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In stars, the Balmer lines are usually seen in absorption, and they are "strongest" in stars with a surface temperature of about 10,000 kelvins (spectral type A). Balmer series|Role in astronomy

At 10,000 K the hydrogen is a plasma, I suppose. How can we talk about Balmer lines if the electrons are not bonded anymore to the nucleus?

The Balmer series is characterized by the electron transitioning from n ≥ 3 to n = 2, where n refers to the radial quantum number or principal quantum number of the electron. Balmer series | Overview.

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Balmer absorption arises from atoms in the $n=2$ level. To have a significant occupation of the $n=2$ level it has to be quite hot, because of the 10.2 eV gap between the ground state and $n=2$. The fraction of atoms in the $n=2$ level just grows with temperature.

But at the same time, the ratio of hydrogen atoms to hydrogen ions decreases because more hydrogen is ionised as the temperature increases. The ionisation fraction depends on both temperature and pressure.

The peak number of atoms in the $n=2$ level is at around 10,000 K. At higher temperatures, too many atoms are ionised, at lower temperatures the occupation of the $n=2$ level is lower. This graph (from http://spiff.rit.edu/classes/phys440/lectures/saha/) might help.

Number of atoms in the n=2 level.

As to why ionisation occurs at lower temperatures than significant occupation of the $n=2$ level, this is because if there are collisions and photons capable of putting any hydrogen atoms in the $n=2$ level then these are also easily capable of ionising an atom that is in the $n=2$ level. The peak temperature for Balmer absorption is telling us what the pressure is in the stellar atmosphere.

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  • $\begingroup$ The answer is ok but astonishing to me. It is needed 10-thousand K to have the most hydrogen atoms with the principal quantum number of 2? At which temperature it is plasma and when it starts glowing in the visible spectra? At say 1,000 K the thermal vibrations do not excite the most electrons out of their orbital? $\endgroup$
    – HolgerFiedler
    Commented Nov 24, 2020 at 11:00
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    $\begingroup$ The ratio of atoms in the first excited state to the ground state is always <1 in a gas in thermal equilibrium. At 1000K almost all the atoms would be in the ground state; there would therefore be no ionisation or Balmer lines. The term "plasma" could be used as soon as there is any ionisation. To "glow" in visible light requires atoms in the $n=3+$ states and or recombination radiation and would begin at ~7000K for that process. In an impure gas, then electrons from sodium and potassium atoms can provide electrons that form a recombination continuum with hydrogen atoms at lower temperatures $\endgroup$
    – ProfRob
    Commented Nov 24, 2020 at 12:46
  • $\begingroup$ A plasma can also be excited/ionized by radiation, not only collisions. External EUV radiation sources can cause cold interstellar clouds to glow for instance. You have to distinguish between thermal and radiation temperature here. $\endgroup$
    – Thomas
    Commented May 30, 2022 at 7:28

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