0
$\begingroup$

It's said in textbooks that electrons won't radiate and fall into nucleus because matter wave of it's form a standing wave but could somebody explain why being a standing wave it doesn't radiate, even standing wave oscillates at a particular position and hence have acceleration and hence it should radiate right but it doesn't happen. could some one explain this . I understand that being standing wave it shouldn't lose energy so that it won't change it's wave property but at the same time it's said that it accelerates over time but acceleration means radiation should happen but it doesn't so what prevents it from radiation

$\endgroup$
6

1 Answer 1

2
$\begingroup$

The standing wave idea doesn't help us with acceleration; as realized by OP, standing waves do indeed have their constituent parts accelerate over time. The idea is that standing waves do not decay: they do not lose energy, they do not change their wave properties over time, they always return to the same initial position, etc. If any part of the wave got lost (if the electron "begins" to radiate), the boundary conditions will no longer hold and we will no longer have a standing wave.

Note that this answer is circular! We just posit that standing waves don't change over time, then use this to explain why electrons don't change over time. This was part of the early quantum theory (https://en.wikipedia.org/wiki/Old_quantum_theory) and was superceded by the Schrödinger equation for explaining where the quantized energy levels come from and why only certain orbits for electrons are allowed.

$\endgroup$
9
  • $\begingroup$ I understood being standing wave it shouldn't lose energy so that it won't change it's wave property but at the same time it's said that it accelerates over time but acceleration means radiation should happen but it doesn't so what prevents it from radiation $\endgroup$
    – JSJ2004
    May 18 at 5:19
  • $\begingroup$ @JSJ2004 by energy conservation, if an electron radiates energy, the electron must lose energy. According to quantum theory, the electron can only change energy by specific [quantized] amounts and there is a lowest-energy state: that directly prevents a continuous radiation over time $\endgroup$ May 18 at 20:28
  • $\begingroup$ So if it doesn't radiate as energy is quantized so what happens to electric and magnetic fields created by it or will any of these component won't be there $\endgroup$
    – JSJ2004
    May 19 at 3:34
  • $\begingroup$ @JSJ2004 there won't be any electric or magnetic fields that corresponding to radiation (ie, to traveling modes that carry away energy). There will still be the fields corresponding to the electron and proton's Coulomb interactions, which technically means there will be virtual photons mediating this interaction that do not radiate energy away from the electron/proton $\endgroup$ May 19 at 21:09
  • $\begingroup$ Could you please explain what are virtual photons . Also you said it won't carry energy so what prevents magnetic and electric field to store energy $\endgroup$
    – JSJ2004
    May 20 at 8:39

Not the answer you're looking for? Browse other questions tagged or ask your own question.