Carbon-13 is stable primarily because of its balanced neutron-to-proton ratio, which contributes to the overall binding energy of the nucleus. The nucleus of Carbon-13 consists of 6 protons and 7 neutrons. This composition allows for a strong nuclear force that holds the nucleus together effectively.
The stability of a nucleus is largely determined by the ratio of neutrons to protons. In lighter elements, such as carbon, the optimal ratio is close to 1:1. In Carbon-13, the ratio is approximately 1.17, which falls within a range that permits stability. Nuclei that have ratios outside this ideal range often become unstable and undergo radioactive decay.
Unlike Carbon-12, which is the most abundant isotope with 6 protons and 6 neutrons, Carbon-13’s additional neutron provides extra binding energy, making it stable. This stability is further reinforced by the absence of significant physical forces that would lead to either beta decay or other forms of radioactive decay.
In summary, Carbon-13 is stable due to its favorable neutron-to-proton ratio, which results in a strong nuclear binding that prevents decay. This characteristic is what makes it useful in various applications, such as in NMR spectroscopy and isotopic labeling in research.