Random Nature of Radioactive Decay

Definition of the random nature of radioactive decay

Radioactive decay is the process of atoms emitting radiation to achieve another configuration. This radiation can be in the form of alpha particles, beta particles, gamma rays, or neutron particles. During the emission of radiation, an atom changes according to the rules of nuclear equations. What is left after the emission will have a different level of radioactivity.

Atoms emit radiation if they are inherently unstable: for any specific isotope at a certain energy level, every second, there is a certain probability$p$that it will emit an alpha particle. The same goes for the other forms of radiation. These are all different probabilities, and some of those probabilities might be zero, meaning that a particular atom will never undergo a certain type of radioactive decay. These probabilities are entirely determined, but the actual emission process is random: we only know the probability.

Half-lives and the random nature of radioactive decay

If we have a lot of identical atoms within a sample (for example, in a chunk of material) that all have a certain probability per second of decaying, then you can imagine that at some point, only half of the original number of atoms are left in the sample. The bigger the probability of decaying per second, the less time it takes until only half is left.

So, a short half-life indicates that an atom is very radioactive: its probability of decaying in the next second is high.

The random nature of radioactive decay now tells us that after one half-life, it is not guaranteed that exactly half of the original atoms remain, but that this is just the most likely, and the average outcome. Any other number of remaining atoms has a lower probability of happening. However, the chances of exactly half of the atoms remaining from an initially very large number of atoms are still minimal.

Examples of half-lives

As every radioactive atom has a half-life that we can measure, we can give a few examples and show that the half-lives of different isotopes can differ by wildly different time scales. The half-life of a carbon-14 atom is about 5700 years, while the half-life of a uranium-235 atom is about 700 million years! This means that carbon-14 is more radioactive than uranium-235, as carbon-14 isotopes have a higher probability of decaying than uranium-235 in the next second. On the other end of the spectrum, copernicium-277 has a half-life of just under a millisecond, making the average lifespan of a copernicium-277 atom very short: this isotope is highly radioactive.

Causes of the random nature of radioactive decay

It might be disappointing, but we will have to accept that every atom simply has an intrinsic probability of decaying every second. For stable isotopes, and thus not radioactive, this probability is zero. For radioactive isotopes, this probability can be measured and is known for many isotopes. The factors that cause this exact probability, and therefore the real causes of the random nature of radioactive decay, are far outside the scope of this article.

You can think of a radioactive atom as an unstable upright pencil. It is in a high-energy state and wants to fall to a lower-energy state. It would only take a tiny gust to make the pencil fall. Still, we know nothing about the exact wind conditions around the pencil, only about the general weather (which can be compared to the probability of radioactive decay). In our eyes, the pencil has a tendency to fall, but we do not know when the deciding nudge will happen. We can only say that in a storm, the pencil will most likely fall earlier than in calm weather, just like atoms with a smaller half-life will most likely decay earlier than atoms with a larger half-life.

Effects of the random nature of radioactive decay

The random nature of radioactive decay states that some atoms in a sample survive while other atoms of the same type decay. This is not a distinguishment based on any difference in properties between the atoms but purely based on probabilities. This also means that only a (random) portion of identical atoms will have decayed at any given time.

The random nature of radioactive decay also lets us calculate the probabilities of the survival of an atom after a specific time. For example, after its half-life, there is a$50\%$chance that an atom in a sample still hasn't decayed yet. After 8 half-lives, there is a$0.4\%$chance that an atom is still intact. Or, equivalently, after 8 half-lives, the most likely outcome is that$0.4\%$of the original atoms remain. The random nature of decay now tells us that there is no way of knowing exactly which atoms remain.

Lastly, the famous exponential graph that illustrates the smooth exponential decay of atoms displays that the original isotope count is roughly halved after every half-life and then draws a smooth line through the data points. This exponential decay is correct on large scales (see the article on half-lives for more on this), but on smaller scales, this graph will be more 'jumpy': in some intervals, there might be no decay, and in other intervals, there might be lots of atoms that decay, purely by chance. The graph will look more like the one shown below.

Examples and experiments on the random nature of radioactive decay

A good experiment to measure the radiation that atoms emit can be done using a Geiger-Müller counter, which is a device that measures alpha, beta, and gamma radiation. If it measures a product of radioactive decay (particle or wave), it will record it as an event.

If you were to hold any radioactive substance close to a Geiger-Müller counter, it would record events at random intervals: there would be no pattern in the intervals between measurement events. This patternless random event recording is experimental evidence that radioactive decay is random in nature. The average frequency of the events will decrease as time goes on because fewer and fewer atoms survive to produce the radiation and cause another event.

Consider two radioactive samples, both with a mass of 1 kilogram. The first sample contains radioactive isotopes with a short half-life, and the other consists of radioactive isotopes with a longer half-life. The sample with a short half-life will have many events occur in rapid succession, but a sample with a long half-life will have longer pauses between events as it will take longer for events to occur. However, the events of both samples will be randomly spaced and thus entirely unpredictable.