A question about the light spectrum

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Discussion Overview

The discussion revolves around the existence of electromagnetic waves at any given wavelength and the implications of quantum states of atoms on the electromagnetic spectrum. It explores theoretical aspects of the spectrum, including continuous versus discrete wavelengths, and factors affecting the creation and detection of electromagnetic waves.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions whether there is always an electromagnetic wave corresponding to any given wavelength, suggesting that the countable nature of quantum states limits the spectrum.
  • Another participant argues that the electromagnetic spectrum is continuous, citing various mechanisms such as energy and momentum conservation during atomic transitions and scattering processes that can produce a wide range of wavelengths.
  • A later reply introduces the idea that at extreme ends of the spectrum, practical limitations may prevent the creation or detection of certain wavelengths, while also noting that the choice of reference frame can influence the perceived wavelength of an electromagnetic wave.
  • Another participant mentions the effects of Doppler shift and cosmological redshift, which contribute to the continuous nature of the spectrum.

Areas of Agreement / Disagreement

Participants express differing views on whether all wavelengths are feasible, with some supporting the idea of a continuous spectrum and others highlighting limitations at both ends. The discussion remains unresolved regarding the implications of quantum states on the spectrum.

Contextual Notes

Participants acknowledge limitations related to the creation, detection, and measurement of electromagnetic waves at extreme wavelengths, but do not resolve these issues. The discussion also depends on the definitions of terms like "feasible" and "continuous."

sangho
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For any given number(length), say L, is always there an electromagnetic wave with the wavelength L ?

As I know, the source of electromagnetic wave is the energy emission of electrons changing it's quantum state in an atom.
But there are at most about 120 atoms there, and the quantum numbers are, mathematically saying, countable. So I think the electromagnetic spectrum is not filled with all numbers in the axis.
 
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The E-M spectrum is a continuous spectrum, and all wavelengths are possible. There are many reasons why. In the case of emission of radiation by an excited atom, since the emission of the radiation must conserve energy and momentum, the wavelength of the light emitted depends on the state of motion of the atom. Also, after a photon is emitted from an atom, the photon can scatter off of something, like a free electron, which changes its wavelength. There are also many other sources of EM radiation besides the de-excitation of an excited atom. For example, an electron scattering off a nucleus can emit radiation through bremsstrahlung. Since the electron and nucleus can have any state of motion and meet at any angle, this results in a continuous spectrum.
 
At the very high end of the spectrum, there may not be enough energy to feasibly create an EM wave of the requisite wavelength or to survive its detection.. Though, if one is given freedom to choose one's frame of reference, then a particular EM wave can have any wavelength one chooses.

At the very low end of the spectrum, the wave may be longer than is feasible to create, detect or measure.
 
There's also the issue of doppler shift and cosmological redshift, which are both continuous in nature.
 

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