Understanding Einstein's photoelectric effect paper

learningphysics

Homework Helper
I have some questions regarding the first two sections Einstein's paper. I'd really appreciate some guidance.

The paper can be found here:
http://lorentz.phl.jhu.edu/AnnusMirabilis/AeReserveArticles/eins_lq.pdf

In section 1 of the paper, he considers a volume of gas surrounded by reflective walls. He goes on to derive what seems to me to be the Rayleigh-Jeans law using "Maxwell theory" and "kinetic gas theory".

$$\rho_\nu = \frac{R}{N} \frac{8\pi{\nu}^2}{L^3}T$$

R/N = k (boltzmann constant) and L = c

Then in section 2... he writes:
"We shall show in the follow that determination of elementary quanta given by Mr. Plank is, to a certain extent, independent of the theory of "black-body radiation" constructed by him.

He writes Planck's formula:
$$\rho_\nu = \frac{\alpha {\nu}^3}{e^{\beta\nu/T}-1}$$

and then shows that at large $$T/\nu$$ this leads to the rayleigh jeans law.

It seems like what Einstein's showing is... first...
"maxwell theory" and "kinetic gas theory" => Rayleigh Jeans Law
then
"planck's formula" => Rayleigh Jeans Law

Is this to demonstrate that Planck's formula is not just applicable to blackbodies? But I thought both of these were already known. It seems to me that there is something significant Einstein's getting at here, but I'm missing it.

I'd appreciate any help.

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marlon

No the problem that needs to be solve is the socalled UV-catastrophe. Just look at the infinity value you get for the radiation energy when you look at high frequencies. This is incosistent with experiment. In order to solve this problem, Planck suggested to quantify energy.

Ofcourse this adaptation of the theory needs to reproduce the correct results of the first model (ie prior to energy quantization) for large wave lengths (this is the limit you denoted) where there is no divergence in the energy of the radiation

regards
marlon

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learningphysics

Homework Helper
marlon said:
No the problem that needs to be solve is the socalled UV-catastrophe. Just look at the infinity value you get for the radiation energy when you look at high frequencies. This is incosistent with experiment. In order to solve this problem, Planck suggested to quantify energy.

Ofcourse this adaptation of the theory needs to reproduce the correct results of the first model (ie prior to energy quantization) for large wave lengths (this is the limit you denoted) where there is no divergence in the energy of the radiation

regards
marlon
Hi marlon. Yes, I realize that planck solved the UV catastrophe. But I'm trying to understand the significance of the first two section of Einstein's photoelectric Effect paper. I think I understand what he's saying, but I'm not sure why he's saying it. Both results (that maxwell=>rayleigh jeans, and planck=>rayleigh jeans in the limit) seem to me to be already known. I just get the vague notion that he's demonstrating that quanta are not limited to blackbodies. But I'm not understanding how.

This is the sentence that is bugging me:
"We shall showing in the follow that determination of elementary quanta given by Mr. Plank is, to a certain extent, independent of the theory of "black-body radiation""

I really don't see how he showed this in that one section.

Rogue Physicist

There is an effect that Einstein is getting at here, and it has more to do with Boltzmann/Maxwell than Blackbody Radiation. The point Einstein is trying to make, and it is very subtle, because the result is subtle, and seems to be poorly understood still, is this:

Boltzmann's assumption of a finite number of discrete states is what actually causes an 'effect' in the mathematical apparatus. That is, it is a general mathematical 'artifact', not a real result based upon physical causes. It is a mirage.

While Boltzmann's results re/ thermodynamics were not well understood for a long time (and probably still aren't), Einstein is perceptively posing that it was a mathematical quirk, not a physical one, caused by some arbitrary but seemingly plausible assumptions or constraints, and resulting in unexpected and remarkable (mathematical) abberations.

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