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# The Ultraviolet Catastrophe?

Can someone explain this to me in simple terms? Here is what I understand so far:

There is a cavity with a small hole in it, into which photons can travel. This approximates a black body. The walls of the cavity will absorb the photons and reach thermal equilibrium when the amount of energy absorbed equals the amount of energy that is re-emitted. This re-emitted energy will be in the form of thermal radiation.

I don't understand why photons with a very high frequency would cause the radiation to approach infinity. I don't understand what is meant by "modes". What is meant by "the probability of occupying modes"? What does it mean for there to be "quantized modes"?

I'm not having very much luck with getting answers to these questions on YA. I have a ton more questions about this kind of stuff that I still don't really understand. Hopefully you can help me out.

Thanks in advance.

### 2 Answers

- Randy PLv 71 decade agoFavorite Answer
Modes are vibrational modes or energy states. For a string on a musical instrument, the modes are the fundamental frequency and the harmonics (multiples of the fundamental). Those are the allowed vibrational states of that string.

I'm afraid it does get kind of technical when you try to calculate, as physicists were doing around the turn of the 20th century, how much energy there is at various wavelengths. Basically it comes down to the thermodynamic theory and a theorem called the Equipartition Theory, which says that every allowed vibrational mode should have the same amount of energy at equilibrium. That works out very nicely for calculating the thermodynamics of gases. But for EM radiation, there are infinitely many vibrational modes. If each one has x Joules of energy at temperature T, that's an infinite amount of energy.

Pretty good discussion here:

http://en.wikipedia.org/wiki/Ultraviolet_catastrop...

So the question was, why does the Equipartition Theorem break down? Why don't the higher frequency states have as much energy in them as classical thermodynamics says they should?

- 1 decade ago
I believe that:

Modes are vibrational modes or energy states. For a string on a musical instrument, the modes are the fundamental frequency and the harmonics (multiples of the fundamental). Those are the allowed vibrational states of that string.

I'm afraid it does get kind of technical when you try to calculate, as physicists were doing around the turn of the 20th century, how much energy there is at various wavelengths. Basically it comes down to the thermodynamic theory and a theorem called the Equipartition Theory, which says that every allowed vibrational mode should have the same amount of energy at equilibrium. That works out very nicely for calculating the thermodynamics of gases. But for EM radiation, there are infinitely many vibrational modes. If each one has x Joules of energy at temperature T, that's an infinite amount of energy.

So the question was, why does the Equipartition Theorem break down? Why don't the higher frequency states have as much energy in them as classical thermodynamics says they should?