A 4.87 MeV alpha particle from a ^226 Ra decay makes a head-on collision with a uranium nucleus

step 1 What is the distance of closest approach for part a? So our expression for our distance of close

A 4.87 MeV alpha particle from a ^226 Ra decay makes a...

A $4.87 \mathrm{MeV}$ alpha particle from a ${ }^{226} \mathrm{Ra}$ decay makes a head-on collision with a uranium nucleus. A uranium nucleus has 92 protons. (a) What is the distance of closest approach of the alpha particle to the center of the nucleus? Assume that the uranium nucleus remains at rest and that the distance of closest approach is much greater than the radius of the uranium nucleus. (b) What is the force on the alpha particle at the instant when it is at the distance of closest approach?

Key Concepts

Coulomb's Law

Coulomb's Law describes the force between two charged particles. It states that the force is proportional to the product of the charges and inversely proportional to the square of the distance between them. This law is fundamental in the calculation of the repulsive force between the alpha particle and the nuclear protons during a scattering event.

Electrostatic Potential Energy

Electrostatic potential energy is the energy stored due to the positions of charged particles relative to each other. In scenarios involving charged particles approaching each other, as in nuclear scattering, the energy associated with their separation can be equated to their initial kinetic energy to determine the distance of closest approach.

Conservation of Energy in Charged Particle Scattering

In the context of charged particle scattering, conservation of energy implies that the initial kinetic energy of the projectile is transformed into the electrostatic potential energy at the point of closest approach. This relationship is essential for calculating how far the particle can approach the nucleus before being repelled.

Distance of Closest Approach

The distance of closest approach is the minimum separation between two charged particles during a scattering event, at which point the projectile's kinetic energy has been completely converted into electrostatic potential energy. This concept is critical in analyzing collisions where one particle is deflected by the repulsion from another, and it provides insight into the interaction dynamics between the particles.

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