Question

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?

Short answer

The most abundant isotopes are generally those that are closest to having a balanced number of protons and neutrons. So, \(_{20}^{40} \mathrm{Ca}\), _{15}^{31} \mathrm{P}, and _{30}^{64}\mathrm{Zn} are the most abundant.

Step-by-step solution

Problem (a)

Consider \(_{20}^{40} \mathrm{Ca}\) and \(_{20}^{42} \mathrm{Ca}\). Both have 20 protons, but differ when it comes to neutrons. The first has 20 neutrons (40-20), while the second has 22 neutrons (42-20). The isotopes with approximately equal number of protons and neutrons are the most abundant. Thus, the answer is \(_{20}^{40} \mathrm{Ca}\), because it has equal number of protons and neutrons

Problem (b)

Consider \(_{15}^{31} \mathrm{P}\) and \(_{15}^{32} \mathrm{P}\). The first isotope has 16 neutrons (31-15), and the second has 17 neutrons (32-15). In this case, \(_{15}^{31} \mathrm{P}\) is more abundant because it has a more evenly balanced number of protons to neutrons.

Problem (c)

Consider \(_{30}^{63}\mathrm{Zn}\) and \(_{30}^{64}\mathrm{Zn}\) . The first has 33 neutrons (63-30), and the second has 34 neutrons (64-30). The answer is \(_{30}^{64}\mathrm{Zn}\) since it is closest to having a balanced number of protons and neutrons.

Key concepts

Isotopes

Isotopes are variations of the same chemical element that have the same number of protons but different numbers of neutrons. This variation in neutron number gives each isotope a different atomic mass. For example, carbon-12 (_{6}^{12}_{}C) and carbon-14 (_{6}^{14}_{}C) are both isotopes of carbon, sharing the same atomic number (6 protons) but having different neutron counts of 6 and 8, respectively. Isotopes exhibit nearly identical chemical behavior but can have vastly different physical properties, such as radioactivity or stability. In natural sources, the abundance of isotopes depends on factors like nuclear stability and the processes that gave birth to the elements, such as nucleosynthesis in stars.

Neutron Number

The neutron number, often denoted as N, represents the count of neutrons in an atomic nucleus. It is a key factor in determining the isotope of an element. Since neutrons and protons are similar in mass, and the atomic mass is the sum of these particles, variations in neutron number create isotopes with different atomic masses. Neutron number is calculated by subtracting the number of protons (atomic number) from the atomic mass number. The balance between neutron and proton numbers is crucial for nuclear stability; having too many or too few neutrons in relation to protons can make an isotope radioactive or unstable. Generally, a balanced ratio leads to greater natural abundance, such as seen with _{20}^{40}Ca, which has an equal number of protons and neutrons.

Proton Number

The proton number, also known as the atomic number, is the count of protons in the nucleus of an atom, and it determines the chemical element. Each element on the periodic table possesses a unique proton number which dictates its placement on the table and its chemical properties. For instance, carbon always has 6 protons, and any atom with 6 protons is carbon. The proton number is crucial in identifying an element, and it remains constant across all isotopes of that element. In isotopic abundance, the proton number is consistent while the neutron number may vary, differentiating isotopes of the same element.

Nuclear Stability

Nuclear stability refers to how well an atom's nucleus is held together and is determined by the forces among the protons and neutrons. Stable nuclei have a balance of protons to neutrons that allows the atom to exist without spontaneously altering its structure through nuclear reactions such as radioactive decay. For lighter elements, a stable isotope often has a balanced or nearly balanced number of protons and neutrons, while heavier elements require a greater number of neutrons to offset the electrical repulsion between protons. As an isotope becomes more imbalanced, it becomes less stable and more prone to radioactive decay, which reduces its natural abundance. Stable isotopes, such as _{20}^{40}Ca and _{15}^{31}P, are more likely to be found in nature due to their enduring nuclear configurations.