Quantization of energy and ultraviolet catastrophe

In summary, the quantization of energy solves the ultraviolet catastrophe by explaining that energy is exchanged in packets rather than continuously, which prevents the math from predicting an infinite increase in energy as frequency increases. This idea was first proposed by Max Planck and later confirmed by Bose's discovery of the indistinguishability of photons. This understanding of energy exchange in packets is also important in probability modeling. For a more detailed explanation, the book From q-numbers to c-numbers by Darrigol offers a comprehensive and interesting discussion on the topic.
  • #1
physics user1
How can the quatization of energy solve the ultraviolet catastrophe?
I tried explanation on internet and on the book but i found nothing, can you help me?
 
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You will get better answers if you can tell us which parts of the explanations you did understand and where you are getting lost.
 
  • #3
Nugatory said:
You will get better answers if you can tell us which parts of the explanations you did understand and where you are getting lost.
I understood that to the old prediction based on raleight jeans model did not work, but why doesn't work? I saw the graph and of course it's because it doesn't fit the experiments, but how can the quantization explain this? How did plank came to the conclusion that energy was carried in packets?
 
  • #4
Cozma Alex said:
I understood that to the old prediction based on raleight jeans model did not work, but why doesn't work? I saw the graph and of course it's because it doesn't fit the experiments, but how can the quantization explain this? How did plank came to the conclusion that energy was carried in packets?

It fails for a couple of reasons. If you assume absorption and emission is continuous the math says nothing stops it being infinite as frequency increases - so must be wrong. Plank tried to prove it, failed and resorted to a trick - not taking a limit properly that was basically the assumption energy was exchanged in packets.

You will find a full discussion of the history here:
https://www.amazon.com/dp/1491531045/?tag=pfamazon01-20

But the simplest reason of all was discovered by Bose. Photons are literally indistinguishable meaning if you exchange two of them it makes no difference. This means the normal counting methods used in Statistical Mechanics do not apply. Do it the right way and low and behold you get the right answer.

Interestingly once you get that it's not really an issue in physics - but of probability modelling. It' even explained in Ross's standard book on the subject:
https://www.amazon.com/dp/0123756863/?tag=pfamazon01-20

Thanks
Bill
 
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The most complete explanation I have seen is in a book, From q-numbers to c-numbers, by Darrigol, Be prepared to read several chapters for a complete interesting explanation including correspondence between Planck and Einstein. Otherwise, many introductory QM texts, for example, Powell and Crasemann graze over the explanation
 
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1. What is quantization of energy?

Quantization of energy is the concept that energy can only exist in discrete, quantized levels rather than in a continuous spectrum. This means that energy cannot be divided infinitely, but only exists in specific amounts or packets.

2. How does quantization of energy relate to the ultraviolet catastrophe?

The ultraviolet catastrophe refers to a problem in classical physics where the predicted energy distribution of a blackbody (an object that absorbs all incoming radiation) was infinite at high frequencies. This contradicted experimental observations and was resolved by the concept of quantization of energy, which accurately explains the observed energy distribution.

3. Why is quantization of energy important?

Quantization of energy is important because it allows us to accurately describe and predict the behavior of particles and systems on a microscopic level. It also helps to explain many phenomena in physics, such as the stability of atoms and the behavior of light.

4. How is quantization of energy related to the development of quantum mechanics?

The concept of quantization of energy was a crucial step in the development of quantum mechanics. It helped to resolve discrepancies between classical physics and experimental observations, and laid the foundation for the later development of quantum theory.

5. Can you give an example of quantization of energy in everyday life?

Yes, a common example of quantization of energy is the behavior of electrons in an atom. Electrons can only occupy specific energy levels, or orbitals, within an atom, and cannot exist at energies in between these levels. This is a result of the quantization of energy in the atom's electron cloud.

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