What is the most stable nucleus?

Category: Physics      Published: July 23, 2024

By: Christopher S. Baird, author of The Top 50 Science Questions with Surprising Answers and Associate Professor of Physics at West Texas A&M University

The most stable atomic nucleus is nickel-62 in its ground state. This is because nickel-62 has the lowest binding energy per nucleon of any type of nucleus. There are 28 protons and 34 neutrons in a nickel-62 nucleus, for a total of 62 nucleons. Books and websites often say that iron is the most stable nucleus, but this is simply not true. Although it's a close call, nickel-62 has a slightly higher binding energy per nucleon than iron-58 and iron-56, as can be seen in the plot below.

Binding energy per nucleon as a function of number of nucleons, zoomed into the peak of the data, with only the nuclide shown for each nucleon number that has the highest binding energy per nucleon. Click to enlarge. Public Domain Image, source: Christopher S. Baird. Data Source: National Nuclear Data Center.

So why do books and websites say that iron has the most stable nucleus? There's two reasons. First of all, iron is far more abundant in the universe than nickel. The complex chains of nuclear reactions that occur in stars end up making far more iron-56 than nickel-62. You could therefore correctly say that iron-56 has the most stable nucleus out of all of the abundant elements.

Secondly, iron-56 has the lowest mass per nucleon out of all possible types of nuclei. This means that all sequences of nuclear reaction chains ultimately drive every other type of nucleus to become iron-56. That's why high-mass stars eventually end up with a core that is mostly made of iron, not nickel. Note that a nucleus's "binding energy per nucleon" and "mass per nucleon" are not exactly the same thing. Binding energy per nucleon determines the stability of a nucleus. The nuclide with the highest binding energy per nucleon is the most stable one, which is nickel-62. At the same time, mass per nucleon determines the ultimate end products of sequences of nuclear reaction chains. Iron-56 has the lowest mass per nucleon and is therefore the ultimate end product of nuclear reaction chains. It's possible for the ranking of nuclides by binding energy per nucleon to be slightly different from the ranking of nuclides by mass per nucleon. This is because a proton has a lightly different mass from a neutron.

The following three statements are all correct and are not contradictory: nickel-62 is the most stable type of nucleus overall, iron-56 is the most stable type of nucleus out of all of the abundant elements, and iron-56 is the ultimate end product of sequences of nuclear reaction chains. It's easy to get lost in all of this technical terminology, so let's go over the meaning of various terms before we dive deeper.

The nucleus of an atom is the small, dense central part of an atom that contains protons and neutrons. A nuclear reaction or transition involves changing a nucleus. In contrast, a chemical reaction involves changing atoms and molecules without changing their nuclei. The number of protons in the nucleus of an atom largely determines how the atom will act in chemical reactions, regardless of the number of neutrons present. However, the behavior of a nucleus in nuclear reactions depends on both the number of protons present and the number of neutrons.

An element is a type of atom, specified according to the number of protons in its nucleus, regardless of the number of neutrons present. The number of protons present in a nucleus is called the atomic number. All atoms of the same element behave the same way in chemical reactions (mostly), even if they have different numbers of neutrons in their nuclei. Examples of elements include gold, iron, oxygen, carbon, silicon, and nickel.

A nucleon is the name for a proton or a neutron, when found in a nucleus, when you don't care to differentiate protons from neutrons. Thus, the nucleon number is the number of protons plus the number of neutrons present in a particular nucleus. The nucleon number is also called the mass number.

Isotopes are the different types of atoms for one particular element, distinguished by the number of neutrons present in the nucleus. The different isotopes of an element will behave the same in chemical reactions (mostly) but will behave differently in nuclear reactions. Examples of isotopes are the isotopes gold-197, gold-198, and gold-199. Note that the number shown in these names is the nucleon number. To calculate the number of neutrons present in a particular isotope, you take the nucleon number and subtract the atomic number. For instance, gold has 79 protons in its nucleus and therefore has an atomic number of 79. A nucleus of gold-197 has 197 neutrons and protons, so that it has 197 - 79 = 118 neutrons.

Nuclides are the different types of nuclei among all of the different elements, distinguished by the number of neutrons present and by the number of protons present. Different nuclides are also specified by their energy excitation state, but it's typically assumed that the ground state is implied if not otherwise specified. Examples of nuclides are gold-197, nickel-62, and iron-59. The words isotope and nuclide may seem to mean the same thing, but they don't. A list of isotopes refers to only one element. A list of nuclides refers to different elements, in a neutron-specific way. If we're just comparing gold-197 to gold-198, they're called isotopes. If we're comparing gold-197 to nickel-62, they're called nuclides.

The binding energy of a nucleus is the minimum energy that would be required to separate the nucleus into a collection of independent, free, widely separated neutrons and protons. The higher the binding energy of a particular nucleus, the more energy that is required to disassemble that nucleus, and thus the harder it is to disassemble that nucleus. With that said, while adding an extra neutron to a neutron-poor nucleus increases its binding energy and therefore makes it more stable, it also introduces an additional particle that needs to be bound. Therefore, the most accurate indication of the stability of a nucleus is actually its binding energy per nucleon, which is its total binding energy divided by its nucleon number. Now that we have the terms clarified, let's return to our discussion of nickel-62 being the most stable nuclide.

Nuclear Stability of the Various Elements Relative to Each Other

You may have known that the nucleus of a particular element such as carbon can be a stable isotope of carbon or can be an unstable isotope. If it's an unstable isotope, it will eventually undergo radioactive decay to become more stable. All of the isotopes of one particular element can therefore be ranked in order stability, which is the same as ranking in order of binding energy per nucleon. More stable isotopes take a longer time to radioactively decay or may never radioactively decay.

You might not have known that the most stable isotope of one element can be less stable than the most stable isotope of a different element. In other words, even if we are talking about the most stable isotope of each element, these nuclides can still be ranked in order of stability. If you transform a nucleus from the most stable isotope of one element to the most stable isotope of another element, and the final nucleus is more stable than the initial nucleus, then there will be a net release of energy. Therefore, given enough time and the right conditions, the less stable nuclide will naturally turn into the more stable nuclide. Let's plot the binding energy per nucleon for all nuclides, so that we can see which nuclides will naturally tend to turn into which other nuclides.

The image below shows the result if you take almost all of the nuclides (a handful of the most unstable nuclides have been omitted), arrange them in order of nucleon number, and then plot their binding energy per nucleon. Note that many different nuclides have the same nucleon number, so that each nucleon number in the plot below has several black dots. For instance, hydrogen-4 has one proton and three neutrons, for a total of four nucleons. At the same time, helium-4 has two protons and two neutrons, also totaling four nucleons. Also, lithium-4 has three protons and one neutron, also totaling four nucleons. This means that hydrogen-4, helium-4, and lithium-4 all show up at the same nucleon number in the plot below.

Click to enlarge. Binding energy per nucleon as a function of number of nucleons, for almost all nuclides. Public Domain Image, source: Christopher S. Baird. Data Source: National Nuclear Data Center.

The image above shows that, as a general trend, nuclides that have less than about 60 nucleons experience an increase in binding energy per nucleon when they gain nucleons, meaning that they become more stable by transforming to different nuclides with more nucleons. As a result, nuclides with a nucleon number less than about 60 will naturally tend to transform to nuclides with more neutrons and protons. In rough language, we can say that, given enough time and the right conditions, elements that are lighter than iron and nickel tend to become progressively heavier elements until they reach iron or nickel. This happens through nuclear fusion, where two smaller nuclei fuse into one nucleus, and through nucleon capture.

At the same time, the image above shows that, as a general trend, nuclides that have more than about 60 nucleons experience a decrease in binding energy per nucleon when they gain nucleons, meaning that they become less stable if they gain nucleons. As a result, nuclides with a nucleon number greater than about 60 will naturally tend to transform to nuclei with fewer protons and neutrons. In rough language, we can say that elements that are heavier than iron and nickel tend to become progressively lighter elements until they reach iron or nickel. This happens through nuclear fission, radioactive decay, and nuclear spallation.

Although the image above shows effectively all nuclides for each nucleon number, they are not all equally important. For a particular nucleon number, the nuclide with the highest binding energy per nucleon is the most stable and therefore the most important. Hydrogen-4, helium-4, and lithium-4 all have the same nucleon number: 4. However, among these three nuclides, helium-4 has the highest binding energy per nucleon and is the most stable. A seemingly small difference in binding energy per nucleon can make a huge difference. Hydrogen-4 lasts only 1×10^-22 seconds before falling apart (i.e. radioactively decaying) and lithium-4 lasts only 9×10^-23 seconds before falling apart, but helium-4 (when left to itself) will last an infinite amount of time before falling apart. Helium-4 is therefore, by far, the most important and the most abundant nuclide with four nucleons.

In summary, the nuclide with the highest binding energy per nucleon, among the nuclides with the same nucleon number, is the most important of those nuclides. With that in mind, let's take the data in the previous image and only show the nuclide with the highest binding energy per nucleon for each nucleon number. The result is shown in the image below.

Click to enlarge. Binding energy per nucleon as a function of number of nucleons, for the most stable nuclide of each nucleon number. Public Domain Image, source: Christopher S. Baird. Data Source: National Nuclear Data Center.

Note that you might have seen this type of plot somewhere else and it looked slightly different. That's because authors often choose to show the most abundant nuclide for each nucleon number rather than the most stable nuclide for each nucleon number, which are not exactly the same thing. Although you might expect the most stable nuclide for a particular nucleon number to also be the most abundant, it's more complicated than that. To exist, a certain nuclide has to be created from other nuclides (except for hydrogen-1), and certain nuclear processes are more efficient than others. As a result, the most stable nuclides are not necessarily the most abundant.

There are good reasons that the curve in the plot above is not perfectly smooth. Although interesting, these reasons involve advanced nuclear physics and are beyond the scope of this article. (If you want to learn more about this, do a search for the phrase "nuclear magic numbers".)

As you can see in the plot above, the nuclear fusion of hydrogen to make helium, and of helium to make carbon, corresponds to a huge jump up in stability. This means that these reactions are very likely to happen and release a lot of energy. These are the main nuclear reactions happening in stars. Also, hydrogen fusion is the main reaction in hydrogen bombs and in nuclear fusion reactors. On the other end of the scale, the nuclear fission of uranium and plutonium to make lighter nuclei also corresponds to a jump up in stability, meaning that these reactions are likely to happen (if conditions are right) and they release a lot of energy. These are the core reactions that happen in uranium bombs, plutonium bombs, and nuclear fission reactors.

We can zoom in a little on the peak in the plot above and the result is the image below.

Click to enlarge. Binding energy per nucleon as a function of number of nucleons, for the most stable nuclide of each nucleon number, zoomed in a little on the peak. Public Domain Image, source: Christopher S. Baird. Data Source: National Nuclear Data Center.

Now that we've zoomed in a little, it becomes obvious that nickel and iron are indeed at the peak, meaning that they are the most stable nuclides overall. There's also an interesting feature noticeable in the image above that was not noticeable when we were zoomed out. As you step up the curve one additional nucleon at a time, the curve alternates higher, lower, higher, lower, etc., making the line look like a zig-zag. This is because an even number of nucleons is generally more stable than an odd number of nucleons, which has to do with the facts that a nucleon has only two possible spin states ("up" or "down") and having all nucleon spins paired up is more stable. (This is similar to how electrons can also only be in two spin states and therefore whether electrons are paired up or not in chemical bonds and atomic structures affects reactivity.)

If we zoom in even more on the peak, we end up with the image below, which is the same image as at the beginning of this article.

Binding energy per nucleon as a function of number of nucleons, zoomed into the peak of the data, with only the nuclide shown for each nucleon number that has the highest binding energy per nucleon. Click to enlarge. Public Domain Image, source: Christopher S. Baird. Data Source: National Nuclear Data Center.

Although the stability values of nickel-62, iron-56, and iron-58 are almost tied, nickel-62 actually wins the title for the most stable nuclide, as you can see in the plot above.

You may wonder at this point, what transforms one element to a different element, and one nuclide to a different nuclide? As I hinted at already, the answer is nuclear reactions. The types of nuclear reactions are shown in the table below.

Nuclear fusion is when two nuclei fuse together to make one, larger nucleus. The two nuclei have to get very close to each other, against the mutual electric repulsion of their protons, in order for nuclear fusion to happen. This means that you need very high temperatures or very high-energy collisions in order to have nuclear fusion. An example of nuclear fusion is the fusion of hydrogen in stars. Nuclear fusion takes small nuclei and creates larger nuclei. For this reason, nuclear fusion is the main process that transforms small nuclei up in size toward iron and nickel.

Nuclear fission is when one nucleus spits into two or more pieces, where each piece is now its own atomic nucleus. Fission can happen spontaneously if a nucleus is too big and unstable. Fission can also be induced by bombarding nuclei with high-energy particles. The particle either slices right through the nucleus, cutting it in pieces, or sticks to the nucleus, bringing a lot of energy with it, causing the nucleus to become unstable and fall apart. If a nuclear fission event involves a large nucleus spitting out a fragment that is much smaller than the nucleus, then it is called cluster decay. An example of nuclear fission is the fission of uranium nuclei in uranium bombs. Fission takes large nuclei and makes smaller nuclei. For this reason, nuclear fission is one of the main processes that transforms large nuclei down in size toward iron and nickel.

Radioactive decay is a small transformation to a nucleus that makes it more stable and spits out radiation in the process. It typically happens spontaneously because the nucleus is unstable compared to similar nuclides. There are many types of radioactive decay, including alpha decay (where a helium nucleus is emitted), beta⁺ decay (where a positron is emitted), beta^– decay (where an electron is emitted), gamma decay (where a gamma ray is emitted), electron capture (where a nucleus absorbs an electron and emits a neutrino), proton emission, neutron emission, and internal conversion (where an atomic electron from outside the nucleus is ejected because of energy from the nucleus). Alpha decay is one of the main processes that transforms large nuclei down in size toward iron and nickel. All types of radioactive decay transform an original nuclide into a nuclide with a different number of protons and/or neutrons, except for gamma decay and internal conversion decay.

Nucleon capture is when an independent proton or neutron comes along and collides with a nucleus and is absorbed by the nucleus.

Nuclear spallation is when an independent object such as a proton or neutron collides with a nucleus and knocks away protons, neutrons, and/or larger fragments.

Nuclear scattering is when an independent object such as a proton or neutron collides with a nucleus and bounces off of it, thereby giving energy and momentum to the nucleus without changing its number of neutrons or protons.

Note that there is some overlap in these definitions. For instance, radioactive alpha decay and nuclear spallation can be thought of as special types of nuclear fission. Also, nucleon capture can be thought of as a type of nuclear fusion.

Nuclear fusion and nucleon capture turn smaller nuclei into bigger nuclei. Therefore, these are the processes that transform small nuclei up in size toward iron and nickel. Nuclear fission, radioactive decay, and nuclear spallation generally turn large nuclei into smaller nuclei, and therefore are what transform large nuclei down in size toward iron and nickel. Nuclear scattering, radioactive gamma decay, and internal conversion do not change the number of protons or the number neutrons at all.

Topics: binding energy, decay, element, isotope, nucleon, nucleus, nuclide