confusion in UV catastrophe (1 Viewer)

[kooltrainer]

what is the UV catastophe saying? .. that lower wavelength would have infinite energy?? why did they think this way... obviously this isnt true because of conservation of energy..

then planck tried to give a solution to this problem .. and he explained that it gotta do with energy being emitted in quanta .. how is this a solution to that catastrophe?

basically, what was the problem that caused Planck to come up with this quantum theory and how does this theory solve the problem.. thx

 

[veloc1ty]

It is called the UV catastrophe because using classical physics the black body radiation models that were produced shows energy approaching infinity at lower wavelengths (near UV waves). As you said, this is obviously not the case so the problem was that they couldn't replicate actual results using classical physics.

By saying energy is emitted in quanta proportional to frequency it solved this problem. I'm fairly sure the exact explanation as to how this solves it is not required by the syllabus, but here is what Wikipedia says:

"Einstein pointed out that the difficulty could be avoided by making use of a hypothesis put forward five years earlier by Max Planck. Planck postulated that electromagnetic energy did not follow the classical description, but could only oscillate or be emitted in discrete packets of energy proportional to the frequency, as given by Planck's law. This has the effect of reducing the number of possible modes with a given energy at high frequencies in the cavity described above, and thus the average energy at those frequencies by application of the equipartition theorem. The radiated power eventually goes to zero at infinite frequencies, and the total predicted power is finite. The formula for the radiated power for the idealized system (black body) was in line with known experiments, and came to be called Planck's law of black body radiation. Based on past experiments, Planck was also able to determine the value of its parameter, now called Planck's constant."

 

[Captain Gh3y]

there was just another thread on the same topic with a few good answers that should explain it:

http://community.boredofstudies.org/showthread.php?p=3515775

 

[kooltrainer]

It is called the UV catastrophe because using classical physics the black body radiation models that were produced shows energy approaching infinity at lower wavelengths (near UV waves). As you said, this is obviously not the case so the problem was that they couldn't replicate actual results using classical physics.

so why would black body radiation produced shows energy approaching infinity at lower wavelengths using classical physics??

 

[RiSeAgAiNSt2538]

because classical physics had light as a wave. not as quanta as that guy who's name i forget theorised.

 

[Forbidden.]

Then Planck generated a theoretical expression for the wavelength distribution that agreed remarkably with experimental curves of a Black Body radiation graph. (Look at 2nd equation)

1st Equation (Rayleigh-Jeans law)
2nd Equation (Planck's wavelength distribution function)

k_B = 1.38 x 10^-23 J.K^-1 (Boltzmann Constant)
c = 3.00 x 10⁸ m.s^-1 (Speed of light in vacuum)
h = 6.63 x 10^-34 J.s (Planck's Constant)

Keep the temperature constant and graph wavelength versus intensity for fun.

 

[Teh Duke]

what was the original equation they had that said that energy would approach infinity as the wavelength shortened?

 

[Forbidden.]

what was the original equation they had that said that energy would approach infinity as the wavelength shortened?

I'm going to summarise all this UV catastrophe shit with reference to these two equations because it's hard to explain without the maths, that's why thank god I have my engineering textbook with quantum physics. (I never understood this during the HSC)
The first equation, Rayleigh-Jean's Law shows as the wavelength approaches 0, the intensity reaches infinity*.

But when they did an experimental plot of the Black Body curve (just like today) they were like "Holy shit OMFG the experimental results don't fit with Rayleigh-Jean's Law !!", then they called it the UV catastrophe because it was apparent at UV wavelengths which were very small compared to most other wavelengths on the spectrum.
They expected the intensity to go to infinity according to R-J's law but experimentally as the wavelength approached zero so did the intensity.

Then Planck made his own wavelength distribution function which corrects this (look at the denominator, some mathematical madness fixes it up) and it does work experimentally.

* - (Like plug in 0.0000000000000000000000000000001 and see what you get for the intensity for the 1st equation, like OMFG huge).

 

[Teh Duke]

but what was R-J's law? What was the equation that he had that made the infinite intensity prediction?

 

[Captain Gh3y]

but what was R-J's law? What was the equation that he had that made the infinite intensity prediction?

dU(f) = kT*(8*pi*V/c^3)*f^2 df
classically the probability of finding a wave of a given energy is independent of its frequency

i posted the mathematical development in the link in post #3

 

[Forbidden.]

but what was R-J's law? What was the equation that he had that made the infinite intensity prediction?

Rayleigh-Jean's law!
Enter the equation into your calculator and enter 0.000000000000000001 into the wavelength (λ⁴ so (0.000000000000000001)⁴) and see what you get as an answer (should be huge intensity)

Rayleigh-Jean's law says as wavelength approaches 0, the intensity approaches infinity.
They tried this experimentally, but experimentally, as wavelength approaches 0, so does intensity.
Something went wrong.
Planck corrected this by bringing his own equation, as wavelength approached zero so did the intensity, so that's why everybody loves Planck.
Experiment agreed with Planck, not Rayleigh-Jean's law.

 

[Omium]

k_B = 1.38 x 10^-23 J.K^-1 (Boltzmann Constant)
.

yay boltzmans constant
Thermodynamics FTW

 

[kooltrainer]

Rayleigh-Jean's law!
Enter the equation into your calculator and enter 0.000000000000000001 into the wavelength (λ⁴ so (0.000000000000000001)⁴) and see what you get as an answer (should be huge intensity)

Rayleigh-Jean's law says as wavelength approaches 0, the intensity approaches infinity.
They tried this experimentally, but experimentally, as wavelength approaches 0, so does intensity.
Something went wrong.
Planck corrected this by bringing his own equation, as wavelength approached zero so did the intensity, so that's why everybody loves Planck.
Experiment agreed with Planck, not Rayleigh-Jean's law.

right okay, theres the formula which states 0 wavelength has infinite intensity..
is it possible to explain in words why this would happen?
When they proved the R-J law was wrong, how did planck's quantum theory explained it? (without using his crazy equation)