All About Nuclear Stability and a Pauli Exclusion Principle

Nuclear stability in chemistry refers to the fact that an element’s nucleus is stable and consequently does not decay spontaneously, releasing radioactivity. Because of energy conservation, only 195 of the 9,000 nuclei anticipated to exist, and the 3,000 identified are stable against spontaneous disintegration.

The Pauli exclusion principle states: Within a quantum system, no more than two electrons can be in the same quantum-mechanical state at the same time.

In terms of quantum numbers, the following are some examples:

The quantum numbers were not the same for any of the two electrons in an atom.

The four quantum numbers cannot be the same for two electrons in a multi-electron atom:

• l is the quantum number (angular)

• n is the primary quantum number

• ml represents the magnetic quantum number

• ms represents the spin quantum number

This indicates that the wave functions of the two particles must be antisymmetric. If the two fermionic particles are identical, the probability amplitude of the wave function will be zero.

The Pauli Exclusion Principle and Nuclear Stability

The nuclear force holds the nuclei of an atom together. Because of their positive charge, protons, on the other hand, repel each other via electromagnetic force. These two forces compete with one another, resulting in nuclear stability in chemistry. Only specific sets or combinations of protons and neutrons produce stable nuclei in the meanwhile. Neutrons attract one another and protons, which helps to keep the factors affecting nuclear stability. This also aids in the counterbalancing of protons’ electrostatic repulsion. The number of protons rises as a result of this. There must be an increasing ratio of neutrons to protons to build nuclear stability.

The atom’s nucleus is not stable if there are too many or too few neutrons for a given number of protons. There will be radioactive decay as a result of this. When we look at actinides with an odd neutron number, we find that they are usually fissile or fissionable with slow neutrons. Actinides with an even neutron number, on the other hand, are usually not fissile or only fissionable with fast neutrons. Similarly, because of ‘paired spin,’ heavy nuclei with an even number of protons and neutrons are particularly stable due to the Pauli exclusion principle. Nuclei with an odd number, on the other hand, are unstable.

Factors Affecting Nuclear Stability

The amount of protons and neutrons in a nucleus is an important factor affecting nuclear stability. There are 157 stable isotopes with an even number of protons and neutrons among the 354 known stable isotopes. Only five nucleons have an odd number of both types. The even-numbered elements in the periodic table are almost always substantially more numerous than the odd-numbered elements close by.

Nuclei have several protons or neutrons equal to one of the so-called “magic” numbers 2, 8, 20, 28, 50, 82, and 126 and have exceptional stability. These statistics represent the filling of shells in the nucleus’ structure.

Nuclear Stability Rules

The stability of an atom’s nucleus is referred to as factors that affect nuclear stability. A very stable nucleus is not able to degrade faster as compared to others. Stable nuclei are found in radioactive elements, which decay spontaneously, generating a variety of radiations.

The neutrons and protons combine the nucleus of atoms. The same charges repel each other while the opposite charges attract each other. The electrostatic force can be overcome easily by applying the strong force of the nucleus, which easily attracts the nucleons between the atoms.

Neutrons are necessary for nucleus stability. When the attractive force between nucleons exceeds the electrostatic repulsion, the nucleus becomes unstable and decays.

A few of the nuclear stability rules are:

• Neutrons equal or exceed protons in all stable nuclei.

• A stable nucleus has an N/Z value near 1.

• The stability of nuclei with an even number of neutrons and protons is higher.

• 2, 8, 20, 28, 50, 82, and 126 are magical protons or neutron numbers.

• There are no stable atoms with atomic numbers greater than 83 and masses greater than 209

Conclusion

Protons and neutrons, called nucleons, collectively make up an atomic nucleus. Even though protons resist one another, the nucleus is held together by a powerful force known as the strong nuclear force. The mass defect is the “missing” mass that, according to Einstein’s mass-energy equivalence equation, E =mc2, has been turned into the binding energy that holds the nucleus together. Only a small percentage of all nuclides exist in stable forms. Even numbers of protons or neutrons and nucleons with magic numbers are more likely to be the factors affecting nuclear stability. On a graph of the number of protons vs. the number of neutrons, these stable nuclides occupy a small band of stability.