Key Features and Applications of Magic Numbers in Nuclear Physics
The magic number in nuclear physics is defined as a number of nucleons consisting of either neutrons or protons separately arranged in a manner of complete shells within their atomic nucleus. Atomic nuclei consisting of a magic number of neutrons and protons are considered much more stable than any other nuclei. As of 2019, the 7 widely recognized magic numbers are 2,8,20,28,50,82,126, with a sequential arrangement of A018226 in their OEIS.
The protons usually correspond with the following elements called oxygen, helium, nickel, calcium, tin, and lead, along with the hypothetical unbihexium, but 126 is so far to be considered as a magic number in terms of neutrons. The atomic nuclei consisting of a magical number in the nucleons are generally occupied with average binding energy, which is very high per nucleon than the one expected based upon the predictions like the semi-empirical mass formula and thus is considered to have much more stability against its nuclear decay. The isotopes with magic numbers have exceptional stability, which means that the transuranium elements can be theoretically created with extremely larger-sized nuclei and still will not be subjected to any extremely rapid radioactive decays, which are typically associated with high atomic numbers. Thus it is assumed that the significant isotopes consisting of magic numbers exist in an island of stability.
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Why are these Numbers Known as the Magic Numbers?
The answer to the question of what is the magic number begins from the Inside of an atomic nucleus, where its neutrons and protons are arranged in the form of shell structures which is similar to the electron shell surrounding an atom. When the neutron and proton shells get filled with 2, 8,20,28,50, and 82, 126 nucleons, they are known as the magic with nuclei in a spherical shape. But when the number of nucleons does not form a magic number, the nuclei lose their spherical shape and get deformed.
As per the recent experimental data, neutron-rich radioactive isotopes can be a significant challenge during the estimation of the magic number as it is the same for all the given nuclei. The neutron-rich isotope 32 of the Mg element is composed of about 20 neutrons and 12 protons and has become deformed due to the absence of magic number 20 of the neutron. A region called the island of deformation in a nuclear chart is made up of elements known to lose their magic number 20 of the neutron. Previously this region was thought to have only a very few nuclei around the isotope 32 of Mg.
Special Features of the Nuclei Having a Magic Number in its Nucleons
It has a nature of higher abundance. Such helium-4 is considered the most stable and abundant nuclei in the whole universe.
All the stable elements at the end of the decay series have a magic number of protons and neutrons. For example, the nuclei of O-16, He-4, and the Pb-208, having 126 neutrons and 82 protons, contain a magic number of protons and neutrons, equally stable.
The nuclei have N= magic number with much lower cross-sections of the neutron absorption than its surrounding isotopes.
The nuclei containing the magic numbers appear to be spherical with absolutely zero electric quadrupled moments.
The nuclei containing the magic number always have a higher first excitation level of energy.
Significance of the Magic Number in Nuclear Physics
The significances of the magic numbers in nuclear physics are as follows:
The magic numbers indicate the number of filled nuclear shells.
They tend to identify the isotopes that are much more stable as compared to other elements.
The magic number shows the energies of each nucleon.
The element that has an atomic number 20 is calcium, and it is doubly magic.
The magic numbers in nuclear physics are described as a number corresponding to its complete shells within its atomic nuclei and is thus considered to be a magic number and the atomic nuclei having such a magic number in its nucleons usually consists of a very high average binding energy per nucleon these magic numbers are usually predicted by its nuclear shell model and are often proved by its observations showing a sudden discontinuity in the energy separations of both protons and neutrons at particular values of N and Z. The magic number in the periodic table with the periodic law forms the most fundamental law of physics responsible for these magic numbers. The magic number example is 2, 8, 20, 28, 50, 82, and 126.
FAQs on What Are Magic Numbers in Physics?
1. What are magic numbers in the context of nuclear physics?
In nuclear physics, magic numbers are a specific sequence of numbers that represent the total count of protons or neutrons in an atomic nucleus. When a nucleus contains a 'magic number' of either particle, it is significantly more stable than other nuclei. The universally recognised magic numbers are 2, 8, 20, 28, 50, 82, and 126. This stability is due to the nucleons filling complete energy shells within the nucleus, similar to how electrons fill shells around an atom.
2. What are 'doubly magic' nuclei and what makes them so special?
A nucleus is called 'doubly magic' if its proton count and its neutron count are both magic numbers. These nuclei exhibit exceptional stability and have a very high binding energy per nucleon compared to their neighbours. This is because both the proton and neutron shells are completely filled, creating a very tightly bound and stable configuration. Examples include:
- Helium-4 (2 protons, 2 neutrons)
- Oxygen-16 (8 protons, 8 neutrons)
- Calcium-40 (20 protons, 20 neutrons)
- Lead-208 (82 protons, 126 neutrons)
3. How does the nuclear shell model explain the existence of magic numbers?
The nuclear shell model explains magic numbers by proposing that protons and neutrons in a nucleus exist in distinct energy levels, or 'shells', much like electrons orbiting an atom. According to this model, the magic numbers correspond to the number of nucleons required to completely fill these energy shells. A filled shell results in greater stability for the nucleus, just as a filled electron shell results in a chemically stable (noble) gas. The specific values of the magic numbers arise from the unique energy level spacing within the nucleus.
4. Are the 'magic numbers' in Physics the same as the numbers for electron shells in Chemistry (2, 8, 18, 32)?
No, they are different concepts related to different particles and forces. The numbers in Chemistry (2, 8, 18, 32, etc.) refer to the maximum number of electrons in their shells, which determines an element's chemical properties based on the electromagnetic force. The magic numbers in Physics (2, 8, 20, 28, etc.) refer to the number of protons or neutrons (nucleons) in the nucleus, which determines nuclear stability based on the strong nuclear force.
5. Why do heavier stable nuclei generally have more neutrons than protons?
This happens due to the interplay between two fundamental forces. The strong nuclear force is a powerful attractive force that binds all nucleons (protons and neutrons) together over short distances. In contrast, the electrostatic (Coulomb) force is a repulsive force that only acts between positively charged protons. As a nucleus gets larger, the proton repulsion builds up and weakens the nucleus. To maintain stability, more neutrons are needed. These neutrons add to the attractive strong force without contributing to the electrostatic repulsion, effectively acting as 'glue' to hold the nucleus together.
6. Is there a 'magic number' in mathematics, and how does it relate to physics?
Yes, there are 'magic numbers' in mathematics, but they are completely unrelated to the concept in physics. For example, the number 1729 is known as the Ramanujan-Hardy number. These mathematical numbers have unique properties based on number theory. Nuclear magic numbers, however, are derived from the physical principles of quantum mechanics and the structure of the atomic nucleus. There is no connection between them besides the shared name.
