Based on magic numbers, which nuclide is the least stable? (a)^59 Ni ;(b)^51 V ;(c)^122 Sb ;(d)^

step 1 Okay, so for this question, they want us to determine the least stable nucleide. So the stabilit

Based on magic numbers, which nuclide is the least stable?...

Based on magic numbers, which nuclide is the least stable? $(\mathrm{a})^{59} \mathrm{Ni} ;(\mathrm{b})^{51} \mathrm{V} ;(\mathrm{c})^{122} \mathrm{Sb} ;(\mathrm{d})^{16} \mathrm{O} ;(\mathrm{e})^{12} \mathrm{C}$

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Key Concepts

Nuclear Shell Model

The nuclear shell model is a theoretical framework that describes the structure of the nucleus in terms of energy levels or shells occupied by nucleons. Similar to the electron shell model in atoms, it explains the occurrence of magic numbers and provides insight into why certain nuclei are more stable than others. This model is fundamental in understanding predictions about nuclear stability based on nucleon arrangement.

Magic Numbers

Magic numbers are specific numbers of nucleons (either protons or neutrons) at which the nucleus exhibits extra stability because of filled nuclear shells. Examples of these numbers include 2, 8, 20, 28, 50, 82, and 126. The concept helps explain why nuclei with these numbers tend to have higher binding energies and are less susceptible to decay.

Nuclear Stability

Nuclear stability refers to the tendency of a nucleus to remain unchanged rather than decay. It is largely determined by the balance between the number of protons and neutrons and how those particles are arranged within the nuclear shell structure. Nuclei with closed shells (where the number of nucleons equals a magic number) are typically more stable, while those far from these configurations may be less stable.

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