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1$\begingroup$ Talking about Bohr model: I don't think it's explain it at all; in modern theories the thickness of absorption/emitting lines due to the uncertainty principle (the one about time-energy). And this was discovered far later than the Bohr model. $\endgroup$– m0nhawkCommented Mar 29, 2015 at 16:01
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4$\begingroup$ Bohr's model was a kludge that barely lasted a decade as the model that scientists actually used. It's still taught, not because it is right but because (a) it's easy and (b) it is a stepping stone to a better theory. With emphasis on the easy part. This question was never tackled in it. $\endgroup$– dmckee --- ex-moderator kittenCommented Mar 29, 2015 at 16:02
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$\begingroup$ I don't think the Bohr model can solve for this, but see this answer for the modern QM physics.stackexchange.com/questions/443054/… $\endgroup$– user213887Commented Dec 7, 2018 at 15:59
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$\begingroup$ If they had no thickness, that would be much harder to explain. How could the universe work in such a way that a photon will get absorbed if and only if it's a precise frequency? I think the lines are thin because the fine structure constant is small. $\endgroup$– TimothyCommented Nov 30, 2019 at 3:05
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