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Ultraviolet Catastrophe 
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#1
Jul2110, 11:24 AM

P: 113

I'm just wondering what the specific problem and solution was for the ultraviolet catastrophe. I understand that it was because scientists were calculating that in an oven, the radiation was showing infinite energy. Is this due to their being an infinite number of waves or what? And whatever the reason was for getting this calculation, why did they assume that.
Then when Planck came along and suggested the idea of a quanta, how did this fix the problem? 


#2
Jul2110, 11:33 AM

PF Gold
P: 7,363

You can google "ultraviolet catastrophe". It's an old problem and there is a lot written about it.



#3
Jul2110, 10:44 PM

Sci Advisor
PF Gold
P: 1,776

From a recent post of mine:



#4
Jul2210, 11:20 AM

P: 113

Ultraviolet Catastrophe



#5
Jul2210, 11:05 PM

Sci Advisor
PF Gold
P: 1,776

[tex]\rho(\nu) = C\nu^3e^{D\nu/T}[/tex] but the RayleighJeans distribution is [tex]\rho(\nu) = A\nu^2 T[/tex] The total energy density is found by integrating the above, [tex] u = \int_0^\infty \rho(\nu)d\nu[/tex] We can easily see that the RayleighJeans blows up as the frequency increases. The Wien does not blow up because it is exponentially convergent. But basically what they found was that by using the classical theory of they day, they could come up with a distribution that matched experiments for the low frequency spectrum. As experiments improved and they were able to measure increasingly higher frequencies, they found that the higher frequencies diverged from predicted behavior. They then found ways to fit functions for these higher frequencies but these distributions failed at mid and low frequencies. Essentially, they could predict the low and high spectrums but they did not have a way to predict the entire spectrum or the region that transitions between the two extremes. Planck came up with a solution and to do so he had to make changes to the statistical theory of the day. But this was not too unexpected as it seems that some physicists suspected that problems with the theory were to blame. 


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