For heavier nuclei (with mass number A>56), the binding energy per nucleon gradually decreases as the nucleon number increases. This trend indicates that heavier nuclei are less stable compared to intermediate-sized nuclei, and this can be explained by the following factors:

1. Nuclear Forces and Distance Between Nucleons

• In a nucleus, protons and neutrons are bound together by the strong nuclear force, which is a short-range force.
• As the number of nucleons increases, the effective range of the strong nuclear force becomes less significant for the nucleons at the edge of the nucleus. These nucleons experience weaker attraction compared to those near the center.
• For larger nuclei, the strong force can’t efficiently hold the outer nucleons together, leading to a lower binding energy per nucleon.

2. Coulomb Repulsion Between Protons

• Larger nuclei contain more protons, which repel each other due to the Coulomb (electrostatic) force.
• This repulsion increases with the number of protons in the nucleus, and it becomes harder to keep the nucleus together as the repulsive force overcomes the attractive strong nuclear force.
• This effect reduces the binding energy per nucleon for heavier nuclei.

3. Nuclear Saturation

• The nuclear force is saturating, meaning it only affects nucleons that are in close proximity to each other. As a result, when the number of nucleons increases, the additional nucleons contribute less to the overall binding energy.
• In lighter nuclei, each nucleon is able to interact strongly with many other nucleons, leading to a higher binding energy per nucleon. In contrast, heavier nuclei have more nucleons that are not as effectively bound, lowering the average binding energy per nucleon.

4. Shell Effects and Nuclear Structure

• In nuclei with intermediate mass (around A≈56, such as iron), nucleons fill nuclear energy levels in a manner that optimizes the strong nuclear force. This results in a relatively high binding energy per nucleon.
• For heavier nuclei, the shell effects (where nucleons fill discrete energy levels) become less pronounced, and the added nucleons do not contribute as effectively to the overall binding, further reducing the binding energy per nucleon.

Conclusion:

The decrease in binding energy per nucleon in heavier nuclei is primarily due to the combination of weaker nuclear forces acting on the outer nucleons, increased Coulomb repulsion between protons, and the saturation of the nuclear force. These factors make it harder to bind additional nucleons, which explains why nuclei with higher atomic numbers (especially beyond iron) become less stable and have a lower binding energy per nucleon.

The nuclear force originates from the fundamental interactions between the constituent particles of nucleons (protons and neutrons), which are quarks and gluons. The nuclear force, also known as the strong nuclear force, is a residual effect of the strong interaction, one of the four fundamental forces in nature. Here’s a breakdown:

1. The Strong Interaction and Quantum Chromodynamics (QCD)

• At the most fundamental level, protons and neutrons are composed of quarks (up and down quarks), bound together by the exchange of particles called gluons.
• The gluons mediate the strong interaction, described by the theory of Quantum Chromodynamics (QCD). This interaction is responsible for keeping quarks tightly confined within protons and neutrons.

2. Residual Strong Force Between Nucleons

• While the strong interaction primarily binds quarks within individual nucleons, a residual effect of this force extends beyond individual nucleons, binding protons and neutrons together in the nucleus.
• This residual strong force is what we refer to as the nuclear force. It acts between nucleons and has the following characteristics:
  • Attractive at medium distances (1–3 femtometers): This attraction binds protons and neutrons together in the nucleus.
  • Repulsive at very short distances (<1 femtometer): This prevents nucleons from collapsing into each other.
  • Short-ranged: It diminishes rapidly beyond about 3 femtometers, which is why it cannot bind nuclei with extremely large numbers of nucleons effectively.

3. Mediators of the Nuclear Force: Pions

• The nuclear force can be described as mediated by the exchange of mesons, particularly pions (particles composed of a quark and an antiquark).
• The exchange of pions between nucleons creates the attractive and repulsive forces that hold the nucleus together.

Summary

The origin of the nuclear force lies in the strong interaction between quarks, mediated by gluons, as described by Quantum Chromodynamics (QCD). The nuclear force is a residual effect of this interaction, manifesting as the force that binds nucleons together within atomic nuclei.

Binding Energy and Stability

• Binding energy is the energy required to separate all the nucleons (protons and neutrons) in a nucleus.
• Higher binding energy per nucleon means the nucleus is more stable.
• Energy is released when nucleons move to a more stable arrangement with a higher binding energy per nucleon.

Energy Release Mechanisms

1. In Fusion (Increase in Binding Energy):

   • Light nuclei (e.g., hydrogen isotopes) combine to form a heavier nucleus.
   • The products of fusion (e.g., helium) have a higher binding energy per nucleon than the reactants.
   • This means the nucleons are now in a more stable configuration.
   • The difference in binding energy between the reactants and products is released as energy.

   Example:

   • When two hydrogen nuclei fuse to form helium, the binding energy per nucleon increases from ~1 MeV (for hydrogen) to ~7 MeV (for helium).
   • This increase translates into the release of a large amount of energy.

2. In Fission (Decrease in Binding Energy):

   • Heavy nuclei (e.g., uranium or plutonium) split into lighter nuclei.
   • The binding energy per nucleon of the products (e.g., barium and krypton) is higher than that of the original heavy nucleus.
   • The nucleons in the products are more tightly bound, making them more stable.
   • The difference in binding energy is released as energy.

   Example:

   • In the fission of uranium-235, the binding energy per nucleon increases from ~7.6 MeV to ~8.5 MeV in the fission products.
   • This small increase in binding energy per nucleon, multiplied by the total number of nucleons, releases a significant amount of energy.

Why Energy is Released in Both Cases?

The release of energy depends on moving toward greater nuclear stability:

• Fusion: Light nuclei increase their stability by increasing their binding energy per nucleon (moving up on the binding energy curve).
• Fission: Heavy nuclei increase their stability by breaking into smaller nuclei with higher binding energy per nucleon (moving down the curve).

Connection to Einstein’s E = mc^2

E=mc2:

The energy released in both processes comes from the mass defect—the difference between the mass of the reactants and the products.

• When binding energy increases, a small portion of mass is converted into energy.
• This energy is released as kinetic energy, heat, or radiation.