KAHIBARO
Table of Contents
What Nuclear Stability Means
Nuclear stability describes whether a nucleus can remain as it is, or whether it tends to change into another nucleus. A stable nucleus does not spontaneously decay. An unstable nucleus is radioactive and changes by emitting particles or radiation.
A nucleus contains protons and neutrons, called nucleons. Since protons are positively charged, they electrically repel each other. If only electric repulsion acted, nuclei would fly apart. The reason nuclei can exist at all is the strong nuclear force, which attracts nucleons when they are very close together. Nuclear stability is the result of a balance between these competing effects.
For a nucleus to be stable, the attractive nuclear force must be strong enough to hold the nucleons together, while the arrangement of protons and neutrons must also be favorable. Stability is therefore not determined by just the total number of nucleons, but by how many are protons and how many are neutrons.
Balance Between Protons and Neutrons
One of the most important ideas in nuclear stability is the neutron to proton balance. Light nuclei are usually most stable when the number of neutrons is close to the number of protons. For heavier nuclei, stability requires more neutrons than protons.
Neutrons help stability in two ways. They add strong-force attraction, but they do not add electric repulsion because they have no charge. As the number of protons increases, the repulsive electric force becomes stronger, so extra neutrons are needed to help bind the nucleus.
A useful way to describe a nucleus is by its proton number $Z$ and neutron number $N$. The total mass number is
$$
A = Z + N
$$
For small values of $Z$, stable nuclei often have $N \approx Z$. For larger values of $Z$, stable nuclei tend to have $N > Z$.
A nucleus is more likely to be stable when its neutron to proton ratio is appropriate for its size. Light stable nuclei usually have $N \approx Z$, while heavy stable nuclei require $N > Z$.
The Band of Stability
If we plot neutron number $N$ against proton number $Z$ for known nuclei, stable nuclei lie in a narrow region called the band of stability. Nuclei outside this band are unstable and tend to decay toward it.
Nuclei with too many neutrons are called neutron rich. They often undergo beta minus decay, in which a neutron changes into a proton. This reduces $N$ and increases $Z$, moving the nucleus closer to the stable region.
Nuclei with too many protons are called proton rich. They often undergo beta plus decay or electron capture, which change a proton into a neutron. This decreases $Z$ and increases $N$, again moving the nucleus toward stability.
Very heavy nuclei can be unstable even if their neutron to proton ratio is near the stable range, because the electric repulsion among many protons becomes too large. These nuclei may decay by alpha emission or other processes.
Why Very Heavy Nuclei Become Unstable
The strong nuclear force is very strong, but it acts only over a very short distance. A nucleon mainly interacts strongly with nearby nucleons. In contrast, the electric repulsion between protons acts over much longer distances and involves many proton pairs across the nucleus.
As nuclei get larger, the short range of the strong force becomes a limitation. The strong attraction does not increase effectively enough to fully overcome the growing proton repulsion. Because of this, very heavy nuclei are harder to stabilize.
This is why the heaviest nuclei are generally radioactive. Beyond a certain size, no completely stable nucleus exists. For example, nuclei with very large proton number tend to decay until they reach more stable forms.
The strong nuclear force is short range, but the electric repulsion between protons acts throughout the nucleus. As $Z$ becomes very large, proton repulsion makes stability increasingly difficult.
Even and Odd Numbers of Nucleons
Another important pattern in nuclear stability is connected with whether the number of protons and neutrons is even or odd. Nuclei with even numbers of protons and even numbers of neutrons are especially common among stable nuclei.
This happens because nucleons tend to form pairs inside the nucleus. Pairing lowers the energy of the nucleus and makes it more stable. Nuclei with both $Z$ and $N$ even often gain extra stability from this effect.
Nuclei with odd values of both $Z$ and $N$ are less often stable. They usually have higher energy and are more likely to decay. This does not mean all odd nuclei are unstable, but stability is less common in that case.
The general trend is shown below.
| Proton number $Z$ | Neutron number $N$ | Typical stability tendency |
|---|---|---|
| Even | Even | Most favorable |
| Even | Odd | Moderately common |
| Odd | Even | Moderately common |
| Odd | Odd | Least favorable |
Magic Numbers and Extra Stability
Some nuclei are especially stable because they contain certain numbers of protons or neutrons called magic numbers. These numbers correspond to particularly favorable internal nuclear arrangements.
Common magic numbers are
$$
2,\ 8,\ 20,\ 28,\ 50,\ 82,\ 126
$$
A nucleus can be extra stable if either its proton number or neutron number is magic. It can be especially stable if both are magic. Such nuclei are sometimes called doubly magic.
This idea helps explain why some nuclei are much more stable than nearby nuclei with similar mass.
Magic numbers, $2, 8, 20, 28, 50, 82, 126$, correspond to especially stable proton or neutron counts.
Stability and Binding
A stable nucleus is generally one with relatively low energy compared with nearby possible nuclear arrangements. If changing into another nucleus would lower the energy, the nucleus is likely unstable and may decay.
One sign of stability is strong binding. A nucleus that is tightly bound is harder to break apart and often less likely to decay. In practice, nuclear stability is closely related to the binding energy per nucleon, although that topic belongs more fully to a later chapter.
For now, the key idea is simple. Stable nuclei correspond to favorable energy arrangements of protons and neutrons.
Common Stability Trends
Several broad patterns are seen across nuclei.
| Trend | Effect on stability |
|---|---|
| Proper neutron to proton ratio | Increases stability |
| Too many neutrons | Tends toward beta minus decay |
| Too many protons | Tends toward beta plus decay or electron capture |
| Very large proton number | Makes stability difficult because of Coulomb repulsion |
| Even-even nucleus | Usually more stable |
| Magic numbers present | Gives extra stability |
Stable and Unstable Examples
Carbon-12, with $Z=6$ and $N=6$, is stable and has a balanced neutron to proton ratio for a light nucleus. Lead-208, with $Z=82$ and $N=126$, is also stable, even though it has many more neutrons than protons. This reflects the need for extra neutrons in heavy nuclei and also the special role of magic numbers.
Uranium nuclei are much heavier and have large proton numbers. Even though neutrons help bind them, proton repulsion is so strong that they are unstable and radioactive.
These examples show that stability depends on several factors acting together, not on just one number.
A Simple Picture of Nuclear Stability
You can think of nuclear stability as a competition. The strong nuclear force tries to hold nucleons together. The electric force pushes protons apart. Neutron to proton balance, nucleon pairing, and magic numbers all affect who wins this competition.
A stable nucleus is one in which the internal arrangement is favorable enough that it does not spontaneously change. An unstable nucleus is one that can move to a lower-energy, more favorable state by radioactive decay.
Key Idea to Remember
Nuclear stability is controlled by the balance of forces and by the internal arrangement of protons and neutrons. Light stable nuclei usually have nearly equal numbers of protons and neutrons, heavy stable nuclei need extra neutrons, even-even nuclei are often more stable, and magic numbers give special extra stability.
A nucleus is stable when its protons and neutrons are arranged so that the strong nuclear attraction can successfully overcome proton repulsion and produce a low-energy configuration.