# Atomic Chain of Decay Due to Half-Life

FROM THE LECTURE SERIES: THE JOY OF SCIENCE

## Research in radioactive elements for minerals led to the discovery of three distinct kinds of radioactive decay. Two fascinating and very important characteristics of radioactivity are called the half-life and decay chains. While half-life is the measure of how rapidly a collection of radioactive atoms decay, decay chain is the connected sequence of radioactive events.

### Half-life of Atoms

Half-life is the measure of how rapidly a collection of radioactive atoms decay.

Every isotope is either stable or radioactive. The vast majority of atoms in our environment are stable, of course, but the radioactive isotopes are the vast majority of known isotopes. The half-life is the time that, on average, it takes for half of that collection of isotopes to decay.

### Carbon-14 Dating

If someone gives you a million atoms of an isotope with a half-life of one day, after 24 hours, there are only going to be half a million of those radioactive isotopes left. A day later, there are only going to be a quarter of a million; and each subsequent day, half of that collection, on average, will have decayed.

These half-lives are extremely important for radiometric dating. You can date the age of an object if you know, first, the number of radioactive isotopes that you started with, their half-life, and finally, the number that you ended with. It’s like a ticking clock inside the sample that you hold. A good example is carbon-14 dating. For example, the Shroud of Turin was dated by carbon-14 dating.

Carbon-14 has a half-life of 5,000 years; and every living thing, as it takes in carbon, takes in a small fraction, about one atom in a million, of carbon-14. So as long as you’re alive, one atom in a million of your body is carbon-14; but as soon as you die, or as soon as any living thing dies, the clock starts ticking, because the carbon-14 starts decaying.

After 5,000 years, you have only half as much carbon-14; after ten thousand years, only a quarter as much, and so forth. So you can date objects by measuring how many carbon-14 atoms are left. In the case of the Shroud of Turin, it turned out that the burial cloth—made of linen, a plant material—was only a little more than a thousand years old, and therefore, it was very unlikely that it was the burial cloth of Jesus.

This is a transcript from the video series The Joy of ScienceWatch it now, on Wondrium.

### Chain of Decay

Another key concept related to radioactivity is the decay chain, which is a connected sequence of radioactive events.

When a radioactive isotope undergoes alpha or beta decay, a new isotope of a new element is formed, and very commonly, almost always, that new isotope is radioactive as well. So when one isotope decays, it leads to another radioactive isotope, which leads to another, and another, in what is called a decay chain.

There are radioactive isotopes all around us all the time. By far, the most common radioactive isotope in our surroundings is uranium-238, which represents about one atom in every two million in rocks and soil. Uranium-238  has a very long half-life, about four and a half billion years, and that’s why there’s still so much of it around from the origin of the earth.

### Uranium-238

Uranium-238 undergoes alpha decay, and it decays in a single step down to thorium-234; two protons are lost, two neutrons are lost, and the element changes from uranium to thorium. The half-life of thorium-234 is just 24 days, and it decays, by beta decay, up to protactinium, with a half-life of just about seven hours, and then back up to uranium-234.

After three more alpha decays, we come to radon-222, and something very new happens.

All the previous elements described in this decay chain are metals, and they bond very easily in minerals; they become part of the soil and are locked in the soil through chemical bonds. However, Radon, element 88, is an inert gas, and an inert gas bonds to nothing.

So all of a sudden, this atom is released from the soil, it is released from the rock; it goes up, it floats around, for example, in someone’s basement. If the basement is well-insulated and well-sealed, radon concentrations can build up.

The true concern about radon is that this radioactive isotope goes through a number of very, very quick transformations. In a few minutes, it transforms to another isotope, and then another one and another one, through a cascade of eight radioactive events, each one of which adds radioactivity to the environment. This is why radon is such a concern.

### Common Questions about the Atomic Chain of Decay Due to Half-Life

Q: What is the concept of half-life?

Half-life is the measure of how rapidly a collection of radioactive atoms decay.

Q: What is a famous example where carbon-14 dating was used?

The Shroud of Turin was dated by carbon-14 dating. It turned out that the burial cloth—made of linen, a plant material—was only a little more than a thousand years old.

Q: Why is the existence of radon in basements concerning?

Radon, a radioactive isotope, goes through a series of transformations in its chain of decay in a short amount of time. Since each transformation adds to the radioactivity of the environment, it can be dangerous for humans.