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The formation of an atomic nucleus involves gathering protons close together, within a tiny space. This is an essential concept in nuclear physics. Protons are positively charged particles. They naturally repel each other due to their like charges. However, in an atomic nucleus, they must be held together through strong interactions.

In our scenario, assembling a nucleus similar to that of beryllium (with three protons), imagine forming an equilateral triangle. You place a proton at each vertex of the triangle. This configuration helps to simplify calculations. The side of the triangle in this exercise is extremely tiny, with a length of about \(2.00 \times 10^{-13} \text{ m}\). This size is typical for nucleons at the atomic level.

Building an atomic nucleus from individual protons requires work against their natural repulsive forces. Understanding how protons are kept together helps us better grasp the concept of nuclear forces. These forces are essential in maintaining the stability of the nucleus.

Coulomb's Law is crucial in understanding interactions between electrically charged particles.

It states that the electric force between two point charges is directly proportional to the product of their charges, and inversely proportional to the square of the distance between them. The equation for the force \( F \) is: \[ F = k \frac{|q_1 q_2|}{r^2} \] where \( k = 8.99 \times 10^9 \text{ N m}^2/\text{C}^2 \) is the electrostatic constant, \( q_1 \) and \( q_2 \) represent the charges, and \( r \) is the distance between the two charges.

In our context, it helps calculate the force between protons. Since both are positive, they repel each other. The Coulomb force gives us understanding of how much they push apart, and this enables us to calculate the work needed to bring them close enough to form a nucleus.

Moreover, Coulomb's Law assists in deriving the potential energy between charges, which is necessary for understanding energy dynamics when assembling atomic nuclei.

Protons are central to nuclear physics, and understanding their interactions is vital.

Each proton carries a positive charge of \(1.6 \times 10^{-19} \text{ C}\). When these protons are placed near each other, like in a nucleus, they experience repulsive forces due to their like charges. This repulsion must be overcome in order to assemble them into a stable formation.

In the example of the equilateral triangle, each pair of protons interacts through electrostatic forces. Using Coulomb's Law, we compute the potential energy created by this repulsion:

• Potential energy, \( U \), for one pair is determined by: \[ U = k \frac{q^2}{r} \]
• Here, \( q = 1.6 \times 10^{-19} \text{ C} \) and the distance \( r = 2.00 \times 10^{-13} \text{ m} \)

Since a triangle has three pairs of protons, you calculate the interaction energy for one pair and then multiply it by three to find the total potential energy. This total represents the work needed to overcome the repulsion and assemble the nucleus. Protons interact not only through electric forces like calculated here, but also through nuclear forces that bind them together in a real nucleus.