Calculating Total Energy of an Electron Orbiting a Hydrogen Nucleus

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Homework Help Overview

The discussion revolves around calculating the total energy of an electron orbiting a hydrogen nucleus, specifically examining the expression Etotal = -e^2/ 8ε0 π r. The subject area includes concepts from electrostatics and orbital mechanics.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants are analyzing the kinetic and potential energy components of the total energy expression. There are attempts to clarify the signs associated with the forces and energies involved, particularly questioning the treatment of negative signs in the equations.

Discussion Status

The discussion is ongoing, with participants questioning the correctness of the signs in the equations and seeking clarification on the interpretation of potential energy. Some guidance has been offered regarding the nature of the expressions being discussed, but no consensus has been reached.

Contextual Notes

Participants are navigating through the implications of signs in energy and force equations, which may reflect underlying assumptions about the system being analyzed. There is an emphasis on understanding the definitions and roles of kinetic and potential energy in this context.

Clara Chung
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Homework Statement


Prove that the total energy of an electron orbiting a hydrogen nucleus is Etotal = -e^2/ 8ε0 π r where e is the magnitude of charge of an electron and r is the orbital radius.

Homework Equations


Knowledge

The Attempt at a Solution


Here is my attempt:
For KE,
mv^2/r = -ke^2/r^2
mv^2/2 = -ke^2/2r

For PE,
PE= k(-e)e/r - k(-e)e/∞
=-ke^2/r
KE+PE =-3e^2/ 8ε0 π r ,why am I wrong? please help
 
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Clara Chung said:
mv^2/r = -ke^2/r^2
Is the left hand side there positive or negative? What about the right hand side?
 
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haruspex said:
Is the left hand side there positive or negative? What about the right hand side?
LHS is positive and RHS is negative? They should both be positive as the negative sign represents the direction?I don't get it
 
Clara Chung said:
LHS is positive and RHS is negative? I don't get it
So the right hand side must be wrong. Try explaining in detail how you arrive at the minus sign there.
 
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haruspex said:
So the right hand side must be wrong. Try explaining in detail how you arrive at the minus sign there.
Thanks for helping me. But why the minus sign in potential energy need not to consider?
 
Clara Chung said:
Thanks for helping me. But why the minus sign in potential energy need not to consider?
That is not an energy expression, it's a force expression.
 
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