Correct way to calculate energy in Bohr Atom Model

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In summary, the conversation discusses the use of the Coulomb's force formula and the integration of energy. The minus sign from the electron's charge in the Coulomb's force formula cancels out when integrated, leading to a workaround for using positive potential energy. The correct way to do this is to use the definition of potential energy and enter charges by their normal value, not absolute value.
  • #1
Bassalisk
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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?
 

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  • #2
Since the F = -dV/dr, that would make dV = -F dr. I think you used a plus.
 
  • #3
Thats by definition? So, I put full charge values into energy too, not by absolute value?
 
  • #4
E_potential = - int Fc dr

please check the definition of potential energy
 
  • #5
Again, I do enter charges by normal value, not absolute value, that would get rid of minus from the electric charge of electron (-e)?
 

What are the postulates of the Bohr Atom Model?

The postulates of the Bohr Atom Model are:

  1. The electrons in an atom move in circular orbits around the nucleus.
  2. The energy of an electron in a particular orbit is constant and does not change as long as the electron remains in that orbit.
  3. An electron can only emit or absorb energy when it jumps from one orbit to another.
  4. The energy of an electron in an orbit is proportional to its distance from the nucleus.
  5. The angular momentum of an electron in an orbit is quantized, meaning it can only have certain values.

Why was the Bohr Atom Model significant in the history of atomic theory?

The Bohr Atom Model was significant because it was the first model to successfully explain the line spectra of atoms. It also introduced the concept of quantized energy levels and paved the way for further advancements in atomic theory.

How does the Bohr Atom Model differ from the Rutherford model?

The Rutherford model proposed that electrons move in orbits around the nucleus similar to planets around the sun, but it could not explain the stability of atoms. The Bohr Atom Model, on the other hand, introduced the concept of quantized energy levels and explained the stability of atoms by stating that electrons can only exist in certain orbits with fixed energies.

What are the limitations of the Bohr Atom Model?

The Bohr Atom Model is limited in its ability to explain the behavior of atoms with more than one electron. It also does not account for the wave-like nature of electrons and their uncertain position and momentum, which is described by quantum mechanics.

How has the Bohr Atom Model influenced modern atomic theory?

The Bohr Atom Model introduced the concept of quantized energy levels, which is still used in modern atomic theory. It also paved the way for the development of quantum mechanics, which provides a more accurate and comprehensive understanding of the behavior of atoms.

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