Quantization of energy in blackbody radiation

[limey]

I have been reading a lot of stuff on blackbody radiation and the ultraviolet catastrophe.
Here is what I have so far.

The ultraviolet catastrophe arises from the classical electrodynamics predicting an infinite amount of energy from a blackbody having any temperature.

As far as I have understood, the way that people imagined how a blackbody absorbed and emitted radiation, were modeled by oscillators in the surface of the blackbody that could absorb (and emit) any incoming EM radiation. (I think today we would call these oscillators electrons?).

Now, the result of this directly led to the ultraviolet catastrophe (the steps I have yet to fully understand). With Planck's introduction quantized energy, the problem was eventually solved.

But here is where it breaks down in my head. As I understand it, the "real" quantization is caused by the fact that the EM radiation can only be absorbed/emitting in energy packets corresponding to the energy levels of the atoms/electrons. However, does this not clash with the definition of a blackbody, i.e. a body capable of absorbing/emitting all wavelengths?

 

[Drakkith]

It's important to understand that the energy of each photon increases as wavelength decreases. This means that higher frequency photons have MORE energy than lower frequency ones. This is ultimately what resolved the UV catastrophe.

As for black body radiation, the key is that electronic transitions, IE electrons moving between energy states in an atom, are not the only way to emit EM radiation. Any electrical charge that is accelerated will emit radiation with a certain spread of frequencies. In a solid, liquid, or compressed gas the atoms and molecules vibrate and move around enough so that this spread of frequencies corresponds to the observed range we see when we look at hot objects. Such as a light bulb. The higher the temperature, the higher the average energy of each particle, and the higher the range of frequencies emitted is.

http://en.wikipedia.org/wiki/Thermal_radiation
http://en.wikipedia.org/wiki/Thermal_motion

 

[Andy Resnick]

<snip>

But here is where it breaks down in my head. As I understand it, the "real" quantization is caused by the fact that the EM radiation can only be absorbed/emitting in energy packets corresponding to the energy levels of the atoms/electrons. However, does this not clash with the definition of a blackbody, i.e. a body capable of absorbing/emitting all wavelengths?

Not exactly- the quantization step comes in by noting that only certain wavelengths can stably exist in a reflective cavity- an integer number of wavelengths must span the distance, or that particular wavelength can't stably exist in the cavity. This information is generally recast as a 'density of states', which is the number of stable radiation modes within a wavelength (or frequency) increment. This is what leads to the final result.

 

[limey]

Thanks for the answers. It changes my perception quite a lot with the thermal radiation.

 

[sardar]

I can understand your confusion and the breakdown in your understanding of the quantization of energy in blackbody radiation. Let me try to clarify some of these concepts for you.

Firstly, the ultraviolet catastrophe is a problem that arises when classical electrodynamics is applied to the radiation emitted by a blackbody. Classical electrodynamics predicts an infinite amount of energy being emitted by a blackbody at any temperature, which is obviously not physically possible. This led to the realization that a new model was needed to accurately describe the behavior of blackbody radiation.

Enter Max Planck, who proposed that energy is not emitted or absorbed continuously, but rather in discrete packets or "quanta". This was a revolutionary idea at the time, as it went against the classical understanding of energy being continuous. Planck's quantization of energy was able to successfully explain the observed behavior of blackbody radiation and solved the ultraviolet catastrophe.

You are correct in your understanding that the quantization of energy is caused by the energy levels of atoms and electrons. In a blackbody, the atoms and electrons are constantly absorbing and emitting radiation, but only at specific energy levels. This is what leads to the quantization of energy and prevents the infinite energy predicted by classical electrodynamics.

Now, to address your concern about the clash between the idea of a blackbody being able to absorb and emit all wavelengths and the quantization of energy. While it may seem contradictory, the quantization of energy does not limit the wavelengths that a blackbody can absorb and emit. Rather, it explains how the energy of the absorbed and emitted radiation is distributed. A blackbody can still absorb and emit all wavelengths, but the energy of each individual packet of radiation is quantized.

I hope this helps to clarify some of the concepts surrounding the quantization of energy in blackbody radiation. It is a complex topic, but an important one in understanding the behavior of radiation and the development of modern physics.