Correct way to calculate energy in Bohr Atom Model

  • Context: Graduate 
  • Thread starter Thread starter Bassalisk
  • Start date Start date
  • Tags Tags
    Atom Bohr
Click For Summary
SUMMARY

The discussion focuses on the correct calculation of energy in the Bohr Atom Model, specifically addressing the integration of Coulomb's force and its implications for potential energy. The user encountered a discrepancy when integrating the attractive Coulomb force, leading to a positive energy result that contradicts expected outcomes. The confusion arises from the treatment of charges and the definition of potential energy, particularly the sign conventions used in the equations. The correct approach involves using the full charge values in the potential energy calculation, ensuring that the negative sign from the attractive force is appropriately accounted for.

PREREQUISITES
  • Understanding of Coulomb's Law and electric forces
  • Familiarity with the Bohr Model of the atom
  • Basic knowledge of calculus, specifically integration techniques
  • Concept of potential energy in electrostatics
NEXT STEPS
  • Review the derivation of potential energy in electrostatics
  • Study the application of Newtonian mechanics in atomic models
  • Learn about the implications of charge signs in physics equations
  • Explore advanced topics in quantum mechanics related to the Bohr Model
USEFUL FOR

Students of physics, particularly those studying atomic models, educators teaching electrostatics, and researchers interested in the foundational principles of quantum mechanics.

Bassalisk
Messages
946
Reaction score
2
I was deriving Bohr model formulas and I stumbled upon a problem.

When I use the postulate that says that you can apply Newtonian Mechanics to orbiting electron, I wrote the Coulomb's force as following:


Fc=(-e)*Z*e/(4pi(epsilon0)*r^2)


Minus from the electron means that the force will be attractive. But when I integrated it to get the energy I got a minus from integration. Now if I put in the charges in, I got that minus like from coulombs force and those 2 cancel out, leaving me with positive energy.


I escaped from this by using potential energy as positive and substituting charges like I did in Coulomb's Force, but this is workaround and its not mathematically correct.

I attached a relevant image.

What is full correct way to do this?
 

Attachments

Physics news on Phys.org
Since the F = -dV/dr, that would make dV = -F dr. I think you used a plus.
 
Thats by definition? So, I put full charge values into energy too, not by absolute value?
 
E_potential = - int Fc dr

please check the definition of potential energy
 
Again, I do enter charges by normal value, not absolute value, that would get rid of minus from the electric charge of electron (-e)?
 

Similar threads

Undergrad Riddle: Where is Epsilon in Bohr Model of Atom?
  • · Replies 10 ·
Replies
10
Views
2K
Undergrad Is the magnetic moment of a hydrogen atom not equal to Bohr's magneton?
  • · Replies 22 ·
Replies
22
Views
2K
Undergrad Will an electron release energy when it is added into an atom?
  • · Replies 6 ·
Replies
6
Views
1K
Undergrad Why the energy inversely propotional to n^2 in Bohr model
  • · Replies 5 ·
Replies
5
Views
2K
High School How is Bohr's atom model convenient with quantum mechanics?
  • · Replies 3 ·
Replies
3
Views
2K
High School Some website about new Bohr model
  • · Replies 3 ·
Replies
3
Views
1K
Undergrad Electromagnetic radiation, photons, quantized energy levels
  • · Replies 1 ·
Replies
1
Views
2K
High School Question on the Bohr atomic model and energy
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Is my interpretation of the g-factor correct?
  • · Replies 4 ·
Replies
4
Views
1K
Undergrad Question about the Bohr model of atom and and electron in an orbital
  • · Replies 7 ·
Replies
7
Views
2K