Are continous Spectra actually discrete?

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    Discrete Spectra
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Discussion Overview

The discussion revolves around the nature of continuous spectra in the context of electromagnetic radiation emitted by charged particles, particularly focusing on the relationship between continuous and discrete values in photon emissions and the implications for the photoelectric effect.

Discussion Character

  • Exploratory
  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • One participant proposes that a charged particle spiraling towards another emits electromagnetic waves, resulting in a continuous spectrum, yet questions the apparent discreteness of photon frequencies when measuring photoelectrons.
  • Another participant clarifies that the term "continuous spectrum" refers to a large collection of photons, which can produce a smooth energy curve, while each photon retains a distinct frequency.
  • A participant argues that if the spectrum is continuous, it implies an infinite number of photons in any frequency range above the threshold frequency, leading to a paradox regarding the photoelectric effect.
  • Another participant notes that a continuous spectrum does not mean all frequencies are present at once, but rather that emitted photons can have any frequency within the spectrum.
  • One participant suggests that the spectrum produced by a spiraling charge could be viewed as a line spectrum with closely spaced lines, questioning if this interpretation is valid.
  • A later reply challenges the characterization of the spectrum as a "line spectrum," suggesting that repeated experiments would yield photons across a range of frequencies rather than discrete lines.

Areas of Agreement / Disagreement

Participants express differing views on the interpretation of continuous spectra and the implications for photon emissions and the photoelectric effect. No consensus is reached regarding the nature of the spectrum produced by the spiraling charge.

Contextual Notes

Participants highlight potential misunderstandings regarding the definitions of continuous and discrete spectra, as well as the implications of the photoelectric effect, but do not resolve these issues.

Rohan Patil
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If we assume that there is a fixed charged particle and another charged particle is spiraling down towards it, it emits electromagnetic waves as it is accelerated motion. We get a continuous spectrum. Now, if I allow the emitted photons to fall on a very photosensitive material, whose efficiency is known, then i can get photo electrons for those photons whose frequency is beyond threshold frequency. By knowing the current, i can know the number of electrons and from number of electrons, i can calculate the number of incident photons by dividing the number of electrons by efficiency. As photons have a unique frequency, i can determine the number of frequencies the photon can assume between the range in which it can make an electron come out. So this means that i am getting discrete values. But the spectrum is continuous everywhere. So, that's my question. Where am I making a mistake?
 
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The "continuous spectrum" statement relates to a vast number of photons taken together. If you plot enough of their energies, you will get a smooth curve. But as you say, each photon on its own is just a data point in that plot with a distinct frequency and energy.
 
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I meant that if the spectrum is continuous, then I can get an infinite number of photons in any range of frequency. Let the frequencies in this range be more that the threshold frequency. As photoelectric effect is one photon one electron phenomenon, i must get infinite number of photo electrons (we make sure that the photo sensitive material remains neutral.) Also efficiency cannot be zero. So zero x infinity thing doesn't work. So that is where the problem is.
 
Continuous spectrum does not mean that at any given time, all frequencies are present. That would indeed mean infinite number of photons, which obviously isn't true.
Continuous here means that the photons that *do* get emitted can have any frequency in that spectrum.
 
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So actually the spectrum that I get from a charge spiraling inward is a line spectrum with the lines very close to each other. Will this solution work out?
 
Rohan Patil said:
So actually the spectrum that I get from a charge spiraling inward is a line spectrum with the lines very close to each other. Will this solution work out?

You'll get a finite number of photons but I wouldn't call this a "line spectrum" with the lines very close to one another. To me that implies a line spectrum implies spectral lines at certain energies, such as the spectral emission lines of a gases. If you were to perform this experiment over and over you would get photons of all frequencies from some lower range to some upper range.
 
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