Radioactive Decay Processes

Amelia Beissler - Fall 2024

The Main Idea

When an atom or compound has extra particles, whether that be an electron, proton, or neutron, it is defined as unstable. This means that the binding energy of the atom and the strong and weak nuclear forces struggle to keep the atom together due to the excess mass. This can lead to spontaneous reactions, where an atom will release a particle or gamma ray in order to lose energy and return to a stable state or transform into a different nuclide that is more stable. Out of all the naturally occurring elements, there are about 251 isotopes that are stable and 28 unstable elements, the most notable among those being Uranium and Thorium.

A key trait of radioactive decay processes is the idea that they are spontaneous and there is no way to truly predict when a molecule will decay. However, with things like the decay constant and half-life, there are ways to predict how a larger group of molecules will behave. The half life is an intrinsic property of each isotope, an amount of time that signifies how long it will take for half of the atoms or molecules to decay into more stable nuclides. The decay constant can be derived from the half life, and helps predict decaying behaviors.

The actual radioactive decay process starts with an excited, unstable parent nuclide. As stated above, at a completely spontaneous point in time, the parent nuclide will decay releasing a particle or gamma ray to return the atom to a more stable state. With this reaction, the energy that is released is positive, which means it is exothermic and does not require any energy to be input for the reation to occur. Sometimes, especially with more atoms, it also takes a few decay processes to return the atom to a stable state.

Spontaneous fission is sometimes considered a radioactive decay process, but not always. In this page, the four main types of decays will be discussed: alpha, beta plus, beta minus, and electron capture decay. More information on fission can be found under the same subcategory as this one.

Alpha Decay

Visualization of Alpha Decay

Alpha decay is common with heavier nuclides, usually bismuth and above, and they usually decay until they reach a stable lead isotope. An alpha particle, which is composed of two protons and two neutrons tightly bound together, is born with a daughter nuclide that has an atomic number two less than its parent nuclide and a mass number four less than its parent. A basic example of an alpha decay reaction is below.

[math]\displaystyle{ _Z^AX \rightarrow _{Z-2}^{A-4}Y + _2^4He + Q }[/math]

In this scenario, Q represents the energy that is released when this reaction is undergone. It can be found using the mass difference, a simple calculation of subtracting the mass of the products from the reactants. This energy is split between the alpha particle and the recoil daughter nucleus. The kinetic energy of the alpha particle can be found from a derivation of conservation of momentum.

[math]\displaystyle{ KE = Q/(1 + (m_a/M)) }[/math]

One key defining feature of alpha particles is how they can be blocked by a piece of paper. Since they are unable to reach under skin, they are not particularly deadly, unless it is ingested someway or another. If alpha particles can make it into your bloodstream or your airways, they can pose a big threat because they impart more radiation dosage than the other particles. It is generally considered to be around 20x more radioactive than gamma and beta radiation. Due to this nature, alpha emitters can be weaponized as a form of poisoning.

However, alpha particles and the radiation they emit can be helpful as well. Alpha emitters, like radium, have been used to target cancerous tumors to kill via alpha radiation. Another practical use of alpha particles and their radiation is within smoke detectors. They can ionize the small gap of air and the smoke particles can interrupt that current, which causes the alarm to go off.

Beta Decay

Beta particles are another type of decay particle. They occur when the nucleus is comprised of extra protons or neutrons. They have a longer range than alpha particles, able to go through paper, but they are typically stopped by metals. Similar to alpha particles, while they can have harmful radiation effects, in moderation, beta particles can be used to target cancerous cells, especially those that provide shielding that alpha particles are not able to permeate through.

Beta Minus Decay

Visualization of Beta Minus Decay

Beta decay occurs when nuclides have extra neutrons and this reaction occurs to reduce the number of neutrons and make the nuclide more stable. The nuclide loses a neutron and gains an electron and an anti-neutrino (anti-matter particle of neutrino). The basic reaction is shown below.

[math]\displaystyle{ _Z^AX^- \rightarrow _{Z+1}^{A}Y + _{-1}^0e^- + ^-_v + Q }[/math]

The process of a neutron turning into an electron and an anti-neutrino is done by emitting a boson, which switches one of the quarks on the neutron from a down quark to an up quark. This converts it into a proton while the boson turns into the electron and anti-neutrino.

The energy that is emitted by this reaction due to the mass difference is split among the daughter nuclide, the electron, and a small bit to the anti-neutrino.

Another use of beta decay, including beta minus decay, is quality control, especially with paper. Firing the beta particles at the paper or product can determine whether the product was made too thick or too thin on whether or not the particle makes it through the product.

Beta Plus (Positron) Decay

Visualization of Beta Plus Radioactive Decay

Beta plus decay occurs when the nucleus is proton-rich, which means it has extra protons. After going through a decay, the proton is converted into a neutrino (another elementary particle with a small mass and neutral charge) and a positron (an electron's antimatter particle: same mass, but opposite charge, and represented by a positive e). This way charge is conserved within the reaction. A standard beta plus decay reaction is below.

[math]\displaystyle{ _Z^AX^+ \rightarrow _{Z-1}^{A}Y + _1^0e^+ + v + Q }[/math]

Due to the fact that the proton is decaying into two smaller particles, the reaction loses about two electrons worth of mass. As a reminder, the rest energy of an electron is 0.511 MeV, so the mass difference energy of the reaction (Q) must be twice that value in order for the decay to occur (1.022 MeV) and have the beta plus particle actually have energy. This is also because a positron is not stable, and always undergoes annihilation with an electron, creating 2 gamma rays that are also 0.511 MeV. Since the Q value of the reaction won't always be above 1.022 MeV, beta plus decay also competes with electron capture.

One practical use of beta plus decay is that it is a source of positrons for positron emission tomography, or PET scans, which are used to look at various organs and tissues to detect if anything is wrong. One of its more well known uses is detecting cancer and tumors.

Electron Capture

Visualization of electron capture

Electron capture is another decay that occurs when the nucleus is proton rich. However, in this decay process, the nucleus captures an orbital electron as its wave motion brings it close enough to the nucleus. This causes a reduction in the number of protons! Most of these captured electrons come from the K shell, and while they are captured by the nucleus, another electron will take its place, emitting a very small EM ray. As you can see below, the electron capture reaction also emits a neutrino.

[math]\displaystyle{ _Z^AX^+ + _{-1}^0e^- \rightarrow _{Z-1}^{A}Y + v + Q }[/math]

As we can see with the positively charged nuclide and the capturing of the electron, it is able to maintain a conservation of charge. Unlike the beta plus decay, the electron capture decay does not lose the mass and so it does not have to meet a minimum threshold. Thus, for any Q value below 1.022 MeV, electron capture is the only way for nuclides to "lose" protons.

Electron capture has some very unique uses, ranging from detectors to mass spectrometry (due to being able to be used with ionization).

Gamma Decay

Visualization of Gamma Radioactive Decay

Gamma emission is the releasing of any excitation energy by the emitting of a gamma or EM ray. When protons or electrons are not in the lowest energy state, or it's ground state, the emission of a gamma ray allows it to jump to a lower orbital. It always follows one of the other processes above, which is why it is also debated as to whether it is truly a decay process. One notable difference is that the nuclide does not change in this reaction like it does with the others, it is simply just no longer excited. Sometimes gamma decay is included withe the previous written chemical reactions, or sometimes it is written as its own reaction. Gamma decay often competes with a non-radioactive decay called internal conversion.

Decay Graphs

When looking at decay processes, they usually occur in chains that continue on until the nuclide is stable. It relays the various processes and likelihood of each occurring, as pictured below. These can be calculated by the numerous trials that have been run over the years, by IAEA (International Atomic Energy Agency), but other groups create their own as well.

The decay graph used as an example below is from 64Cu (unstable) to either 64Ni or 64Zn.

Example of a Radioactive Decay Flow Chart

See also

Further reading

read the pages on fission: https://www.physicsbook.gatech.edu/Nuclear_Fission

read the pages on fusion: https://www.physicsbook.gatech.edu/Nuclear_Energy_from_Fission_and_Fusion

internal conversion: https://en.wikipedia.org/wiki/Internal_conversion

External links

The IAEA website interactive decay chart: https://www-nds.iaea.org/relnsd/vcharthtml/VChartHTML.html

Model for various nuclear events: https://www-nds.iaea.org/exfor/endf.htm

References

https://en.wikipedia.org/wiki/Beta_decay

https://en.wikipedia.org/wiki/Stable_nuclide

https://en.wikipedia.org/wiki/Radioactive_decay#:~:text=Radioactive%20decay%20(also%20known%20as,unstable%20nuclei%20is%20considered%20radioactive.

https://en.wikipedia.org/wiki/Alpha_particle

https://en.wikipedia.org/wiki/Electron_capture

https://openstax.org/books/university-physics-volume-3/pages/10-4-nuclear-reactions