An alpha particle with kinetic energy 11.0 MeV makes a...

An alpha particle with kinetic energy 11.0 MeV makes a head-on collision with a lead nucleus at rest. What is the distance of closest approach of the two particles? (Assume that the lead nucleus remains stationary and that it may be treated as a point charge. The atomic number of lead is $82 .$ The alpha particle is a helium nucleus, with atomic number $2.)$

Key Concepts

Electrostatic Potential Energy

Electrostatic potential energy quantifies the potential energy stored in a system of charges due to their positions. It is calculated using the product of the charges, Coulomb's constant, and the inverse of the separation distance, which makes it crucial for analyzing how kinetic energy can be converted into potential energy during interactions.

Point Charge Approximation

The point charge approximation treats distributed charges as if all of their charge were concentrated at a single point. This simplification allows for easier application of Coulomb's Law in problems involving particle interactions, particularly when the physical size of the particles is negligible compared to the distances involved.

Distance of Closest Approach

The distance of closest approach is defined as the minimum separation between two interacting charged particles during a collision. It is found by setting the initial kinetic energy equal to the electrostatic potential energy at this point and solving for the distance, offering insight into the extent of the interaction between the particles.

Coulomb's Law

Coulomb's Law explains the force between two point charges by stating that the force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. This law is the foundation for understanding electrostatic interactions in a variety of physical systems.

Conservation of Energy

The principle of conservation of energy asserts that the total energy in an isolated system remains unchanged over time. In collision scenarios, this means that the initial kinetic energy of a moving charged particle can be entirely converted into electrostatic potential energy at the point of closest approach, thereby enabling calculations of key interaction distances.

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