I thought I would continue the topic of the last entry, isotopes, and this time talk about how they are used for dating. The key to using isotopes in this way is that some of them are radioactive, meaning that some isotopes decay into other elements. Without getting too much into the quantum physics of it, the reason decay happens is because this process causes an atom to lose energy, which tends to be a more stable state. There are a few different modes of radioactivity, but for our purposes we'll focus on two: alpha and beta decay. In alpha decay, an atom loses two neutrons and two protons (an alpha particle) from the nucleus, reducing its atomic number by two and its weight by four. In beta decay, a neutron changes into a proton, releasing an electron (a beta particle) in the process, increasing its atomic by one but not changing its weight. Radiometric dating is the method of using this radioactive process to date things from the past.
Take carbon dating. Carbon occurs in three different isotopes on the Earth. Most of it is carbon-12. About 1% is carbon-13, and about one part per trillion is carbon-14. Carbon-12 and carbon-13 are stable, meaning they don't radioactively decay. Carbon-14 is radioactive, and decays, via beta decay, into nitrogen-14. It's half-life is around 5,700 years. This means that in 5,700 years about half of the carbon-14 in any sample will have decayed. Wait another 5,700 years and half of the remaining carbon-14 will have decayed, leaving 1/4 of the amount we started, and so on. So the amount of carbon-14 is exponentially decreasing over time.
Animals and plants incorporate carbon (which they get from their food or from carbon dioxide) into their bodies as part of the various organic molecules that make up their cells and other structures. They incorporate all the isotopes in the same ratio as the environment around them. This ratio is well known both for the present, and for the past. Once an organism dies it stops taking in new carbon. The carbon-14 that is part of their bodies starts to radioactively decay, bringing the ratio of carbon-14 to carbon-12 down. So by looking at this ratio in a fossil sample, and knowing the half-life of carbon-14, we can get an estimate of the age of the specimen. As an example, if the ratio of carbon-14 to carbon-12 is half of what it should be, then we know that one half-life has passed, so the specimen is 5,700 years old.
A diagram showing how carbon-14 gets made and how it gets incorporated into fossils
One thing to note about carbon dating is that the half-life of carbon-14 is relatively short. You can imagine that after a more than few half-lives the amount of carbon-14 that hasn't decayed is very small. This means that carbon dating is only useful to date objects no older than about 60,000 years ago (about 10 half-lives). This means we do not use carbon dating to date dinosaurs! Dinosaurs lived over 60 MILLION years ago. Carbon dating is best for things from the relatively recent past, like the Pleistocene megafauna - sabertooths, mastodons, etc.
A figure showing the uranium=lead decay in a rock sample
So what do we use for dinosaurs? We would have to use a different radioactive isotope, one with a longer half-life. There are actually a couple different choices; Uranium-Lead and Potassium-Argon dating are the most widely used in paleontology. In both cases the first element is the starting element, some sort of radioactive isotope, (the "parent") and the second is the stable product of radioactive decay (the "daughter"). In both of these cases, rather than look at the ratio of a radioactive isotope to a stable isotope, you simply look at the ratio of parent to daughter. If it's 1-to-1, then one half-life has passed. If it's 1-to-3, then two half-lives have passed, and so on. The half-lives of both of these radioactive parents have half-lives on the order of hundred of millions of years, so they can be used for dating much older fossils than carbon dating.
A graph showing the percentage of parent and daughter elements in a radioactive sample
There is one caveat to using these is that in the case of uranium-lead or potassium-argon dating - we don't date the fossils directly. Instead we date rocks, and use these to date fossils. It's a longer story, ancient really, so stay tuned...