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One of the basic experiments everybody learns about when it comes to physics is the spectroscopy of hydrogen gas. The typical set-up has a charge discharge lamp containing the hydrogen. The resulting spectra are then discussed with the atomic properties of the hydrogen atom.

The gas however is not mono-atomic but it is present as $\textrm{H}_{2}$. The 1s orbitals creating the $\sigma$-bond and the electrons are occupying the bound state. This is at a lower energy when compared to the 1s states of the atomic hydrogen. The higher energy orbitals will also influence each other as they are overlapping. So my question is, why does the atomic hydrogen description works for this experiment?

Possible answers I could think of are:

  • The bounding effects are negligible

  • The $\textrm H_{2}$ spectra are only visible shortly after the lamp is switched on. The constant electron bombardment is slowly dissociating all $\textrm H_{2}$.

For the later I am very unsure if a charge discharge lamp is able to produce conditions to archive that. If it comes out that this is the answer, does anyone know where to find more details on the spectroscopic properties of $\textrm H_2$?

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    $\begingroup$ Did you search for "molecular spectrum H2"? $\endgroup$
    – CuriousOne
    Commented May 31, 2016 at 7:57
  • $\begingroup$ See here: physics.stackexchange.com/a/768678/313612. The plasma has H atoms, hydrogen molecules, various ions and electrons. The excited H atoms emit their characteristic emission lines, e.g., the Balmer series in the visible, and the excited hydrogen molecules also emit light, e.g., the Fulcher alpha bands. These are shown in my spectra in my linked answer. The molecular emissions can be weak compared to the atomic emission intensities, so what you see or detect depends on how good your spectrograph or spectroscope happens to be. $\endgroup$
    – Ed V
    Commented Jul 21, 2023 at 16:14

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The lamp does indeed contain molecular hydrogen but:

  1. the discharge dissociates (a small proportion of) the $H_2$ molecules to produce excited hydrogen atoms

  2. the emission from molecular $H_2$ is quite weak under these conditions, though it can can sometimes be observed as braod bands between the blue, green, and red lines hydrogen atom lines.

So the spectra of $H_2$ is present but is weak compared to the hydrogen lines. Exactly why the molecular emission is low I'm not sure, but I'd guess it's because a low pressure discharge lamp works by colliding electrons with the gas molecules at energies well above the dissociation energy of molecular hydrogen. Only a small percentage of collisions will leave the molecule excited and undissociated. The molecular hydrogen lines appear as bands because they contain vibrational and rotational fine structure that is generally not resolved in a discharge lamp.

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    $\begingroup$ Probably most importantly, the molecular H2 spectrum is mostly a band spectrum (many energy levels due to the rotation-vibration states of the two nuclei) so it contains no sharp lines similar to the atomic spectrum. $\endgroup$ Commented May 31, 2016 at 9:13
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    $\begingroup$ Careful! Only vibrational, no rotational (no dipole). But spectral lines from electron transitions exist in both and are different for atomic and molecular hydrogen. pdfs.semanticscholar.org/0b53/… (page 504 a picture of all hydrogen forms) $\endgroup$
    – e-motiv
    Commented Dec 18, 2017 at 13:30

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