Blackbody Radiation: Explaining Ultraviolet Catastrophe & Planck's Solution

[Jordan Regan]

Hello, I'm an English student and external candidate, hoping to take my Physics with me through life. I have some questions regarding a topic I'm researching, currently.

I have a book "Advanced Physics - Steve Adams, Jonathan Allday", which details 'Blackbody Radiation', as evidence for a particular nature of light.

I imagine a blackbody, emitting light from the thermal energy generated inside the box. The energy of this light will correspond [E ∝ f], where 'E' is the transferred energy from material oscillation, to photonic oscillation, and 'f' is the frequency of the light. I can accept this, as it's an observational fact. The more energy that is heating the box, the higher the frequency of the emerging light.

Now, an "Ultraviolet Catastrophe" came about, when physicists plotted the relationship between the energy and the emerging light, as they concluded the low wavelengths - and respectively high frequencies [C = fλ] - of light, would have an asymptotic correspondence with the energy of the light. Integrating this would yield an infinite sum of energy, and that's weirdness that we generally avoid.

Supposing an infinitely increasing frequency, I would assume that, yes, as frequency approaches ∞, energy will approach ∞. How does quantising the energy solve this? Why is [E = hf] any different from [E ∝ f]?

'h*f' still tends to infinity, as 'f' tends to infinity.

The other worry I have, is about 'f' actually tending to infinity. I've seen the electromagnetic spectrum, and I'm sure that it's not infinite. If [E_k ∝ v²], then there's only a maximum amount of energy that light can have?

I require a good explanation, please, as I'm really struggling with this.

-EDIT- I am now familiar with the Rayleigh-Jeans law (unfortunately not with the derivation of it, though), and can see how it would predict an infinite sum of energy for the radiance. This does not clear up how Planck and Einstein solved this, though.

 

[phinds]

Just FYI we just had a full exposition of all this on a recent thread. I suggest a forum search for "ultraviolet catastrophe"

 

[Jordan Regan]

I've searched this and nothing suits my taste for a complete answer. I may have not understood very well when I posted the question, but after continuous research I'm still dissatisfied.

According to 'Advanced Physics', Planck's desperate remedy worked because only some of the oscillators would have the energy to emitt waves. It says that the oscillators responsible for low-wavelengths would require even more energy to reach the threshold, than the high-wavelength oscillators would to reach a much higher vibrational state. I can kind of visualise what this has to do with quanta, but I would very much like this solidifying. Please S.O.S., I'd love to progress with this.

In the meantime, I'm going to do an internet search for answers. Thank you, Physicists

 

[PeterDonis]

when physicists plotted the relationship between the energy and the emerging light, as they concluded the low wavelengths - and respectively high frequencies [C = fλ] - of light, would have an asymptotic correspondence with the energy of the light.

That's not the Ultraviolet Catastrophe; as you correctly point out, quantizing the light still means that as frequency increases without bound, energy per quantum increases without bound.

The Ultraviolet Catastrophe arises from the fact that, in classical physics, a black body is equally likely to emit radiation of any frequency. So classical physics predicts that the total energy emitted by a black body is infinite, since it's the integral of an equal amount of energy per frequency over an infinite range of possible frequencies.

The quantum hypothesis solves this problem by making it no longer equally likely that a black body emits radiation of any frequency. Since energy now has to be emitted as whole quanta, it's much more likely for a given black body to emit radiation of low frequency (since it takes very little energy to make a single quantum of low frequency radiation) than to emit radiation of high frequency (since it takes a lot of energy to make a single quantum of high frequency radiation). So now when we compute the total energy emitted by a black body, the integral no longer gives an infinite answer, since the energy emitted per frequency goes down as the frequency goes up (and goes down fast enough that the integral converges).