Energy levels of atoms and spectroscopic analysis

In summary: But I digress. Basically, you solve Schrödinger's equation for the system in question. Undergraduate physics students learn how to do this for the hydrogen atom, which is the simplest case (one electrron in a ##1/r## potential). I learned many of the details in a second-year "introduction to modern physics" course (and later taught such a course for many years), and the rest in full-on quantum mechanics courses.This is a good start, but I'm still a little confused. Can you explain a little more about how you solve Schrödinger's equation and what it is that you get by doing so?
  • #1
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Hello !

My question is how the energy levels and sublevels that atoms are considered to have were obtained, and if these energy levels and sublevels were obtained as a result of the different spectroscopic analyzes of energy emission and absorption of atoms, or as it was concluded that atoms have the energy levels and sublevels that atoms are currently considered to have ?

Thanks for your answers.
 
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  • #2
MartinG said:
Hello !

My question is how the energy levels and sublevels that atoms are considered to have were obtained, and if these energy levels and sublevels were obtained as a result of the different spectroscopic analyzes of energy emission and absorption of atoms, or as it was concluded that atoms have the energy levels and sublevels that atoms are currently considered to have ?

Thanks for your answers.
This might be worth studying:

http://www.columbia.edu/~nas2173/Lab7_SpectrumOfTheHydrogenAtomNS.pdf
 
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  • #3
Thanks Perok !So my question is answered like this:

The levels and sublevels of energy that atoms are considered to be made of, are obtained from the conclusions made by the spectral analyzes made throughout history to the different atoms ?
 
  • #4
MartinG said:
Thanks Perok !So my question is answered like this:

The levels and sublevels of energy that atoms are considered to be made of, are obtained from the conclusions made by the spectral analyzes made throughout history to the different atoms ?
To be precise, experimental spectroscopy gives you energy differences that each atom or molecule may absorb or emit. The QM model of the atom explains this in terms of energy levels based on four quantum numbers.
 
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  • #5
MartinG said:
My question is how the energy levels and sublevels that atoms are considered to have were obtained, and if these energy levels and sublevels were obtained as a result of the different spectroscopic analyzes of energy emission and absorption of atoms, or as it was concluded that atoms have the energy levels and sublevels that atoms are currently considered to have ?
Your question is a bit difficult to understand, but I believe you're asking how we discovered the energy levels that atoms and molecules have, and if we used spectroscopic analysis to do so. The answer to this question is yes, we used spectroscopic analysis combined with quantum mechanics to obtain and explain the different electronic energy levels of atoms and molecules.
 
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  • #6
I also don't quite understand the question, but it seems to be related to "which came first" - understanding of energy levels or understanding spectroscopy. They progressed together.
 
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  • #7
Drakkith said:
Your question is a bit difficult to understand, but I believe you're asking how we discovered the energy levels that atoms and molecules have, and if we used spectroscopic analysis to do so.
Yes, my question is that.

And to continue with this topic I ask you again how you use the "quantum mechanics" to obtain and explain the different electronic energy levels of atoms and molecules.

I appreciate you if you can explain a little more about how you use quantum mechanics for this.

Greetings.
 
  • #8
There are entire books on the subject. It's not easy to condense a book into a few lines.
 
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  • #9
MartinG said:
And to continue with this topic I ask you again how you use the "quantum mechanics" to obtain and explain the different electronic energy levels of atoms and molecules.
I'm afraid my experience with doing detailed quantum mechanics never got past the very basics that I needed for my 201 solid state chemistry class. As V50 said, it's a deep and detailed subject with many, many books written about it. It can't be explained in a forum post if you don't have any of the prerequisite knowledge.
 
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  • #11
MartinG said:
I ask you again how you use the "quantum mechanics" to obtain and explain the different electronic energy levels of atoms and molecules.

I appreciate you if you can explain a little more about how you use quantum mechanics for this.
Basically, you solve Schrödinger's equation for the system in question. Undergraduate physics students learn how to do this for the hydrogen atom, which is the simplest case (one electrron in a ##1/r## potential). I learned many of the details in a second-year "introduction to modern physics" course (and later taught such a course for many years), and the rest in full-on quantum mechanics courses.

A Google search for "hydrogen atom schrodinger equation" finds many sets of university lecture notes. Here's one that appears to follow the book that I taught my "intro modern" course out of (Beiser's Concepts of Modern Physics).

https://web.mst.edu/~sparlin/phys107/lecture/chap06.pdf
 
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  • #12
Of course that's the tip of the iceberg - even within the hydrogen atom. Fine structure, hyperfine structure, relativistic corrections. At MIT, when I took 8.05, the second semester of QM, it was nicknamed "the hydrogen atom" because that was the bulk of the course. Not everything, of course: there was also the H2+ ion. :smile:
 
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  • #13
Yep. Then there are the multi-electron systems: atoms other than hydrogen; molecules; solid-state systems like crystals; etc.
 
  • #14
jtbell said:
multi-electron systems
Actually, H2+ and H- are the same problem, as is the helium atom. Sort of.

One has two electrons in the potential of the proton (or the potential of an alpha particle), and the other has two protons in the potential of the electron. If you had an exact solution to one, you'd have the exact solution to the other.

However, there is no exact solution, and the approximations for the various alternatives are completely different.
 

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