Which member of the following pairs of nuclides would you...

Which member of the following pairs of nuclides would you expect to be most abundant in natural sources: (a) $_{20}^{40} \mathrm{Ca}$ or $_{20}^{42} \mathrm{Ca} ;$ (b) $_{15}^{31} \mathrm{P}$ or $_{15}^{32} \mathrm{P} ;$ (c) $_{30}^{63} \mathrm{Zn}$ or 64 $\mathrm{Zn} ?$ Explain your reasoning?

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Key Concepts

Stable vs. Radioactive Isotopes

This concept involves understanding that isotopes with stable nuclei are typically more abundant in nature than those that are radioactive. Radioactive isotopes decay over time, so even if they are created in nuclear reactions, their concentrations are generally low in natural sources. The stability of a nuclide is influenced by its nuclear binding energy and the balance between protons and neutrons.

Nuclear Stability Principles

Nuclear stability principles explain why certain combinations of protons and neutrons make a nucleus more likely to remain unchanged over time. Nuclei with configurations that result in lower energy states tend to be more stable. In contrast, nuclei that have imbalances or are energetically excited may undergo decay, affecting their natural abundance.

Natural Isotopic Abundance

This concept refers to the proportion of the different isotopes of an element that are found in nature. Natural abundance is determined by the stability of the isotopes; stable isotopes generally have higher natural abundances because they do not decay into other elements or isotopes, thereby persisting over geological time scales.

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