Emission Spectrum of elements other than Hydrogen

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Homework Help Overview

The discussion centers around the emission spectrum of elements other than hydrogen, particularly focusing on how spectral lines are predicted and the methods used to calculate energy differences between electron states. The original poster expresses confusion regarding the applicability of the Rydberg Equation beyond hydrogen and seeks clarification on the methodologies for other elements.

Discussion Character

  • Exploratory, Conceptual clarification, Problem interpretation, Assumption checking

Approaches and Questions Raised

  • Participants discuss various methods for calculating spectral lines, including Hartree-Fock and density functional theory (DFT). Questions arise about the historical context of spectral line discovery and the lack of theoretical frameworks at the time.

Discussion Status

The conversation is ongoing, with participants sharing insights about different theoretical approaches and historical anecdotes. Some guidance on the complexity of calculations and the historical discovery of spectral lines has been provided, but multiple interpretations and questions remain open.

Contextual Notes

Participants note the absence of simple equations for elements other than hydrogen and question the historical methods used to identify spectral lines before modern theories were established. There is also mention of the Schrödinger equation's timeline and its relevance to the discussion.

Plez0r
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*This isn't actually coursework but i was under the assumption that questions go to this forum*

Homework Statement


Hi, for while I've been under the impression that spectral lines of all the elements can be calculated. I did some research and found that there is a simple equation (Rydberg Equation) to determine the spectral lines of Hydrogen.
However, I found a source that stated there is no simple equation to determine the spectral lines of the other elements.
So my questions are:
  • How are spectral lines predicted for elements other than hydrogen?
  • How is the energy difference for an electron in its excited state and its ground state calculated?
 
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One can calculate them with Hartree-Fock (electrons does not interact among themselves) and other approximation methods: the thing is that you will have a many-body problem, which can not/ is really diffictult, to solve exactly.The two questions are the same, spectral lines are energy differences of levels and photon distributions due to different angular momentum transitions will require different multipole transitions.

So the reason for why the formula for hydrogen is exact and very accurate, is that we have a 2-body problem which can be solved exactly by using the schrödinger equation.
 
I believe that density functional theory can be used to accurately calculate the spectra.
 
yeah, density functionals are also often used
 
Wow, those are some really complex formulas, i really wonder how they ever found them..
So, DFT was extended to Density-Functional Theory for Time-Dependent Systems in 1984. Now I'm sure i read somewhere that hydrogen was seen on the sun (not sure by who) before it was ever found on Earth (which was in 1766). So how could anyone possibly isolate individual spectral lines and link them to hydrogen. Elements such as Beryllium, Boron, Lithium and even Oxygen hadn't been discovered at that time. So how did anyone do this without concepts such as DFT, Hartree-Fock. Rydberg's equation wasn't even around until the 1880's.
Maybe I just misread and the spectral lines were seen as a new element but whoever discovered them had no idea which element they belonged to.
 
they could find out that spectral lines came from different samples by playing "detectives", they had no theory that could explain WHY boron has these levels. They did experiemts and said, hey, I have found new lines here not found in any other known sample - it must have been a new element which I discovered! Let's call it boron. And so on, one puzzled with available combinations, and of course, not all of them were correct assigned ;-)

Also, the Schrödinger equation is from 1926 ...

I believe it was Fraunhoffer who saw them...

This is from wikipedia:

The English chemist William Hyde Wollaston was in 1802 the first person to note the appearance of a number of dark features in the solar spectrum. In 1814, Fraunhofer independently rediscovered the lines and began a systematic study and careful measurement of the wavelength of these features.

And if you think H-F is 'complex', wait til you see string theory ...
 
Actually, it was helium which was discovered in the solar spectrum. Hydrogen gas was discovered much earlier.
 

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