# Help with Understanding Conclusions of the Planck Hypothesis

## Main Question or Discussion Point

Let me start off by saying that I really only have a few weeks experience beyond the introductory physics courses, so I apologize in advance for any gross misconceptions I have. In trying to understand Planck's theory, I came upon a number of confusions that I am having trouble reconciling. Any help on any part is greatly appreciated!

1) The first hangup I have is with energy for low frequencies equal to KT. The way I have read about it is with an artificial blackbody with EM waves inside. I read online that each wave contributes KT to the radiation of the box. Is this the radiation absorbed by each wave? And this is regardless of the frequency of the wave--how so? Now, also Planck talks about the limit as the frequency approaches zero, the average energy approaches KT. I assume this is for the energy radiated, right? If so, is this because any oscillators that are part of the blackbody are simply radiating whatever energy that they absorb because the quantity "hf" is very low and thus easy to absorb?

2) In my text it says that Plank found that average energy is around KT when the adjacent energies delta E is small and that the average energy is about zero when delta E is large. They then show a graph of energy vs energy*probability of the energy level. It is obvious that small delta E corresponds with low frequencies, because the average energy equal KT, where large delta E seems to be for large energies, as the average is zero First of all, I may be confused about what delta E really is. Is this the quantization that Planck described, such as a large delta E is the step between energy levels? But then why is E*P(E) almost zero for large delta E-- shouldn't it depend on the frequency? One last thing, it says that delta E large is such that it is greater than KT-- what does this mean?

3) The setup for this artificial blackbody is that it is a metal cavity with a hole where EM waves can enter escape. I believe that I understand the basic setup and why this necessitates that they must be standing waves, but what about something like the Sun, which isn't made (primarily) out of metal. If it emits blackbody radiation, why don't all the previous arguments go out the door? Because it isn't a hollow metal, I don't see why it should have standing waves, and all the rest that follows.

Thank you!

## Answers and Replies

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3) The setup for this artificial blackbody is that it is a metal cavity with a hole where EM waves can enter escape. I believe that I understand the basic setup and why this necessitates that they must be standing waves, but what about something like the Sun, which isn't made (primarily) out of metal. If it emits blackbody radiation, why don't all the previous arguments go out the door? Because it isn't a hollow metal, I don't see why it should have standing waves, and all the rest that follows.

Thank you!
The Sun doesn't emit blackbody radiation. Instead it has a spectrum that contains useful information.

mfb
Mentor
Concerning 3: One interesting point is that you do not need a cavity (and even in a real cavity, standing waves are not as simple as the derivation assumes) - you get the same absorption/emission on every surface, including the surface of sun (in a good approximation, if you neglect spectral lines).

1+2: Sorry, I do not understand your text at all.
kT is an energy which corresponds to a specific temperature T, this is true for all temperatures and is unrelated to any frequency (of what?).