When atoms get heated up, they start emitting EM radiation because of accelerating electrons. But why don't the protons emit EM waves which destructively interfere with other emitted EM waves, because they're also accelerating just as the electrons do, because they're both jiggling as one (atom)?


The existing answer is correct, but it's in a sense 'orthogonal' to the question, and it doesn't really address the core concern.

Atoms are indeed quantum mechanical objects, and the classical understanding in terms of accelerating charges no longer works, and it needs to be replaced with transitions between different states of the atom, but this does not make the problem go away.

The reason for that is that the transition has an amplitude - a number which governs how likely the atom is to change states, known technically as an electric dope transition matrix element - which depends on the position of the electron with respect to the center of mass, but also in the position of the nucleus, which therefore also contributes to the radiation, exactly as in the classical case.

So, why doesn't the radiation cancel out? Well the word dipole should give it away: what really matters for the radiation isn't so much the movement of charge, but the dynamics of the electric dipole, and here the contribution of the nucleus adds constructively with that of the electron: it has the opposite charge, sure, but it also moves in the opposite direction, so the global sign is $+$, and the two contributions to the radiation / acceleration / transition dipole / whatever are in the same direction.

Moreover, this is also the case for the classical dynamics of the Rutherford model of the atom: the nuclear charge is opposite to that of the electrons, but it moves in the opposite direction, and the contributions add constructively. This is why I said the answer "because QM" is orthogonal to the question - the answer doesn't really care whether you're doing classical or quantum dynamics.

Now, why do we normally ignore the nuclear motion? Well, it is much heavier than the electrons, by a factor of ~1800 and up, so it doesn't move much, but it still has a contribution and its effects can be seen in the atomic radiation if you do a careful enough experiment. However, because its effect is constructive, the answer wouldn't change even if you had two opposite charges of the same mass orbiting each other (as in, say, positronium).

  • $\begingroup$ Wow. This answer feels so satisfying. So bassicly the atoms still jiggle inside a material, but the majority of the movemen't is done by the electrons bouncing around? Is that correct? But accelerating free charges still radiate EM waves right? And so do the ions, but not atoms. How does that extra electron in an ion know to radiate EM waves while ion is accelerating, but the rest of electrons don't? $\endgroup$ – MaDrung May 31 '17 at 8:49
  • $\begingroup$ "Jiggle" is a terrible term, and it doesn't describe what goes on particularly well, but I feel you're misinterpreting this answer. It's impossible to define "the majority of the movement", but as far as the electric dipole of an atom goes, the bulk of the contributions (by a factor of 1800 to 1) comes from the electrons. If by "but not atoms" you mean that an acceleration of the center of mass of a neutral atom does not emit radiation, then that is correct, but that doesn't mean that atoms don't emit radiation at all due to the internal 'motion'. And seriously, pick up an intro-QM book. $\endgroup$ – Emilio Pisanty May 31 '17 at 8:57
  • $\begingroup$ I have worded it badly. I think I understand what you meant. I just had a follow-up questions to it. Which is to make it clear why accelerating atoms (not bound by material) don't emit EM waves, while ions with 1 extra electrons emit pretty much the same amount as a free electron if their accelerations are exactly the same in one unchanging direction. How does that one extra electron in an ion know to start emiting light? And yes I will start reading a QM textbook as soon as my 3 weeks of leave come this year. :) $\endgroup$ – MaDrung May 31 '17 at 9:02
  • $\begingroup$ It's not that 'the extra electron knows' that it needs to radiate. If you accelerate the center of mass, all the electrons radiate, but here the nucleus does emit radiation that interferes destructively with that of the electrons; for the neutral they cancel, but for ions the cancellation is imperfect. This is different to your original question, though: thermal emission is not due to accelerations of the center of mass, but rather to reorganisations of the internal motion (and, for neutral atoms, any thermal COM acceleration does not radiate, because of the cancellations. $\endgroup$ – Emilio Pisanty May 31 '17 at 9:54
  • $\begingroup$ ... this is why "jiggle" is a terrible term, among other factors. Handwavy language can carry you to a point, but without a more solid foundation it is subject to these sorts of pitfalls. $\endgroup$ – Emilio Pisanty May 31 '17 at 9:56

The classical idea that the electrons emit energy because they are accelerating does not work in the atomic realm. This was the precise reason that Rutherford's atomic model was rejected by the classical physicists in the early 20th century.

The atoms emit light when the electrons from one energy level make a transit to a lower energy level due to the instability of the atom. The same happens with the case of the proton too, but the energy gap between the consecutive energy levels of the proton is so large that the thermal energy cannot excite them to the higher energy levels. Thus, when an atom is heated, the electrons excite to the higher energy level and then fall off to the ground state giving light.

  • $\begingroup$ Thank you. It's annoying that I find what I wrote everywhere on the internet, even in textbooks. :/ $\endgroup$ – MaDrung May 31 '17 at 6:29
  • $\begingroup$ But it is still correct that accelerating charges create electromagnetic waves? If so, if we're accelerating an atom, is it true that electrons are creating their EM wave and protons are creating their counter EM wave, so they together emmit almost nothing? But wouldn't that mean that ions emmit EM radiation when accelerated, while atoms don't? $\endgroup$ – MaDrung May 31 '17 at 6:32
  • $\begingroup$ It is not quite right that the electrons accelerating always emit radiation (If this is so, the atom would continuously emit radiations and at the end, the electrons would collapse into the nucleus). You can find more about it here: pbs.org/wgbh/aso/databank/entries/dp13at.html. $\endgroup$ – lattitude May 31 '17 at 6:37
  • $\begingroup$ Not sure what then decides if electron is going to emmit light. I thought this is happening because of electric charge moving, so it creates something simmilar to Doppler effect. But I'll try reading up more about it. It's annoying that there is so much contradictory information. $\endgroup$ – MaDrung May 31 '17 at 6:48
  • $\begingroup$ @MaDrung Regarding that 'contradictory information', have you tried looking in an introductory quantum physics textbook? Something along the lines of Beiser's Concepts of modern physics should be clear enough. $\endgroup$ – Emilio Pisanty May 31 '17 at 7:50

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