Odds of photon from one element being able to be absorbed by another?

My limited understanding is that for a photon to be absorbed by an atom, it must be of a precise energy to kick an electron up to a higher orbital. So a few questions if you will:

  1. Is there a tolerance level, however miniscule, for the energy level? I know the energy is delivered in discrete quanta, but does the orbital energy (right word?) have just a little wiggle room?

  2. What are the odds that one element can emit a photon able to be absorbed by another element? I know there are myriad combinations and permutations, so I’m just looking for an example, generality, etc. So, for example, can the first 3-4 n levels in carbon produce a photon with the exact energy required to be absorbed by an oxygen atom?

No doubt the questions themselves betray a vulgar misunderstanding of reality but, hey, I gotta start somewhere. Thanks in advance!

I’m just generally knowledgeable on the topic, not an expert in the specifics, so take this with the necessary grains of salt.

There’s no wiggle room for elements in monatomic form, every element will have its specific wavelengths.

But the moment you have molecules you get bands instead of lines, with the “wiggle”-energy being stored in the wiggling of the atoms relative to each other.

Every object that you see is photons from one element being absorbed by another. Also, everything your cameras see. That is what seeing is.

Uhhhhh yeah. I get that. But that’s not answering the question.

There is wiggle room. It is called the spectral linewidth.

Ok so you’re referring to the various broadening effects (natural, thermal Doppler, pressure, the non-local ones, etc) I’m guessing? Thanks that all makes sense.

Anyone care to take a crack at question 2?

I think many photon emissions and, especially in typical human experiences, absorptions couple to phonons. That is, absorbed photons turn to heat. Less sure, I think photons are able to couple into both an electron transition plus a phonon, for an inefficient transition.

No one has yet mentioned what I think is a key point: the Uncertainty Principle. If the photon’s energy is wrong by some ΔE that’s OK as long as the Uncertainty Principle 2ΔEΔt < ℏ is satisfied. (The probability of the “violation” is determined by the Schrödinger wave equation IIUC.) The system will be “in debt” by ΔE, but that’s OK if the debt is repaid (e.g. by an adjusted-energy photon emission) within the next Δt seconds.

Disclaimer: I am not competent to address such matters and am awaiting just rebuke. :o

If you’re restricting this to interactions of photons with quantum systems that comprise single atoms with no Doppler shift, and no influencing fields (i.e. as far removed from typical conditions on earth as possible) then you’re going to find minimal, if any, overlap.

For molecules, you also have transitions that involve rotations, vibrations, charge transfers, etc. Plus all the aforementioned broadening. You get more possibilities if you include ions.

So are you saying that without the various broadening effects that it’s unlikely a photon from one element could be absorbed by another element? Don’t we have some statistical estimate of, say, the likelihood of a carbon atom being able to emit a photon that could be absorbed by an oxygen atom? I’m obviously not a scientist, but that strikes me as something one would want to know.

What would be the purpose?

Absorption/emission lines are useful for identifying the chemical composition of star atmospheres and cosmic gas clouds (and doing spectroscopy in the lab here on Earth). That relies on identifying the lines, or more specifically the patterns of lines.

Absorption lines are seen in the full spectrum of stars, where the probabilities you mention would not be useful, and I can’t see where they would be. But again, I’m not an astrophysicist.

I don’t know - quantum chemistry maybe? Don’t really know enough to speculate intelligently. It would seem to me that knowing whether or not a photon emitted from a carbon atom has the ability to potentially excite or ionize an electron from an oxygen atom (or whatever element) would be pretty important.

Absorption/emission lines are also important for understanding the flow of energy, which determines how things change over time. Whether radiation from one layer is absorbed by another layer, or passes right through it, makes a huge difference.

That said, I don’t see why it would be useful to do this calculation while ignoring line broadening. Every real-world system has non-zero line width.

It is important for some ideas about performing quantum computing. And I don’t have my head wrapped around the physics.
Here’s a study, although that focuses more on scattering: https://www.nature.com/articles/ncomms13716