Emission Spectrum of elements other than Hydrogen

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SUMMARY

The discussion centers on the prediction of spectral lines for elements other than hydrogen, highlighting the limitations of simple equations like the Rydberg Equation. It emphasizes that while hydrogen's spectral lines can be accurately calculated due to its two-body problem solvable by the Schrödinger equation, other elements require complex methods such as Hartree-Fock and Density Functional Theory (DFT). The conversation also touches on historical discoveries of spectral lines, noting that early chemists like William Hyde Wollaston and Joseph von Fraunhofer identified these lines before the development of modern theoretical frameworks.

PREREQUISITES
  • Understanding of the Rydberg Equation for hydrogen spectral lines
  • Familiarity with the Schrödinger equation and its applications
  • Knowledge of Hartree-Fock approximation methods
  • Basic principles of Density Functional Theory (DFT)
NEXT STEPS
  • Research advanced methods in Density Functional Theory for predicting spectral lines
  • Study the historical context of spectral line discovery and its implications in chemistry
  • Explore the complexities of many-body problems in quantum mechanics
  • Investigate the applications of Hartree-Fock methods in modern spectroscopy
USEFUL FOR

Students and researchers in physical chemistry, quantum mechanics, and spectroscopy, particularly those interested in the theoretical underpinnings of spectral analysis and historical discoveries in the field.

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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