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The valley of stability of atomic nuclei

Stability limits of isotopes

 Automatic translation  Automatic translation Updated December 14, 2021

In nature, all matter is concentrated in the mass energy of nuclei 100,000 times smaller than atoms, but thousands of times heavier than all of their electrons.
In matter, many atomic nuclei are stable and their state remains the same indefinitely. An isotope is stable when it has a harmonious number of protons and neutrons. On the other hand, many more are unstable because they have too many protons or neutrons or too many of both.
Physicists have identified just fewer than 300 stable isotopes and nearly 3,000 unstable. If the nuclei are unstable it is because of the Coulomb barrier which establishes a competition between the force of electrostatic repulsion between the protons and the attractive nuclear force between the neutrons and the protons. This is why nuclei have to integrate more and more neutrons as they grow larger.
All the nuclei of matter seek parsimonious energy stability. So to return to a stable state, they must transform by expelling energy in the form of mass or radiation (E = mc2). This is called radioactivity.
This phenomenon of natural radioactivity is at work everywhere in matter, both in minerals and in our food (the European Community has set doses of radioactivity not to be exceeded in food) and even in our body (due to the presence of carbon 14 and potassium 40).
• When we represent all the known isotopes on a graph (image opposite) by their number of protons (Z) and their number of neutrons (N), we see that all the stable isotopes (black dots) are grouped around d 'a line. This line is in the hollow of a valley called "valley of stability".
The unstable nuclei are distributed on the sides of the valley on either side of this black line representing the river of stable matter flowing at the bottom of the valley. The more unstable the nuclei, the higher they are in the valley. Thus, in this valley, the shortest way to reach stability is to descend to the bottom of the valley.
• The nuclides on the left flank of the valley (in blue in the image), surplus in neutrons compared to their number of protons, regain stability by a cascade of decays β- with emission of electrons and neutrinos which allows them to gradually descend the slopes of the valley.
• The nuclides on the right side of the valley (in orange), excess in protons, regain stability by a cascade of β+ decays with emission of positrons and neutrinos.
• The nuclides on the small left crest of the valley (in purple) at the peripheral limit of the blue zone, regain stability by emission of neutrons, the nucleus keeps the same atomic number (Z) but its atomic mass decreases.


• The nuclides located on the small right crest of the valley (in red) at the peripheral limit of the orange zone, regain stability by emission of protons, the atomic number (Z) and the atomic mass of the nucleus decrease.
• On the side of very heavy nuclei, it is fission that will take place. The nuclides, beyond the stable isotope line (in pale green), regain stability by dividing the nucleus into two lighter nuclei with the emission of one or more neutrons.
• High atomic mass nuclides (in yellow) undergo α often accompanied by the emission of high energy photons or gamma rays. If the slope is too high then β decays are inserted between α decays. A cascade of radioactive decay is needed to reach the valley floor.
• Finally, particularly stable nuclei have a certain number of nucleons (2, 8, 20, 28, 50, 82 and 126) which correspond to the layered model of the atomic nucleus (quantified energy levels based on the Pauli exclusion principle ). These so-called magic numbers are identified along the staircase steps of the black curve. Nuclei which have both a magic number of protons and neutrons and a number of protons equal to the number of neutrons are said to be doubly magic because they are very stable.
This is the case with lead 208, which is made up of 82 protons and 126 neutrons, and calcium 48, made up of 20 protons and 28 neutrons.
• The discontinuities of the black curve in neutrons (19, 21, 35, 39, 45, 84, 115 and 123) and in protons (43 and 61) correspond to cases where there is no stable nucleus with these quantities of nucleons.

In conclusion, the valley of stability contains around 3000 observed nuclides, stable, unstable and very unstable. But we do not know the stability limits (drip lines) of nuclides. For protons (maximum number of protons) it is relatively well known through Mendeleyev’s table. For neutrons (maximum number of neutrons) the stability limits are only known for the first elements, from hydrogen to oxygen 15. For example, for Z = 8, the maximum number of neutrons is 16, yielding oxygen 24 as the heaviest possible oxygen isotope.
The full extent of the Valley of Stability remains unknown, and it appears that what remains to be discovered is enormous.

NB: The nucleus of the atom is made up of protons and neutrons. Atoms of the same chemical element have the same number of protons but can have a different number of neutrons, these are isotopes. Stable atoms do not undergo radioactive decay.

 Valley of stability

Image: The valley of isotope stability by type of radioactive decay.
- In black: stable nuclei, they do not undergo radioactive decay and do not emit radiation.
- In orange, blue and yellow: unstable nuclei which disintegrate either by radioactivity β either by radioactivity α to descend into the valley.
- In red and purple: unstable nuclei which have too many protons or neutrons emit either a proton or a neutron to descend into the valley.
- In pale green: unstable nuclei which have too many protons and neutrons must crack in order to descend into the valley.
We can notice that for Z<20, the set of stable nuclei lie on the bisector N = Z.
For Z>20, the set of stable nuclei lie above the line N = Z in the valley of stability. Nuclei must integrate more and more neutrons than protons as they grow larger.
For Z>83, there are no more stable nuclei despite observable limit of the number of protons which is estimated at around Z=126.
The unstable nuclei undergo a cascade of radioactive decays to ultimately throw themselves into the river of stable matter flowing at the bottom of the valley.

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