# Hydrogen, Deuterium, and Tritium Ionization Spectra

## Main Question or Discussion Point

Hello Everybody,
I'm looking in to 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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fresh_42
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2018 Award
Ok that is not a complete answer, only deuterium, but quick and it can be the origin of further search, e.g. Balmer lines.

DrClaude
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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.

fresh_42
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2018 Award
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?

DrClaude
Mentor
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.

mfb
Mentor
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.

fresh_42
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2018 Award
Thank you both. Something learned today.