How was the electron in Rutherford's model producing a continuous spectrum and not a line spectrum? What is the logical thinking behind that it will produce a continuous spectrum?

  • $\begingroup$ It sounds like you think it should produce a line spectrum. Could you explain why? Otherwise people will probably not be able to clear up your confusion. $\endgroup$ – Ben Crowell Jan 22 at 14:15
  • $\begingroup$ No it's not that. Actually the book I'm reading has not given reason and has just mentioned that it produces a continuous spectrum and not a line spectrum. $\endgroup$ – Mad Dawg Jan 22 at 14:16
  • $\begingroup$ Well, Rutherford’s model was before quantum. Having a small positive nucleus with electrons ‘orbiting’ it was a problem that had to be solved, and quantum was the answer eventually. $\endgroup$ – Jon Custer Jan 22 at 15:28
  • $\begingroup$ The continuous spectrum of the orbiting electron at Bohr radius would have strong peaks at multiples of the fundamental frequency, it would not be a smooth featureless spectrum. $\endgroup$ – Ján Lalinský Jan 22 at 16:36

If you are familiar with Poynting vector you can derive/calculate the vector for both the accelerated charge and an electromagnetic radiation with a fixed frequency, i.e. a line spectrum. Or you can google them. The Poynting vector formula for accelerated charge is well-known as Larmor formula. And for an electromagnetic radiation with a fixed frequency you can see here. If you compare both, you'll see the Poynting vector of accelerated charge doesn't not have a well-defined frequency dependence, in other words, it radiates a continuous spectrum!

  • $\begingroup$ care to explain the down vote? $\endgroup$ – rnels12 Jan 22 at 17:23

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