Hydrogen Atom; energy state transitions

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Homework Help Overview

The discussion revolves around the energy state transitions of a hydrogen atom, specifically focusing on the transition from the n=3 state to the ground state and the associated photon emission. Participants are examining the implications of energy calculations related to this transition.

Discussion Character

  • Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants are exploring the formula for calculating energy levels in a hydrogen atom and questioning the negative value obtained for ground state energy. There is uncertainty regarding the correct application of the energy formula and its implications for ionization energy.

Discussion Status

The discussion is active, with participants questioning the validity of the formula used and the interpretation of the negative energy value. Some guidance has been offered regarding the correct formulation of energy levels, indicating a productive exploration of the topic.

Contextual Notes

There is mention of potential confusion regarding the derivation of energy levels and the assumptions about ionization energy, which may affect the understanding of the problem.

hhhmortal
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Homework Statement



A hydrogen atom is initially in the state n=3. Subsequently it falls to its ground state with the emission of a photon. If the photon energy is ћω , then what is the ground state energy?

The Attempt at a Solution



I tried using E= h².n²/8ma².

and got -9ћω/8

I wasn't to sure how to go about with this question.
 
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Uh, how did you get a negative ground state energy using that formula?
 
Dick said:
Uh, how did you get a negative ground state energy using that formula?

Not too sure. I think that formula would just give you the energy of the level, but doesn't the electron in that level require that amount of energy to be ionised, hence the negative sign.
 
hhhmortal said:
Not too sure. I think that formula would just give you the energy of the level, but doesn't the electron in that level require that amount of energy to be ionised, hence the negative sign.

You are right about that. And in fact, I think your answer is right. On the other hand the formula you gave for E is wrong. Why do you try and write down a clear derivation of your result?
 
Dick said:
You are right about that. And in fact, I think your answer is right. On the other hand the formula you gave for E is wrong. Why do you try and write down a clear derivation of your result?

I'm not too sure, I think I just used that equation then I canceled out certain terms and multiplied it by ћω. This is wrong, but I can't find the right way of doing it.
 
hhhmortal said:
I'm not too sure, I think I just used that equation then I canceled out certain terms and multiplied it by ћω. This is wrong, but I can't find the right way of doing it.

Start by finding the correct formula. The formula for the energy levels has an n^2 in the denominator, not the numerator. How can you be 'not to sure' of how you got the answer?!
 

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