Isotopes with even atomic numbers are more abundant than isotopes with odd atomic numbers due to the way atomic nuclei are formed.
The stability of atomic nuclei is influenced by the nuclear forces that hold the protons and neutrons together. Nuclei with even numbers of protons and neutrons tend to have greater stability because the pairing of particles in energy levels is more favorable. This phenomenon is known as the "even-odd effect."
In atomic nuclei, protons and neutrons occupy specific energy levels or shells. According to the nuclear shell model, these energy levels are filled in pairs, with each pair consisting of particles of opposite spins. This pairing of particles leads to increased stability because it minimizes the overall energy of the nucleus.
When an atomic nucleus has an even number of protons and/or neutrons, it allows for complete pairing of particles within their respective energy levels. This complete pairing contributes to greater nuclear stability. As a result, isotopes with even atomic numbers (both protons and neutrons) are more abundant because they have a higher likelihood of forming and being stable.
In contrast, isotopes with odd atomic numbers have an imbalance of particles in their energy levels, which can lead to slightly higher energy states and reduced stability compared to their even-numbered counterparts. This relative instability can make them less abundant in nature.