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There are various absorption lines that correspond to the difference in energy levels between electron orbits. E.g. the https://en.wikipedia.org/wiki/Lyman-alpha_line correpsonding to the difference in energy between an electron orbiting a hydrogen atom in its ground state and the $n=2$ orbital.

But how "wide" are these lines? How large is the range of values that can cause a hydrogen atom to absorb these photons and excite the electron. And what happens to the energy above the bare minimum required?

Similarly, how wide are the emission lines?

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There are basically 3 broadening mechanisms for spectral lines

  1. natural broadening due the finite lifetime of atomic states (states that decay faster lead to broader lines),

  2. Doppler broadening due to the thermal velocities of the atoms,

  3. pressure/collisional broadening due to collisions of the radiating atom with other particles (whilst these collisions may not actually shorten the lifetime of the level, they introduce random phase jumps of the emitted wave, which have the same effect on the observed line width).

For more see http://www-star.st-and.ac.uk/~kw25/teaching/nebulae/lecture08_linewidths.pdf

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  • $\begingroup$ There are others: proximity broadening, opacity broadening, ... $\endgroup$
    – John Doty
    Commented Jul 16, 2023 at 14:52
  • $\begingroup$ @JohnDoty Proximity broadening is in practice only relevant for fluids and solids, and thus hardly for the spectral line series of atomic hydrogen. Opacity broadening is only a secondary effect due to radiative transfer effects (radiation being redistributed by scattering/absorption from the line center to the line wings) and does not affect the absorption/emission line profile of the atom as such.. $\endgroup$
    – Thomas
    Commented Jul 16, 2023 at 15:23
  • $\begingroup$ These are both things that affect real spectra in the real world. They don't affect whiteboard abstract spectra that are rarely seen in reality. $\endgroup$
    – John Doty
    Commented Jul 16, 2023 at 16:15
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    $\begingroup$ @JohnDoty I am trying to answer the OP's question. Proximity broadening has zero relevance for the spectra of atomic hydrogen in the real world. $\endgroup$
    – Thomas
    Commented Jul 16, 2023 at 16:33
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    $\begingroup$ @JohnDoty On the contrary, it would be misleading if I would make the OP believe that irrelevant or marginal physical effects are relevant for his particular question. It is called didactics. $\endgroup$
    – Thomas
    Commented Jul 16, 2023 at 17:09
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I have seen line widths in the lab of about 100 MHz from the Doppler shift in an ion beam.

This article says that a transition in Cs has a natural linewidth of approximately 5 MHz. https://nopr.niscpr.res.in/bitstream/123456789/13997/1/IJPAP%2050%285%29%20295-298.pdf

Emission and absorption widths are going to be the same if the atoms in the gas have the same distribution of velocities.

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