Black Bodies, the UV Catastrophe, and Plank's Quantum assertion

[joshgreaves332]

What exactly did Max Planck assert regarding the discrete quantum nature of energy that was so significant to the observations obtained of black bodies, which contradicted the classical predictions of the time? i.e. the UV catastrophe?


My overall understanding is flawed I wonder if you could right me:

Incident radiation of a range of frequencies heats up the black body to thermal eq with the environment.

A given atom inside the box will begin to emit radiation energy at a range of frequencies.

At 1 given frequency, there could be a number of standing waves (or modes) and this number of possible modes increases quadratically with frequency? (correct?, why is this?)

The energy radiated is stored in these modes/standing waves, why? By this I mean to say, why was it concluded from classical physics that the energy should be proportional to the frequency?

This was theorized to increase constantly leading to the UV catastrophe; why is this not the case exactly? I understand there is only a certain amount of energy that can be emitted so, is it just that it follows a probability distribution, falling off at the higher frequencies? (Why?)


Many thanks

 

[joshgreaves332]

From what I said: "why was it concluded from classical physics that the energy should be proportional to the frequency?"

What I am struggling with is why was it ever postulated that infinite energy would be released at higher frequencies? Why wasnt it said that 'In order to emit higher frequencies, a higher energy would be required'. I don't understand the classical physics assertion and why the UV Catastrophe was ever considered. What am I missing?!

 

[jtbell]

Have you seen a derivation of the Rayleigh-Jeans law? (the "classical" blackbody radiation formula)

for example, http://hyperphysics.phy-astr.gsu.edu/hbase/mod6.html#c6

(and the links from that page)

It would help to indicate what level of math you know.

 

[PeterDonis]

"why was it concluded from classical physics that the energy should be proportional to the frequency?"

It wasn't; that was what Planck's quantum hypothesis said. See below.

What I am struggling with is why was it ever postulated that infinite energy would be released at higher frequencies?

That's not quite what classical physics said. What classical physics said was this: a black body will, on average, radiate an equal amount of energy in every available frequency. But there are an infinity of available frequencies, so according to classical physics, a black body should radiate an infinite amount of energy (the infinite number of frequences times the amount of energy per frequency, which is the same for all frequencies). Of course, the black body doesn't have an infinite amount of energy to radiate, so what this is actually telling us is that classical physics has *no* consistent way of describing radiation from a black body.

Planck's hypothesis was that a black body will *not* radiate an equal amount of energy in every available frequency. Instead, he hypothesized that a black body radiates energy in "quanta" which have finite energy, and the energy of a quantum goes up with the frequency. This makes it less likely that a black body can radiate energy at higher frequencies, because it has to radiate the energy a full quantum at a time (whereas, according to classical physics, energy at any frequency can be radiated in arbitrarily small amounts). That allows the total energy radiated by the black body to be finite.