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Electric potential energy plays a crucial role in understanding how charged particles interact with each other. Imagine it like energy stored between two charges due to their positions. When you move these charges closer or further apart, you're dealing with electric potential energy.
In our context, an alpha particle is approaching a gold nucleus. The alpha particle has a positive charge, and so does the nucleus. As these positively charged bodies move closer, the electric potential energy between them increases. This energy becomes important as it is the point at which the alpha particle temporarily halts its motion.
The formula for electric potential energy between two point charges is: \[ U_e = \frac{k \cdot q_1 \cdot q_2}{r} \]where:

• \( k \) is the Coulomb's constant,
• \( q_1 \) and \( q_2 \) are the charges, and
• \( r \) is the distance between the charges.

Consequently, as the alpha particle moves closer to the nucleus, the conversion of kinetic energy into electric potential energy halts its progress.

Kinetic energy relates to the motion of an object. For the alpha particle coming toward a nucleus, its motion embodies its kinetic energy. But as it nears the nucleus, this energy undergoes conversion.
In the experiment, when the particle halts, it indicates that its kinetic energy has transformed completely into electric potential energy. This phenomenon follows the conservation of energy principle which states that energy cannot be created or destroyed, only converted from one form to another.
In practical terms, the kinetic energy \( K \) given to the alpha particle is \( 5.0 \times 10^{-13} \text{ J} \). Upon nearing the nucleus, the kinetic energy converts to electric potential energy at the pointing exactly where the particle stops its forward motion.
This conversion helps us determine how close the alpha particle can approach the nucleus before stopping completely.

Coulomb's Law describes the interaction between two charged particles. It quantifies the amount of force between them based on their charges and the distance between them. The law is a cornerstone in understanding electrostatic forces.
The formula of Coulomb's Law is given as:\[ F = \frac{k \cdot |q_1 \cdot q_2|}{r^2} \]Here, the symbols represent:

• \( F \): the magnitude of force between the particles,
• \( k \): Coulomb's constant, \( 8.99 \times 10^9 \text{ Nm}^2/\text{C}^2 \),
• \( q_1 \) and \( q_2 \): the electric charges, and
• \( r \): the distance between the charges.

Coulomb's Law explains why the alpha particle stops. As it approaches the gold nucleus, the ever-increasing repulsive force due to their like charges brings the alpha particle to a standstill.

The atomic number is a defining trait of an element, indicating how many protons reside in its nucleus. It's symbolized as \( Z \).
In our case, the gold nucleus has an atomic number of 79, denoting 79 protons. This information becomes critical in scaling the electric potential energy during the alpha particle scattering experiment.
Each proton carries a charge of \( e = 1.6 \times 10^{-19} \text{ C} \). Therefore, the charge of a gold nucleus is \( 79e \), a crucial value in calculating the forces and potential energy between the interacting particles.
Understanding the atomic number helps calculate the level of interaction between the charges, guiding us in solving how closely the alpha particle can approach the nucleus based on energy calculations.