# Radioactive Decay

Radioactive decay is a natural process that happens all around us. This process is what makes nuclear materials like uranium dangerous, but it can also help us figure out how old things are. Radioactive decay is basically how unstable elements become stable again. So, if you ever hear someone talking about radioactive decay, they're just talking about how atoms change over time. It's a pretty cool process!

## The definition of radioactive decay

Radioactive decay is a natural process that happens when atoms are unstable due to having too many particles or too much energy. This causes the atom to release radiation in the form of alpha particles, beta particles, or gamma radiation until it becomes stable again. This process can happen until the unstable atom reaches a stable state where it no longer releases radiation. If you want to learn more about the different types of radiation involved in radioactive decay, check out our article on Alpha, Beta, and Gamma radiation.

## What are the types of radioactive decay?

There are several types of decay depending on the emitted particles. Below we describe two of them: alpha decay and beta decay.

### Alpha Decay

Alpha decay is a type of radioactive decay where an unstable nucleus emits an alpha particle, which is made up of two protons and two neutrons. This emission causes the proton number of the nucleus to decrease by two, while the nucleon number (which is the total number of protons and neutrons) decreases by four. An example of an alpha decay equation is:

Parent nucleus → Daughter nucleus + Alpha particle

This means that the parent nucleus undergoes alpha decay, producing a daughter nucleus and an alpha particle as products.

### Beta Decay

Beta decay is the process by which a beta particle is emitted from the nucleus. A beta particle can either be an electron or a positron. If the emitted particle is an electron, the proton number increases by one, and the disintegration process is called beta minus decay (β−). The simplified equation is:

X → Y + e−

If the emitted particle is a positron, the proton number decreases by one, and the disintegration process is called beta plus decay (β+). The simplified equation is:

X → Y + e+

In these equations, X is a certain unstable element, Y is another element that may be stable, e+ is a positron, and e- is an electron. The upper index denotes the nucleon number (protons + neutrons), while the lower index denotes the proton number.

These are simplified equations because we are just writing some of the particles involved in the process. A thorough analysis shows that there are also neutrinos and antineutrinos in these reactions. Although we will not dive into how these processes work, it’s important to note that there are conservation laws associated with them, like the conservation of electric charge.

The four kinds of radioactive decay are alpha, beta plus, beta minus, and gamma decay. We don’t discuss gamma decay in this explanation.

Radioactive decay happens until the element reaches a point where the excess of energy and particles has been released due to decay processes. The atoms have achieved a stable number of subatomic particles. For most isotopes of elements, especially elements with a low number of protons, we find that stability is mainly achieved by alpha and beta decay.

An example of this decay process is the disintegration of a heavy element like uranium (with a high number of neutrons) into lead. The decay of heavy radioactive elements can take millions of years (as is the case with uranium-238), but it can also take just a few seconds for others.

Isotopes = two or more types of atoms with the same atomic number (number of protons) and different nucleon numbers (number of protons and neutrons).

## How can we calculate radioactive decay?

Radioactive decay is indeed a random process, and it is impossible to predict exactly when a specific atom will decay. However, we can calculate the probability of an atom decaying within a certain time period, using the concept of half-life. The half-life of a radioactive element is the time it takes for half of the atoms in a sample to decay.

We can calculate the decay rate by measuring the number of decayed atoms in a sample of radioactive material over a certain period of time. The decay rate is expressed in units of activity, such as becquerels (Bq) or curies (Ci), which represent the number of decays per second.

The accuracy of decay rate predictions for a high number of atoms allows us to use radioactive decay as a precise measurement of time. Carbon dating, for example, uses the decay of carbon-14 to determine the age of organic materials. Other radioactive isotopes, such as uranium-lead or potassium-argon, are used to date rocks and minerals. These techniques have revolutionized our understanding of the age of the Earth and the evolution of life on our planet.

In addition, the study of radioactive decay has important applications in medicine, such as in nuclear imaging and cancer treatment. It is also used in industry for radiography, sterilization, and power generation in nuclear reactors.

### Radioactive decay formula

The exponential decay equation is a fundamental equation in the study of radioactive decay. It relates the number of unstable nuclei in a sample to time and the decay constant, which is characteristic of each element and isotope. This equation allows us to calculate the rate of decay and predict the number of unstable nuclei at any given time.

One important property of the exponential decay equation is that the ratio of the number of unstable nuclei at two different times is independent of the initial number of unstable nuclei. This means that we can use this equation to determine the age of a sample by measuring the ratio of the number of unstable nuclei to the number of stable nuclei.

Another important property of the exponential decay equation is that the percentage decrease of unstable nuclei is the same for a fixed time interval, regardless of the initial number of unstable nuclei. This means that the decay rate is proportional to the number of unstable nuclei present in the sample.

The graph below shows the decay of a sample with a certain value for the decay constant. As you can see, the total number of unstable nuclei decreases exponentially with time, and the rate of decay is proportional to the number of unstable nuclei present in the sample. The ratio of the number of unstable nuclei at two different times is also shown, illustrating the fact that this ratio is independent of the initial number of unstable nuclei.

Yes, that's correct. The number of unstable nuclei decreases by 50% in each time interval equal to the half-life of the sample. In this example, the half-life is one second, so the number of unstable nuclei decreases by 50% in each second.

After one second, half of the unstable nuclei have decayed, leaving us with 5 unstable nuclei. After two seconds, half of the remaining unstable nuclei have decayed, leaving us with 2.5 unstable nuclei (which is just a statistical measure, as you mentioned). After three seconds, half of the remaining unstable nuclei have decayed, leaving us with 1.25 unstable nuclei.

This exponential decay pattern continues until all of the unstable nuclei in the sample have decayed. The rate of percentual decrease is constant because the decay constant is a fixed characteristic of the element or isotope, which determines the probability of decay per unit time.

### The half life of radioactive decay

The half life is the time it takes for a particular unstable element to have its number of unstable atoms halved. It depends only on the decay constant. Using the general decay equation, we can derive its expression:

## Example of radioactive decay and carbon dating

Carbon plays a vital role in the functioning of organic beings. Although carbon-12 and carbon-13 are stable isotopes, the most abundant is carbon-12, which we usually find in every organic structure. On Earth, we also find an unstable isotope (carbon-14), which is continuously formed in the atmosphere due to the radiation from outer space.

It turns out that organic beings absorb this isotope, and both the production and absorption processes are very well studied. Here are two facts regarding this isotope:

The ratio of carbon-12 and carbon-14 nuclei in alive organic structures is a well-known quantity. The absorption of carbon-14 stops when an organic structure is dead.

These facts give us the number of carbon-14 nuclei when an organic structure died, and by knowing the current amount, we can estimate the time passed since the organic structure’s death. As a result, we can accurately estimate the deaths of humans and animals or give very good estimations for making things with wood and paper. This technique works well in periods under 50,000 years.

Imagine we are given a mummy found in a prehistoric burial site, and we want to know when the body was buried. We are given a carbon-14 analyser. Due to theoretical models, we already know that the number of carbon-14 atoms present in the body before its death was 6 · 1026. With our equipment, we measure that the current number of carbon-14 atoms present in the mummy is 9.77 · 1025.

Theoretical models also tell us that the decay constant of carbon-14 is λ = 1.21 · 10-4 years-1. We can solve the decay equation for t to find that:

As you can see, all we needed for this calculation was the initial number of carbon-14 (which can be estimated by biological models), the value of the decay constant (which is precisely known due to experimentation), and a device to measure the current amount of carbon-14 atoms.

To add to it, the rate of decay of a radioactive substance is measured by its half-life, which is the time it takes for half of the original substance to decay. This can vary widely depending on the substance, ranging from fractions of a second to billions of years.

In addition to carbon dating, radioactive decay is also used in fields as medicine (for radiation therapy and imaging), energy (nuclear power), and geology (to determine the age of rocks and minerals).

It's important to note that radioactive decay can also have harmful effects, as high doses of radiation can damage cells and cause cancer. Therefore, proper safety measures must be taken when working with radioactive substances.

## Radioactive Decay

What is radioactive decay?

Radioactive decay is a process through which unstable nuclei become stable by emitting radiation.

How do radioactive isotopes decay?

Radioactive isotopes usually decay by emitting alpha or beta particles because they need to decrease their neutron number.

What are the four kinds of radioactive decay?

The four kinds of radioactive decay are alpha, beta plus, beta minus, and gamma decay.

Why do atoms go through radioactive decay?

Atoms undergo radioactive decay because there is an excess of particles making them unstable. Radioactive decay is a process through which unstable nuclei become stable by emitting radiation.

What is radioactive decay used for?

Radioactive decay is used to determine the age of certain entities.

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