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Isotopes are atoms of the same element with the same number of protons but different numbers of neutrons in the nucleus. Elements are defined by the number of protons in the nucleus, which determines their atomic number. However, the number of neutrons can vary, leading to isotopes with different mass numbers.

An isotope's stability is largely determined by the balance of forces within its nucleus. Nuclear stability is influenced by the strong nuclear force, electromagnetic force, and weak nuclear force. The strong nuclear force is attractive between nucleons (protons and neutrons) at short range, while the electromagnetic force is repulsive between protons. Nuclei with the same number of protons and neutrons are more stable because of the strong force. However, as the number of protons increases in heavier elements, the repulsive electromagnetic force starts to overcome the strong force. Therefore, heavier elements require more neutrons relative to protons to achieve stability. In the case of nuclear physics, there are certain "magic numbers" of protons and neutrons in isotopes that create additional nuclear stability. These magic numbers arise due to the filling of nucleon shells in the nucleus, similar to electron shells in atomic structure. Isotopes with magic numbers of protons and/or neutrons exhibit increased stability.

Tin (Sn) has an atomic number of 50, while antimony (Sb) has an atomic number of 51. Tin has 10 stable isotopes, with neutron numbers ranging from 62 to 76, because it has a magic number of protons (50). This magic number gives tin an enhanced nuclear stability, resulting in a higher number of stable isotopes. On the other hand, antimony has only two stable isotopes with neutron numbers 61 and 64. This difference is primarily because antimony does not have a magic number of protons or neutrons. The two stable isotopes of antimony are stable due to a balance between the strong nuclear force and the repulsive electromagnetic force. In conclusion, the difference in the number of stable isotopes for tin and antimony can be explained through nuclear stability and the role of magic numbers in determining the stability of isotopes. Tin, with its magic number of protons, exhibits increased stability and therefore has more stable isotopes compared to antimony with no magic numbers.