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I'm not asking about how emission and absorption lines are created, nor am I asking why different elements have unique spectral "fingerprints". Those two questions have already been answered multiple times.

My question is simply if there is any fundamental reason why we couldn't find any pair of elements that have a single spectral line in common?

As a second question; if there is no reason why this couldn't be the case, have we actually found a example of this in nature, or is it just theoretically allowed?

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    $\begingroup$ -1. No research effort. Google "spectral lines of elements" and you will find astro.u-strasbg.fr/~koppen/discharge at the #1 hit. $\endgroup$ – sammy gerbil Sep 5 '17 at 10:40
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    $\begingroup$ @sammygerbil I don't want to be rude but I fail to se how that page answers my question? $\endgroup$ – Spade Sep 5 '17 at 10:57
  • $\begingroup$ It shows the spectral lines of dozens of elements. You can see at a glance which spectral lines coincide. Isn't that what you are asking? $\endgroup$ – sammy gerbil Sep 5 '17 at 10:59
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    $\begingroup$ If you reject two things being equal when they are arbitrarily close, then you are rejecting measurement as a method of deciding if two things are equal. This would make your 2nd question unanswerable, because we cannot measure anything with infinite precision. We cannot tell the difference between two lines which are theoretically identical and two which are only too close for us to distinguish the difference. $\endgroup$ – sammy gerbil Sep 5 '17 at 11:20
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    $\begingroup$ Granted my second question might be "practically" unanswerable if I require infinite precision but it could still be "theoretically" answerable. I mean if you read @emilio-pisantys answer below it basically answers all my questions perfectly. I'm (obviously?) just a random person on the internet with an interest in physics and not a fancy double physics master like yourself so I'll apologise for my less then satisfactory use of proper terminology :P I hope we can agree to disagree but from "down here" my question and the given answer are still interesting :) $\endgroup$ – Spade Sep 5 '17 at 11:33
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It's theoretically allowed, but extremely unlikely. Spectral lines are very, very narrow: they're normally separated from each other by hundreds of terahertz (few to tens of eV) but their natural widths are rarely bigger than a gigahertz, so there's some five orders of magnitude between the two scales. For two lines to meaningfully coincide, they'd have to match up to the fifth significant figure, which is extremely unlikely.

That said, if you don't care all that much about precision, odds are that you'll be able to find an example - but then you need to specify what precision you find acceptable and how far two lines need to be for you to take them as separate.

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    $\begingroup$ maybe one should add that coincidence of a single spectral line would not matter inusing spectra for identifying elements, since it isseries of lines that are sought, not single lines. $\endgroup$ – anna v Sep 5 '17 at 7:47
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    $\begingroup$ @annav indeed, particularly in astronomical contexts, where any given line can be Doppler shifted far out of its original position, so one relies on the structure of a line series to identify spectra. $\endgroup$ – Emilio Pisanty Sep 5 '17 at 8:03

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