Potential Energy of a Finite Proton

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SUMMARY

The discussion revolves around deriving the potential energy of a finite-sized proton in a hydrogen atom, modeled as a uniform spherical charge distribution with a charge of e and a radius of R = 8.7 x 10-16 m. Participants emphasize the application of Gauss's law and the definition of electric potential to formulate the expression for potential energy. The conversation highlights the necessity for a solid understanding of electrostatics to tackle the problem effectively.

PREREQUISITES
  • Gauss's Law
  • Electric Potential Theory
  • Understanding of Charge Distributions
  • Basic Quantum Mechanics Concepts
NEXT STEPS
  • Study the derivation of electric potential using Gauss's Law
  • Explore the implications of charge distribution on potential energy
  • Investigate the differences between point charges and finite-sized charge distributions
  • Review quantum mechanics principles related to atomic structure
USEFUL FOR

Physics students, educators, and researchers interested in atomic models and electrostatics, particularly those focusing on the behavior of protons in hydrogen atoms.

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Homework Statement


This was in a problem set I found. Suppose that the proton in a hydrogen atom is not a pointlike object, but instead described by a uniform spherical charge distribution with charge e and radius R = 8.7 x 10^-16 m. Using Gauss's law and the definition for the electric potential, derive an expression for the potential energy of this finite sized proton.

Homework Equations


CodeCogsEqn (1).gif

CodeCogsEqn (1).gif

The Attempt at a Solution


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I tried to solve this but got lost in it. Any help?
 

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