Solving the Mystery of Energy Levels in Hydrogen Atom - Jules

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Discussion Overview

The discussion revolves around the energy levels of electrons in a hydrogen atom, specifically focusing on the equation En = -RH(1/n²). Participants explore the implications of the equation, particularly the relationship between the principal quantum number n and the energy of the electron, as well as the significance of the negative sign in the energy values.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Jules expresses confusion about the relationship between the principal quantum number n and the energy of the electron, noting that a larger n seems to imply greater distance from the nucleus but results in lower energy according to the equation.
  • One participant points out the importance of the negative sign in the equation, suggesting it ensures that energy differences are positive when moving to a higher n.
  • Another participant explains that the electron is bound to the atom, resulting in negative energy, and discusses the analogy of a planet to clarify why the energy is negative and what happens as n approaches infinity.
  • There is a challenge regarding the understanding of negative numbers, with a focus on how moving from a more negative value to a less negative value represents an increase in energy.
  • Participants suggest plotting the energy values to visualize which is "higher" in the context of negative numbers.

Areas of Agreement / Disagreement

Participants express varying levels of understanding regarding the implications of the negative energy values and the significance of the quantum number n. There is no consensus on the interpretation of the negative sign or its implications for energy levels.

Contextual Notes

Some participants demonstrate confusion about the concept of negative energy and its implications, indicating a need for further clarification on the relationship between energy levels and quantum numbers.

Who May Find This Useful

This discussion may be useful for students and enthusiasts of quantum mechanics, particularly those interested in atomic theory and the behavior of electrons in hydrogen atoms.

Jules18
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Here's the equation I'm dealing with (it describes the energies that an electron in a hydrogen atom can occupy) :

En = -RH(1/n2)

The way I understood, the bigger n was the farther away the e- was from the nucleus, so it would have more potential energy.
But n is in the denominator in this eq'n, so the bigger the n the less energy the electron occupies.

So I'm kinda confused. Help?

~Jules~
 
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Jules18 said:
Here's the equation I'm dealing with (it describes the energies that an electron in a hydrogen atom can occupy) :

En = -RH(1/n2)

The way I understood, the bigger n was the farther away the e- was from the nucleus, so it would have more potential energy.
But n is in the denominator in this eq'n, so the bigger the n the less energy the electron occupies.

So I'm kinda confused. Help?

~Jules~

Note the negative sign in the equation. Potential is zero at r=infinity, and indeed as r increases, so does energy.
 
okay. I'll take your word for it.
 
Why take his word for it? Plug in some numbers and see what energies you get for n = 1 and n = 2! :smile:
 
yeah, I did a little while ago and the negative sign still bugs me a little bit.

But I'm sort of able to grasp why it's there ... it's to make sure the difference will be positive when your final n is higher than your initial n, right?

or is it to make sure that even thought the absolute value of the energy at a lower n is higher, the negative sign makes it technically lower?
 
The electron is bound to the system, meaning it has negative energy. If it were able to get an infinite distance away, which corrosponds to n -> infinity, it would have 0 energy. For example, imagine a planet. If an object orbits that planet, it has a negative energy because it's bound (all this of course, taking V = 0 at infinity). If it had some kinetic energy greater then the magnitude of the potential energy, it would obviously be free from the orbit and no longer bound. Now, of course, by no means is this the same situation, I'm just hoping to clarify why it's negative and what happens as n-> infinity.
 
Jules18 said:
yeah, I did a little while ago and the negative sign still bugs me a little bit.

But I'm sort of able to grasp why it's there ... it's to make sure the difference will be positive when your final n is higher than your initial n, right?

or is it to make sure that even thought the absolute value of the energy at a lower n is higher, the negative sign makes it technically lower?

Mmm, seems you're somewhat confused about negative numbers ?

What's the highest value, -5 or -2 ? Do you INCREASE or DECREASE X when X goes from -5 to -2 ?
 
increase?
 
Jules18 said:
increase?

Right :smile:

So when you go from -1/4 to -1/9, you also increase, right ?
 
  • #10
As a check, plot them along the vertical axis of a graph. Which one is "higher"?
 

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