Nuclear Instability

How can nuclear instability be represented?

The process of nuclei becoming atomically stable may involve a variety of radiation emissions in combination with each other. We can represent this graphically to aid our understanding. Below we describe the N-Z curve and the decay series.

Elements and isotopes

For light elements, instability is usually due to an excess of neutrons, so only some light isotopes undergo decay processes. For heavy elements, instability is due to an excess of protons and/or neutrons, so all heavy isotopes undergo decay processes.

The N-Z curve

As you’ll see in the graph below, the neutron number is shown on the vertical axis and the proton number on the horizontal axis. You can also see a straight line corresponding to N = Z, which gives a quick reference of elements that are below, above, or on the line. This provides information about their decaying properties.

We can also add another method of representation (like a colour code) that indicates which type of decay unstable atoms undergo to achieve energetic stability. This is usually done to extract general, relevant information about the structure of atoms and their decaying properties.

Here are some of the general features of this graph:

• The curve gets steeper (above the N = Z line) as the number of protons increases. This means that for heavier elements, atoms typically have more neutrons than protons because of the complex interactions happening inside nuclei.
• Alpha decay processes occur in atoms that have a high ratio of neutrons to protons. All unstable isotopes subject to alpha decay are over the N = Z line.
• The ratio of neutron number to proton number is higher for beta minus decay processes than for beta plus decay processes. The latter can also occur even if an atom has more protons than neutrons.
• For light elements (less than 20 protons), stability is roughly achieved by having the same number of protons and neutrons.
• For heavier elements, stability is achieved by having a higher number of neutrons than protons.
• For certain elements, there are various stable isotopes (vertical black lines in the graph). The case of tin (N = 50) is remarkable since it has ten stable isotopes.
• For elements with more than 82 protons, there are no stable forms and decay processes are bound to happen.

There are other kinds of decay processes atoms can undergo, like fission or neutron disintegration, which we will not consider here.

Also, it’s important to note that this graph does not contain the information of the nuclei that result after decaying processes – this is a very complex matter that cannot be described graphically in a simple way. While most unstable atoms decay into a certain atom that will stabilise without further alpha/beta decay, there are four elements that decay in four characteristic sequences that are very well studied. These sequences are what we call radioactive series. The elements that decay following these sequences are thorium (Z = 90), uranium (Z = 92), actinium (Z = 89), and neptunium (Z = 93).

Gamma radiation graphics

Metastable is a temporal stable state: it is not as stable as the ground state and not as unstable as an excited state. This instability is caused by excess energy resulting from the decay process/es. Since the particle content corresponds to a stable state, atoms usually release the surplus of energy through gamma radiation.

The diagram below shows two possible decay processes for a cobalt isotope. After the two possible beta decays, there is an emission of gamma radiation that takes the atom to its stable state. The blue lines indicate possible beta minus emissions associated with certain energies (all measured in megaelectron volts). The red lines indicate possible gamma emissions. Depending on the energy of the beta particle emitted, the gamma emission will have more or less energy.

What are some applications of nuclear instability?

After Becquerel’s discovery of nuclear radiation at the end of the nineteenth century and through Marie Curie’s (and other scientists’) studies, the applications of nuclear radiation have appeared everywhere. Here are some examples.

Nuclear fusion and fission

Nuclear power plants are one of the best-known forms of energy production. Although they are not a perfectly clean or perfectly renewable energy source, the waste they produce is much less than the waste produced by non-renewable sources (however, its waste is extremely dangerous).

Unstable atoms that need to lose neutrons to reach a stable state can be forced to do so in a chain reaction that can release an incredibly massive amount of energy. This chain reaction is based on breaking unstable nuclei, a process called nuclear fission. When controlled, the reaction can produce energy that can be used for everyday purposes. If the production is not controlled, it can be dangerous.

There are, however, some light atoms that need to gain particles to reach a stable state (those below the N = Z line in the N-Z curve). It turns out that the joining of nuclei of this kind (nuclear fusion) into a new stable nucleus releases energy. This is the process that happens inside of stars. No one has been able to use it as a source of energy on Earth, but it would be ideal because the waste would be less dangerous and more abundant than in fission. Also, the nuclei susceptible to being used in fusion occur much more abundantly in nature than those susceptible to being used in fission.

Isotopes used as tracers (metastability)

Metastable nuclei can decay very fast (in a matter of days or hours). This short-time characteristic radiation emission allows us to use these atoms as tracers. By using gamma radiation detectors and by reconstructing the measured path, we can accurately trace specific movements.

Graph of isotopes by type of nuclear decay. https://commons.wikimedia.org/wiki/File:Table_isotopes_en.svg