Problem 63 - Master Resource Book in JEE Main Physics

Question

Two nucleons are at a separation of \(1 \mathrm{fm}\). The net force between them is \(F_{1}\), if both neutrons, \(F_{2}\) if both are protons and \(F_{3}\) if one is a proton and the other is a neutron. (a) \(F_{1}>F_{2}>F_{3}\) (b) \(F_{2}>F_{1}>F_{3}\) (c) \(F_{1}=F_{3}>F_{1}\) (d) \(F_{1}=F_{2}>F_{3}\)

Step-by-Step Solution

Answer

Option (d) is correct: F1 = F2 > F3.

Step 1: Understanding the Forces

There are essentially three types of forces acting between nucleons: the strong nuclear force, which is attractive and acts between all nucleons (neutrons and protons), and the electromagnetic force, which is repulsive and acts between protons due to their positive charge. Neutrons do not carry an electric charge.

Step 2: Comparing Forces F1, F2, F3

- **F1** represents the force between two neutrons. Since neutrons are neutral, this is purely due to the strong nuclear force. - **F2** is the force between two protons. This involves both the strong nuclear force and the repulsive electromagnetic force. - **F3** is the force between a proton and a neutron. This is purely the attractive strong nuclear force.

Step 3: Evaluating Net Force Strengths

Between two protons, the net force (F2) is weaker than between two neutrons (F1) because it is the sum of strong attraction and electromagnetic repulsion. Therefore, F2 < F1. The forces F1 and F3 involve purely nuclear forces, but F1 is not significantly greater than F3 as they involve similar attraction by the strong force.

Step 4: Identifying the Correct Option

Given the evaluations: - F1 > F2 due to the lack of repulsive forces in F1, - F3 is comparable to F1 as both are purely strong force interactions without repulsion, resulting in: **F1 = F3 > F2**.

Key Concepts

Strong Nuclear Force

The strong nuclear force is a powerful yet short-range force that binds nucleons (protons and neutrons) within an atomic nucleus. It is the strongest of the four fundamental forces in physics, though its effects are only noticeable at subatomic distances, typically less than a few femtometers (1 fm = 10^{-15} meters).
This force is primarily responsible for holding the atomic nucleus together despite the repulsion between protons due to electrostatic forces.

• Within the nucleus, the strong nuclear force acts to overcome the electrostatic repulsion between positively charged protons.
• It is a short-range force, meaning it quickly diminishes in strength beyond a few femtometers. This confines its effects to only neighboring nucleons within the nucleus.
• Because neutrons are neutral, they only participate in the strong nuclear force, making their interactions with protons and each other solely dependent on this force.

The strong nuclear force contributes significantly to nuclear stability, ensuring that atomic nuclei remain intact. In scenarios involving nuclei particles like two neutrons (F1) or a neutron-proton pair (F3), this force prevails without the interference of other forces, as seen in atomic interactions.

Electromagnetic Force

The electromagnetic force, which acts between charged particles, is a long-range force responsible for a multitude of physical phenomena. In the context of nucleons, it plays a crucial role in interactions involving protons.
The electromagnetic force is one of the two forces considered when examining the interactions among nucleons, particularly when the particles are charged.

• Protons, carrying a positive charge, repel each other due to electromagnetic forces, impacting the net force calculations in nucleonic interactions.
• This force extends over a larger range compared to the strong nuclear force, but it weakens much slower as the distance increases.

When discussing nucleon interactions, particularly between two protons (F2), the electromagnetic force contributes a repulsive component.
This repulsion is balanced by the strong nuclear force, though it diminishes the net attractive force, resulting in F2 being less than the force between purely neutral nucleons (F1 or F3).
This interplay of forces highlights the balance that defines atomic structure and stability.

Nucleons

Nucleons refer to the particles found in the nucleus of an atom, namely protons and neutrons. These are considered the basic building blocks of the atomic nucleus.
Understanding nucleons involves comprehending their interactions and properties, given they contribute most of the mass of an atom.

• Protons are positively charged nucleons, meaning their interactions include both strong nuclear and electromagnetic forces.
• Neutrons are neutral particles, so they engage only through the strong nuclear force.

The distinction between these nucleons is fundamental when assessing forces like F1, F2, and F3. For instance, two neutrons (F1) interact through the strong nuclear force alone, while two protons (F2) experience both strong nuclear attraction and electromagnetic repulsion.
In a mixed pair (F3), the interaction follows the pattern of strong attractive force, similar to two neutrons.
This complexity within nucleon interactions underscores their critical role in atomic and nuclear physics, affecting both the stability and behavior of atoms in different conditions.