Spectroscopy question about a Paschen series absorption I had this question on a test and got it wrong but I can't understand the explanation.


I don't get why we receive a Paschen series absorption. Could anyone explain?
The Paschen series absorption requires a population of H atoms in the $n=3$ level and a radiation field containing infrared photons $\leq 1875$ nm, that can boost them in to the $=4,5,6...$ levels.

If hydrogen gas is at 25,000K, you can use the Saha equation to work out the fractional ionisation. This depends on both the temperature and density of the gas. For the temperature you have been given, the ratio of ionised to netutral hydrogen is $1.7\times 10^{25}/n_e$, where $n_e$ is the electron number density in m$^{-3}$,

The typical particle number densities of an interstellar gas cloud are much, much less (many orders of magnitude) than $10^{25}$ m$^{-3}$, so the gas is totally ionised.

If that is the case then there can be no Paschen absorption and no Balmer absorption due to the cloud since there are no atoms in the $n=2,3$ states. There may be small amounts of Paschen and Balmer emission from the cloud via recombination.

Thus what you basically see is the spectrum of the star and since you aren't told what kind of star it is, then it's impossible to rule out the presence of emission lines or absorption lines of any kind. It is thus a dreadful and unanswerable question.