Question

Nuclei with an even number of protons and an even number of neutrons are more stable than those with an odd number of protons and/or an odd number of neutrons. What is the significance of the even numbers of protons and neutrons in this case?

Short answer

Even numbers lead to pairing energy and complete nuclear shells, enhancing stability.

Step-by-step solution

Understanding Nuclear Stability

Nuclei are made up of protons and neutrons, and their stability is influenced by the number of these particles. A nucleus with an even number of protons and neutrons tends to be more stable compared to one with odd numbers.

Explanation of Pairing

Protons and neutrons pair up with their counterparts (proton with another proton, neutron with another neutron) due to an effect known as pairing energy, which adds stability to the nucleus. Thus, even numbers of each maximize pairing and stability.

Application of Shell Model

The shell model of the nucleus is similar to the electron shell model in atoms. Nuclei with complete shells of protons and neutrons are more stable. An even number of each particle ensures pairs fill these shells, leading to greater stability.

Key concepts

Even Number of Protons

In the nucleus, protons are positively charged particles, which means they naturally repel each other due to electromagnetic forces. However, having an even number of protons helps to balance these repulsion forces, as protons can pair together.

• Proton pairing minimizes repulsive force through the benefit of pairing energy.
• This scenario contributes to a substance we call nuclear stability.

Every proton needs a partner in this pairing mechanism to achieve a more stable configuration. When protons are paired, the overall nuclear force — responsible for holding the nucleus together — is maximized, creating a bigger barrier against tendency to break apart due to repelling forces. Thus, an even number of protons is one of the keys to a stable nucleus.

Even Number of Neutrons

Similar to protons, neutrons also prefer to exist in pairs within the nucleus. Although neutrons do not possess an electrical charge, they play a substantial role in nuclear stability by acting as a buffer between protons.

• Even neutron numbers mean more complete pairs, enhancing stability.
• Neutron pairs help neutralize the destabilizing effects of proton-proton repulsion.

Having an even number of neutrons allows for optimal packing of these particles within the nuclear shell, contributing to a sturdy nuclear structure. This packing efficiency is one of the elements that help to defuse potential instabilities and adds a layer of resilience to the nucleus.

Pairing Energy

Pairing energy is a concept integral to nuclear stability. It refers to the energy released when protons or neutrons form pairs in the nucleus. This release of energy is indicative of a more stable arrangement.

• Maximized pairing energy occurs with even numbers of protons and neutrons.
• It enhances the energetic stability of the nucleus, reducing the likelihood of decay.

The physics behind pairing energy can be understood as analogous to electron pairing in atomic orbitals, albeit within the nucleus among nucleons. Each proton and neutron strive to achieve a stable pair, thereby releasing energy that aids in keeping the nucleus intact. Pairing energy, therefore, is fundamental in understanding why even-numbered nucleons contribute to a more resilient nucleus.

Nuclear Shell Model

The nuclear shell model provides a framework to understand the arrangement and stability of nucleons within the nucleus. It's comparable to the electron configurations found in atomic physics. The model suggests that nucleons (protons and neutrons) fill discrete energy levels or "shells."

• Nuclei with completely filled shells are more stable and less likely to react.
• Even numbers of protons and neutrons help ensure these shells are fully occupied.

Just as electrons fill atomic shells in a manner that minimizes energy, protons and neutrons in a nucleus fill nuclear shells following a similar principle. The energy levels are defined such that when they are filled completely, the nucleus is in a minimum energy state, achieving maximum stability. The presence of full shells aligns with the pattern observed in more stable nuclei having an overall even count of these subatomic particles.