How does quantization of energy solve the ultraviolet catastrophe?

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Discussion Overview

The discussion revolves around the ultraviolet catastrophe, specifically how the quantization of energy in photons relates to this phenomenon. Participants explore the implications of quantum mechanics on the radiation emitted by oscillating electrons in black bodies, addressing both classical and quantum perspectives.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants assert that classical physics allows electrons to radiate at all frequencies if they have sufficient energy, leading to the ultraviolet catastrophe.
  • Others propose that quantum mechanics restricts the emission of high-frequency radiation by introducing the concept of energy quantization, where photons have discrete energy levels dependent on frequency (E=hv).
  • One participant emphasizes that quantum theory prevents the combination of energies from multiple electrons to produce higher energy photons, which contrasts with classical expectations.
  • There is a suggestion that the energy distribution of emitted radiation in classical theory does not align with the quantized nature of energy in quantum mechanics, leading to a finite total radiated energy.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between classical and quantum theories regarding radiation. While some agree on the fundamental role of quantization in addressing the ultraviolet catastrophe, others challenge the clarity of this relationship, indicating that the discussion remains unresolved.

Contextual Notes

There are limitations in the assumptions made about energy distribution and the behavior of electrons in both classical and quantum frameworks. The discussion does not resolve the complexities of these interactions or the implications of energy conservation in different contexts.

Shawn Garsed
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Hi everybody,

I have a question concerning uv catastrophe.
I know light is quantized (photons) and I know the energy of a photon depends on the frequency (E=hv). However, I don't quite understand how this 'solves' the problem of uvc. I know the emission of light in a black body is due to oscillating electrons, but how do these things all relate.
 
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Shawn Garsed said:
Hi everybody,

I have a question concerning uv catastrophe.
I know light is quantized (photons) and I know the energy of a photon depends on the frequency (E=hv). However, I don't quite understand how this 'solves' the problem of uvc. I know the emission of light in a black body is due to oscillating electrons, but how do these things all relate.

It is simple. Classical charge radiates all frequencies if accelerated, so a low energy charge can formally radiate a photon with the energy E=hv even higher than the charge proper kinetic energy. Here quantum mechanics forbids higher frequencies, the energy conservation law is different. It suppresses high frequency intensity so the total radiated energy becomes finite.

Bob.
 
Last edited:
So, according to classical physics, when an electron is oscillating it radiates all frequencies so long as it has enough energy, which depends on the amount of oscillation, which in turn depends on the overall temperature of the black body, but then Planck said that the amount of energy given of by an oscillating electron comes in 'packages' or photons and the energy-level of these photons depend on the amount of oscillation. And since electromagnetic waves with short wavelengths and therefore high frequencies have 'powerful' photons (E=hv), it follows that electrons can never radiate at all frequencies since their photons wouldn't be 'powerful' enough.

Is this the right picture?
 
Not quite.
Classical theory say that it will radiate all frequencies - but the energy of the individual photons isn't limited to the energy of individual electrons. Classically all the energy is distributed among the photons in some Gaussian distribution, so a coal fire could put out some small number of x-rays.
Quantum theory says that you can only have energy in discrete packets and more importantly this also applies to things like electrons.
A single photon comes from a single electron transition - so you can't take the energy from a few different electrons add them up and get a higher energy photon.
 

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