Final answer:
Nuclide stability is mainly determined by the neutron-to-proton ratio, the presence of magic numbers, and even numbers of protons and neutrons. The correct option is (c).
Step-by-step explanation:
The key factors that determine the stability of a nuclide are primarily based on nuclear physics principles. The most critical factor for nuclear stability is the ratio of neutrons to protons in the nucleus, often represented as the n:p ratio. This ratio is fundamental in achieving a stable configuration that overcomes both the electrostatic repulsion between protons and the strong nuclear force that binds the nucleus together. For light nuclei, a n:p ratio of approximately 1:1 is most stable, whereas heavier nuclei require more neutrons than protons due to increased proton-proton repulsions.
Additionally, the presence of magic numbers of protons or neutrons, which are specific numbers that complete nuclear shells, can significantly enhance stability. Nuclides with even numbers of protons and neutrons are also observed to be more stable compared to those with odd numbers. Binding energy per nucleon is another critical factor, with the most stable nuclei having the highest binding energy per nucleon and mass numbers near 56. Electronic factors such as the total number of electronic energy levels or the number of electrons do not directly influence nuclear stability, as these aspects relate to chemical rather than nuclear behavior.
Therefore, the correct option that determines the stability of a nuclide is 'the ratio of neutrons to protons in the nucleus'.