How does quantization of energy solve the ultraviolet catastrophe?

[Shawn Garsed]

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.

 

[Bob_for_short]

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.

 

[Shawn Garsed]

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?

 

[mgb_phys]

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.