The UV Catastrophe (1 Viewer)

[Kaido]

Alrighty, so I understand the predictions made by classical physics, but I'd like to know how everything ties in together. I'm interested in the math, derivations etc. of say the gas laws and the temperature regulation of distribution of energy as well as Planck's quantisation theory and his derivation of the spectral distribution function.

Ultimately, if you could also tie them all together to explain the catastrophe, it would be nice.

Sanks

 

[InteGrand]

Alrighty, so I understand the predictions made by classical physics, but I'd like to know how everything ties in together. I'm interested in the math, derivations etc. of say the gas laws and the temperature regulation of distribution of energy as well as Planck's quantisation theory and his derivation of the spectral distribution function.

Ultimately, if you could also tie them all together to explain the catastrophe, it would be nice.

Sanks

I found this PDF to be very helpful: http://disciplinas.stoa.usp.br/pluginfile.php/48089/course/section/16461/qsp_chapter10-plank.pdf

 

[InteGrand]

Read Section 10.5 starting on Page 5 of that document for info about the UV catastrophe. Basically, classical physics came up with the Rayleigh-Jeans Law for the spectrum of black-body radiation as a function of frequency :

, where k is the Boltzmann constant, T is the temperature of the black body, and is the frequency of light in question. The area under this curve () should represent the total energy emitted at the given temperature T. Unfortunately, with this model, the total energy emitted would be , and infinite energy is a problem. So a new model for , and hence a new model of physics, was needed.

As that document will explain, Planck's assumption of discretised energy states for black-body oscillators resulted in finite energy emission.

Something like this is needed for HSC Physics: At first, Planck was just doing this thinking it was a mathematical trick to get a finite answer. But Einstein believed that his assumption of discrete energy was actually true, and came up with his Photoelectric effect based on the idea of discrete packets of energy in photons, etc.

 

[Kaido]

nice find , just doing further reading since HSC skips everything

 

[Kaido]

How did they calculate the probability of the energy of photons.
Is this tied with the fact that there is a probabilistic energy per atom (gaseous)
If so, please derive that probability as well, thanks

 

[InteGrand]

How did they calculate the probability of the energy of photons.
Is this tied with the fact that there is a probabilistic energy per atom (gaseous)
If so, please derive that probability as well, thanks

I'd suggest reading through the following for starters (and checking the pages they link to as well):

- http://en.wikipedia.org/wiki/Planck's_law – Planck's Law (Wikipedia)
- http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/phodens.html (from Hyperphysics - a very good physics site)
- http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/disene.html#c1 (distribution of energy)
- http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/disbe.html#c1 (Bose-Einstein distribution)
- http://www.physik.uni-regensburg.de...es of mf_statistical_physics/BE_integrals.pdf (How to calculate Bose-Einstein integrals, which appear in the derivations of Planck's Law etc.)

 

[InteGrand]

How did they calculate the probability of the energy of photons.

Also helpful:

- http://www.spms.ntu.edu.sg/PAP/courseware/statmech.pdf (mini-textbook on statistical mechanics)
- Derivations of Bose-Einstein distribution: http://en.wikipedia.org/wiki/Bose–E...ons_of_the_Bose.E2.80.93Einstein_distribution

Is this tied with the fact that there is a probabilistic energy per atom (gaseous)
If so, please derive that probability as well, thanks

The distribution you want for this is the Maxwell-Boltzmann distribution (http://en.wikipedia.org/wiki/Maxwell–Boltzmann_distribution - includes derivations).