Bohr Model Equations: Kinetic and Potential Energy in Hydrogen Atom

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SUMMARY

The discussion focuses on the relationship between kinetic energy (KE) and potential energy (PE) in the context of the Bohr model of the hydrogen atom. It establishes that KE is equal to negative PE (KE = -PE) and explores the implications of a hydrogen atom absorbing a photon of energy E, which leads to a change in potential energy. The participants clarify that the change in kinetic energy during this transition can be expressed as the difference between final and initial kinetic energies (KEf - KEi). The discussion emphasizes the derivation of these relationships using centripetal force and electric force principles.

PREREQUISITES
  • Understanding of the Bohr model of the hydrogen atom
  • Familiarity with kinetic and potential energy concepts
  • Knowledge of centripetal force and electric force interactions
  • Basic proficiency in integrating functions in physics
NEXT STEPS
  • Study the derivation of kinetic and potential energy relationships in the Bohr model
  • Learn about the implications of photon absorption on atomic energy levels
  • Explore the mathematical integration of forces in circular motion
  • Investigate the concept of energy conservation in quantum systems
USEFUL FOR

Students studying quantum mechanics, physics educators, and anyone interested in atomic energy transitions and the Bohr model's implications.

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Homework Statement



Write an expression relating the kinetic energy KE of the electron and the potential energy PE in the Bohr model of the hydrogen atom. (Use any variable or symbol stated above as necessary.)

b) Suppose a hydrogen atom absorbs a photon of energy E, resulting in the transfer of the electron to a higher-energy level. Express the resulting change in the potential energy of the system in terms of E.

(c) What is the change in the electron's kinetic energy during this process? (Use any variable or symbol stated above as necessary.)

Homework Equations



THATS THE QUESTION!

The Attempt at a Solution



KE = -PE
Ef - Ei
KEf - KEi
 
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I don't think KE = - PE. How did you arrive at this?
I used centripetal force = electric force for a circular orbit to get the velocity and kinetic energy. I integrated F*dr in from infinity (where PE = 0) to get the PE. I found a simple relationship between KE and PE, but not that one.
 

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