Hydrogen, Deuterium, and Tritium Ionization Spectra

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Discussion Overview

The discussion revolves around the spectral analysis of hydrogen isotopes (hydrogen, deuterium, and tritium) in discharge tubes, specifically focusing on whether different isotopes exhibit distinct ionization spectra and the underlying reasons for any differences.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant inquires about the existence of different spectra for hydrogen isotopes and seeks data on this topic.
  • Another participant mentions that observable differences in spectra may primarily arise from the mass effect, suggesting that scaling results for hydrogen could yield correct results for deuterium and tritium.
  • A participant questions whether the electron configuration remains the same across the isotopes, noting that gravitational effects are negligible and charges are equal.
  • Further elaboration is provided on the two-particle system of the nucleus and electron, emphasizing the importance of using reduced mass in calculations for accurate energy levels and spectra.
  • It is noted that the hyperfine structure will differ among the isotopes due to their different spins.
  • Another participant clarifies that the mass effect is not related to gravity and discusses how energy levels are calculated using reduced mass, providing specific mass ratios for hydrogen, deuterium, and tritium.

Areas of Agreement / Disagreement

Participants express differing views on the implications of mass effects and the role of electron configuration in determining spectral differences. No consensus is reached regarding the specifics of the spectral differences among the isotopes.

Contextual Notes

Participants highlight that the calculations for energy levels should consider the reduced mass, which varies for each isotope, but there is no agreement on the extent of its impact on the spectra.

nwfusor
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Hello Everybody,
I'm looking into spectral analysis, and I couldn't find anything online about the spectra of different isotopes in discharge tubes (i.e. neon signs and the like ). Do different hydrogen isotopes have different spectra? If so, where could I find the data on the spectra?
Thanks,
NWFusor
 
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Ok that is not a complete answer, only deuterium, but quick and it can be the origin of further search, e.g. Balmer lines.
 
I would venture to say that only the observable difference will be due to the mass effect. Scaling properly the results for H should give the correct results for D and T.
 
DrClaude said:
I would venture to say that only the observable difference will be due to the mass effect. Scaling properly the results for H should give the correct results for D and T.
Shouldn't the electron configuration be the same on all three? Gravitation plays no role and charges are equal?
 
fresh_42 said:
Shouldn't the electron configuration be the same on all three? Gravitation plays no role and charges are equal?
The mass effect has nothing to do with gravitation!

You have a two-particle system, so the correct way to go about it is to separate the motion into two parts: center-of-mass motion and relative motion of the nucleus-electron system. The latter is the one relevant to the spectrum and the energy levels. In the Hamiltonian, you have to use the reduced mass
$$
\mu = \frac{m_N m_e}{m_N + m_e}
$$
In many texts, this is not fully explained, and you will find ##m_e## instead of ##\mu##, but this is only an approximation. Actual calculations should use the reduced mass, and it will be different for the different isotopes.

I should specify that I am considering here the presence of "ionization" in the title of the thread. In the full spectrum, the hyperfine structure will also be different due to the different spins of the isotopes.
 
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The mass effect is not related to gravity. When solving for the energy levels, the two-body system (nucleus and electron) is reduced to a one-body system with a reduced "electron" mass. This takes into account that both nucleus and electron can "move". The effect is of the order of the electron to nucleus mass ratio, ~1/1800 for hydrogen, ~1/3600 for deuterium and ~1/5400 for tritium as relative shift (compared to a hydrogen-like atom with an infinite nucleus mass).

Edit: too slow.
 
Thank you both. Something learned today.
 

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