain. The older the bones are, the less carbon-14 they’ll contain, because more of the carbon-14 will have decayed into nitrogen. Of course, we can’t estimate the age of the bones in this way unless we know how much carbon-14 the bones contained when the animal died. So how do we figure that out?

Here’s how. While an animal is alive, the matter that constitutes its body is continually replaced by new matter, which comes from the food it eats. The carbon in an animal’s body comes primarily from carbon dioxide in the air, which is absorbed by plants, which in turn are eaten by the animal. For this reason, the ratio of carbon-14 to carbon-12 in a living animal tends to match that of the atmosphere. Surprisingly, the ratio of carbon-14 to carbon-12 in the atmosphere doesn’t change much, even over long periods of time. Although carbon-14 atoms eventually decay into nitrogen-14, new carbon-14 atoms are created when high-energy particles from outer space (called cosmic rays) collide with nitrogen-14 atoms in Earth’s atmosphere. So the ratio of carbon-14 to carbon-12 in an animal’s body remains approximately constant while the animal is alive, but begins to decrease after the animal dies.

The proportion of carbon-14 to carbon-12 in the atmosphere does fluctuate a little over time, but numerous techniques are used to determine when major fluctuations occurred. For example, the ages of tree rings can be determined independently, so measuring the ratio of carbon-14 to carbon-12 in each ring provides a way of determining if and when any major fluctuations occurred during the tree’s lifetime. That information can then be used when estimating the ages of other things, like animal remains.

The methods, accuracy, and limitations of radiometric dating will be further discussed in chapter 9.