We wondered what it might be like to swap classes, perhaps my students could learn to swoon over the moon as hers do, and perhaps her students might enjoy raiding my language for their own purposes. I would tell them about the daughters of the moon, that carry the history of their mothers with them in their cores, bearing it forward billions of years. A process in which decay does not mean loss and despair, but instead transformation and eventual stability.
My students are peevish about the moon because of a problem we worked about dating the rocks brought back by the Apollo missions. It's a problem that crosses two of the topics we've discussed, chemical kinetics and nuclear chemistry. I'm fond of the problem because it uses material from the very beginning of the course and from the very end and shows both how they are connected and can be used in a very practical way by another field. But making connections can be challenging, and at the end of the semester my students are tired. They are less intrigued and more resigned.
The moon, like the earth and pretty much everything on it, contains radioactive elements. Sometimes these radioactive atoms are versions of stable elements, sometimes all of the versions of an element are radioactive. (Carbon-14 is radioactive while the most common carbon atoms on earth, called carbon-12, are not. On the other hand, there are no stable versions of uranium.) Radioactive elements are like tiny clocks, transforming themselves from one element into another at a particular and fixed rate. Comparing the amounts of a radioactive element at two different times can tell you the time spanned. For example, if an artifact like a wooden carving has 50% of the carbon-14 that it had when it was made, 5500 years have elapsed since its creation. We say carbon-14 has a half-life of 5500 years.
These built-in atomic clocks can run on short timescales, a matter of days or seconds, or on incredibly long timescales. The rule of thumb is that a given radioisotope can measure out time spans up to 10 times the half-life. So carbon-14 can be used to date materials up to about 55,000 years old. Potassium-40, the main reason human beings themselves are radioactive, has a half-life of 1.3 billion years and can time processes going back to the Big Bang.
Uranium-238 gives birth to daughters such as thorium-234, radium-226 and polonium-218. (I note that some of these daughters were discovered by a daughter and a mother, Marie Curie.) Eventually all her energy is exhausted and U-238 finally plops down onto the island of stability as lead-206. This is not a short process, it takes 45 billion years for (nearly) all of the U-238 to find its way to the stable space of lead-206. But her daughters will hold tight to her history all along the way. And we can read it in their very identities.
