Hydrogen line spectrum [closed]

Question

lately I have come across the hydrogen line spectrum, I quite understand it as I could easily solve all numerical questions. However, conceptually I feel stuck at two points.

1. If an electron absorbs the em radiation of a particular wavelength to jump to a higher shell say $n=1$ to $n=3$, then when it returns to the ground state (from $n=3$ to $n=1$) will it emit the radiation of the same wavelength or of a different wavelength. Kindly explain what exactly happens?

2. In the absorption spectrum of hydrogen, em wavelengths of 434 nm, 486 nm, and 656 nm are absorbed because they correspond to the energy difference between the shells so they are not present on the photographic plate but I don't understand that if excited electrons (from the absorbed light) jump back to their ground state in nanoseconds releasing the same radiation with the same wavelength then why does it not appear in the spectrum? Also, how do the electrons figure out which light to be absorbed (I know it sounds dumb but I just can't understand how do electrons figure out that a particular wavelength does not suffice the energy requirement to jump?)

P.S.: Please consider my doubt and excuse it if they appear dumb as I have taken these questions to various platforms and have never received any satisfactory response.

Answer 1

1.) An electron falling down from level n=3 can decay into the ground state in two ways, either directly into the ground state n=1, or first into n=2 and then into n=1. These decay paths have certain statistical probabilities, so from many atoms you will see three lines in this case with a relative intensity given by these probabilities.

2.) The absorption lines in a spectrum are caused by the fact that a beam of light travelling in a given direction will be re-emitted again in all directions, so light is lost from the beam and re-appears in other directions instead. See the following graphic for an illustration

from https://courses.lumenlearning.com/astronomy/chapter/formation-of-spectral-lines/)

Classically, you can explain the physical mechanism here by a forced harmonic oscillator. Light will only be absorbed by the atom at the resonant frequencies, which correspond to the spectral lines.

Answer 2

An excited hydrogen atom in its $n=3$ state might relax directly to the $n=1$ ground state. But it might also go through a “cascade,” emitting two lower-energy photons and passing through the intermediate state with $n=2$. The probability of a direct decay versus a cascade is independent of how it got to $n=3$: all states with the same quantum numbers are indistinguishable.

Also because of indistinguishablity, the emitted photons are almost certainly traveling in a different direction than the absorbed photons. So if you shine a white light through a hydrogen cloud, the transmitted light will be missing the characteristic colors associated with hydrogen transitions — but if you look at the cloud from the side, it’ll be glowing in those colors. In astronomy, this is the difference between an “absorption nebula” and an “emission nebula”: they’re made of exactly the same stuff, but we view them from different angles.