In this lesson, we will learn how to explain the half-life of radioactive elements. The radioactivity of an atom is dependent on the stability of its nucleus. The nucleus, found at the center of the atom, is made up of protons and neutrons. The nucleus we’ve drawn here is the nucleus of a neon-20 atom. We can represent this nucleus another way by indicating that it has 10 protons and 10 neutrons. Neon-20 happens to be a stable isotope. The 10 protons and 10 neutrons in the nucleus are content to stay there together permanently. However, some nuclei are unstable, especially the nuclei of the heavier elements on the periodic table. For example, polonium-210 has an unstable nucleus. And this unstable particle will spontaneously break down into two or more parts to reach a lower-energy, more stable configuration.
In polonium’s case, it releases a chunk of two protons and two neutrons called an alpha particle. By releasing an alpha particle, a polonium atom with 84 protons becomes a stable lead atom, with 82 protons. When a nucleus releases particles and shrinks in this way, we call that radioactive decay. When the nucleus of an element or isotope is unstable, we call that element or isotope radioactive. The radio- in radioactive shares the same root word as the word radiation. The instability of the nucleus causes energy in particles to radiate outward. In the case of polonium-210, it radiates an alpha particle. The decay of the polonium-210 atom also involves the release of a small amount of gamma rays, or energy.
A third type of radiation present in the radioactive decay of other elements and isotopes is a beta particle or a high-energy electron. The radiation of these particles and rays can damage living tissue and alter DNA, potentially causing cancer. Scientists who work with radioactive materials are constantly monitored to ensure that they aren’t exposed to too much radiation. Marie Curie, one of the pioneers in discovering radiation, eventually died of health complications related to radiation exposure. Of course, not all polonium atoms are the same. Polonium has different isotopes or versions of the polonium atom with differing numbers of neutrons. The two most common isotopes of polonium, polonium-210 and polonium-209, both have unstable nuclei.
We might be wondering, how do we quantify or compare the instability of two different elements or isotopes? The answer is something called a half-life. Let’s say we start with a sample of 100 percent polonium-210. If we wait 138.4 days and measure what remains, we will find that half of the polonium-210 remains, while the other half has decayed into lead. The half-life is the time it takes for one-half of a quantity of a radioactive isotope to decay. The half-life of polonium-210 is 138.4 days. If we wait another half-life or another 138.4 days, the amount of polonium-210 will be cut in half once again, this time down to 25 percent remaining. Every 138.4 days, half of the remaining polonium-210 will decay into lead. This is how it works for any radioactive element or isotope. The half-life is the time it takes for half of a sample of that element or isotope to decay.
In the case of polonium-209, the half-life is 102 years. That means it takes 102 years for half of the sample to decay and another 102 years for the next 25 percent of the sample to decay. Although atoms of both of these isotopes have unstable nuclei, we can say that polonium-209 with its longer half-life has atoms with more stable nuclei. A longer half-life means slower, more gradual decay and less radiation emitted over a given time period. On the other hand, polonium-210, with its shorter half-life, is less stable. Its atoms more readily break down into lead and alpha particles. And it releases more radiation over a given time period.
It’s also worth noting that the half-lives of isotopes have a wide range of possible values. An extremely unstable isotope could have a half-life of near nanoseconds or even shorter, while an extremely stable isotope could have a half-life over trillions of years long. We can visualize radioactive decay and half-lives in graphs as well. This graph shows the radioactive decay of fermium-253. This graph shows us the percent of the radioisotope remaining on the 𝑦-axis over the course of the number of days indicated by the 𝑥-axis. We might look at this graph and wonder, how long is the half-life of fermium-253? Well, we know that we start at time zero with 100 percent of the isotope remaining. To find the half-life of fermium-253, we need to find the time when only 50 percent of the isotope remains.
Following the lines on the graph, we can see that 50 percent of the isotope remains after three days. So our half-life is three days. As a reminder, 50 percent of the radioisotope remaining means that 50 percent of the fermium-253 particles in the initial sample have decayed, releasing energy and particles to form a more stable arrangement. In the case of fermium-253, it decays into the element californium.
Another question we might wanna know the answer to is, how much remains after four half-lives? We already know that 50 percent of the fermium-253 remains after one half-life. After two half-lives or six days, 25 percent of the fermium-253 remains. Another half-life later and the remaining radioisotope gets cut in half once again, this time down to 12.5 percent. After our fourth and final half-life at 12 days and another cut in half of the remaining radioisotope, we end up with 6.25 percent of fermium-253 remaining. So our final answer is 6.25 percent.
One takeaway from this graph is that radioactive decay is extremely consistent to the point of being mathematically predictable. While the length of the half-life will change from isotope to isotope, we do know that for any isotope after one half-life, 50 percent of the original radioactive isotope will remain. After two half-lives, 25 percent will remain. After three half-lives, 12.5 percent will remain and so on. So we can use the half-life of an isotope to accurately predict, with the help of a mathematical model, how much of it will remain at any given time. Surprisingly enough, we can actually measure radiation as it happens using an ingenious device called a Geiger–Muller tube.
A Geiger–Muller tube is essentially a battery connected to two electrodes. The negatively charged cathode is an aluminum tube, while the positively charged anode is the central wire suspended in the middle of the aluminum tube. The tube is enclosed and filled with a low-pressure noble gas such as argon. Interestingly enough, in the absence of radiation, this device is an incomplete circuit. The central wire and the aluminum tube do not touch. And there’s nothing to carry the flow of charged particles across this gap in the circuit, that is, until radiation enters the mica window on the front of the tube.
When radiation strikes one of the noble gas particles, in this case an argon particle, it can knock free an electron, creating an argon cation. These electrons are attracted to and accepted by the positively charged central wire anode. These electrons flow through the circuit, ending up at the negatively charged aluminum tube cathode at the other end. The positively charged argon ions are attracted to the negative cathode. So at the cathode, the electrons that have flowed through the circuit eventually get donated back to argon ions, creating argon atoms once again.
So we’ve traced the circuit from beginning to end. We can say that a Geiger–Muller tube is an incomplete circuit that is completed when radiation ionizes the noble gas particles in the gap in the circuit. More radiation means more electrons knocked off of argon atoms and a stronger electric current.
One part of the Geiger–Muller tube that we haven’t talked about yet is the counter. In many Geiger–Muller tubes, the counter is a mechanical device that turns electrical current into audible clicks. As the Geiger–Muller tube encounters more radiation, the counter will create a louder, denser crackling sound, although in many Geiger–Muller tubes, the mechanical counter has been replaced by a simple digital readout.
The counter from a Geiger–Muller tube can give us a reading in CPM or counts per minute. This unit is dependent on the number of clicks from the machine. It does not directly tell us the amount of energy in the radiation released or the number of particles that have decayed. Nevertheless, a CPM reading from a well-calibrated Geiger–Muller tube can give us important information about the intensity of the radiation and how hazardous it is. Overall, Geiger–Muller tubes are a clever, handheld way to measure radiation.
As we mentioned earlier, different isotopes of an element have different half-lives. This works to our advantage in carbon dating. A significant source of carbon on Earth is the carbon dioxide in the atmosphere. This carbon is absorbed by plants during photosynthesis. The carbon is used in part to make the fruits, leaves, and other edible parts of plants that are then eaten by animals. The animals use carbon to build their bodies and also breathe out excess carbon dioxide as waste back into the atmosphere. The vast majority of carbon atoms in this system are the stable isotope carbon-12. However, an extremely small number about one out of every 1.35 trillion atoms are the radioactive isotope carbon-14.
While carbon-14 naturally decays, cosmic rays from the sun can strike nitrogen atoms and turn them in to carbon-14 atoms. Because the carbon-14 created by cosmic rays perfectly replenishes the decaying carbon-14, the isotopes of carbon in the atmosphere and in living things maintain this constant ratio. However, when an organism dies and leaves behind, say, bones, fur, or wood, the carbon in those materials is removed from the carbon cycle. Its levels of carbon-14 will no longer be able to be replenished by cosmic rays. Without those cosmic rays, the ratio of carbon-14 to carbon-12 will begin to decline. The half-life of carbon-14 is 5730 years. So every 5730 years, half of the carbon-14 will decay.
Because the ratio of carbon-14 to carbon-12 begins to decline upon the death of an object and because the decay of carbon-14 is mathematically predictable, we can estimate the age of a once-living object by measuring the carbon-14 to carbon-12 ratio and comparing it to the living ratio. For example, what if we found a fossilized piece of plant matter with a ratio of one carbon-14 atom for every 2.70 trillion carbon-12 atoms? This ratio is half of the living ratio. In order for the ratio to be cut in half, one half-life must have elapsed, so the age of this object is 5730 years.
What if we find a piece of bone with one carbon-14 atom for every 21.6 trillion carbon-12 atoms? Well, this ratio is one sixteenth of the living ratio of carbon-14 atoms to carbon-12 atoms. For the ratio to decrease by a factor of 16, four half-lives must have elapsed. So the age of this object is four half-lives, or 22920 years old. It’s worth noting that carbon dating works on objects up to about 50000 years old. Objects older than that have such a trace amount of carbon-14 that it’s difficult to accurately measure the ratio of carbon-14 to carbon-12. We can carbon-date fossils like bones, shells, and plants to get a better understanding of the biology of the age. We can also date the objects that humans have made out of living things as well, such as woody paper, animal leather, or bone tools.
Now that we’ve learned about half-lives, let’s review some key points. Unstable nuclei are radioactive. They decay by releasing energy and particles. The half-life of an isotope is the time it takes for half of the quantity of that isotope to decay. The more stable the nucleus, the slower it will decay and the longer half-life it will have. Radioactive decay is mathematically predictable. Geiger–Muller tubes measure radiation. In a Geiger–Muller tube, radiation ionizes noble gas particles, which completes a circuit whose current we can measure. Carbon-14 dating lets us find the age of once-living objects. The prevalence of carbon-14 begins to decline after the organism dies. So the ratio of carbon-14 atoms to carbon-12 atoms can indicate the age of the object.