Question

The increase in potential energy as two atoms in a diatomic molecule get closer is partly due to the core electrons being forced by the exclusion principle to higher energies. Can you argue why the residual strong force the inter nucleon attraction of Chapter \(11-\) should have a "hard core"?

Short answer

The residual strong nuclear forces should have a 'hard core' due to the Pauli's exclusion principle. When the nucleons inside an atomic nucleus try to get too close, they are forced by the exclusion principle to assume higher energy states, resulting in a steep rise in the potential energy, which is translated as a hard core repulsion. This repulsion prevents the nucleons from coming too close to each other, thereby maintaining their identities.

Step-by-step solution

Understanding the Exclusion Principle

Firstly, note that according to the Pauli's exclusion principle, two or more identical fermions cannot occupy the same quantum state within a quantum system at the same time. This is the reason why electrons in atoms occupy different energy levels, thus causing the increase in potential energy when atoms get closer.

Apply Exclusion Principle to Nucleons

Now, apply the exclusion principle to nucleons (protons and neutrons) within an atomic nucleus. Since nucleons are fermions, they also follow the Pauli's exclusion principle. Therefore, when nucleons try to come too close to each other, they are forced by this principle to higher energy levels. This results in a hard core repulsion (a steep rise in potential energy).

Concept of 'Hard Core'

The term 'hard core' in nuclear forces refers to the behavior of the strong force that becomes extremely repulsive at distances so short that the involved particles (nucleons) are forced by the exclusion principle to assume higher energy states. This acts as a barrier preventing them from merging together, thereby keeping their identities intact.

Key concepts

Modern Physics

Modern Physics is a branch of physics which deals with the post-Newtonian concepts of the 20th century. It primarily focuses on the theory of relativity, quantum mechanics, and the interaction of matter and energy. One of the monumental discoveries in Modern Physics is the Pauli's exclusion principle, which fundamentally explains why particles with certain properties (fermions) cannot occupy the same quantum state simultaneously. This principle has far-reaching implications, including its substantial effect on the behavior of electrons in atoms, nucleons in nuclei, and the structural integrity of objects. As we delve deeper into the study of atomic interactions, such as those in diatomic molecules, and the powerful nucleon-to-nucleon forces, we’re continually confronted with the nuanced consequences of this quantum law.

Diatomic Molecule Potential Energy

Potential energy in diatomic molecules is closely related to the distances between the two bonded atoms. As they approach each other, their potential energy landscape exhibits a well-defined behavior — initially decreasing as they bond, reaching a minimum (the equilibrium bond distance) and then steeply increasing as they get too close, a phenomenon partly due to electron-electron repulsion magnified by the Pauli exclusion principle. This interaction curve explains the bond strength and distance through quantum mechanics, depicting a balance between the attractive forces that hold the atoms together and the repulsive forces that prevent them from collapsing into each other.

Nucleon Strong Force

Within the atomic nucleus, nucleons (protons and neutrons) are bound together by the strong force, also known as the strong nuclear force. This force is responsible for keeping the nucleus stable despite the electrostatic repulsion between like-charged protons. The strong force is powerful, but only over short ranges. It ensures that nucleons adhere tightly to one another, but as distances between nucleons shrink below a critical threshold, the potential energy begins to climb drastically due to the onset of hard core repulsion. This is crucial for maintaining nucleic stability across the vast array of known isotopes.

Hard Core Repulsion

Hard core repulsion is an essential concept in nuclear physics, referring to a very short-range, highly repulsive interaction between particles. Due to the Pauli's exclusion principle, nucleons are forbidden from being in the same quantum state. When the distances are so close that overlapping might occur, this principle dictates that the nucleons must occupy higher energy levels. This leads to a sharp increase in potential energy, acting as a 'hard core' that disallows any further approach. In essence, hard core repulsion serves as a natural barrier enforcing the principle and hence, safeguarding the integrity of the nucleus.