Quantisation Of Light - UV Catastrophe

[sajochi]

I am wondering how the quantisation of light accounts for the experimental data for blackbody radiation as the frequency decreases.

Alot of resources simply state that it explains and accounts for the blackbody radiation curve (notably the decrease toward UV), but none explain HOW it does this.

Any help greatly appreciated

[jamonwindeyer]

Hey sajochi! Welcome to the forums

Just before I answer, shout out to a whole bunch of short guides I wrote on the course last year. I do explain it a little in the relevant section of those too, so if you want to hear it slightly differently, jump over there

So a few things for the Black Body Curve. The law that predicted the theoretical shape was called Rayleigh Jeans Law, but you don't need to know that law or WHY it predicted that specific curve. Just know that it did, and why it was an issue (the issue being even beyond not matching observation, that energy can't approach infinity for high frequencies, that makes no sense).

Putting energy in packets, with the energy per packet related to frequency, solves the ultraviolet catastrophe. Think of it like this. A BB releases a quanta due to some change inside the BB. An electron might fall down a band and release the lost energy as EMR, for example. So, the frequency of the emitted photon is directly related to the energy change that occurred in the BB, by \(E=hf\). Now, for a super high frequency photon of EMR, we need a huge energy change all in one go. This is rare. This explains the shape of the curve - At high frequencies, you need a huge energy change in the BB, and these just aren't as common as the smaller energy changes that characterise the big peak in the middle of the curve. The peak of the graph purely represents the frequency corresponding to the most common energy change in a BB of that temperature - This is called the characteristic wavelength. Basically, we get more intensity in the middle, because it is far more likely that an emitted photon falls in that range. More photons, more intensity - And that's where the graph comes from

This is a tough concept to explain- Happy to clarify or explain again if you need!

[sajochi]

The peak of the graph purely represents the frequency corresponding to the most common energy change in a BB of that temperature - This is called the characteristic wavelength. Basically, we get more intensity in the middle, because it is far more likely that an emitted photon falls in that range. More photons, more intensity - And that's where the graph comes from

Thank you! So it's basically more about probability and thus intensity as some frequencies are much more commonly occurring?

[jamonwindeyer]

Thank you! So it's basically more about probability and thus intensity as some frequencies are much more commonly occurring?

Essentially yes! Probability of having a really high energy photon is low, so less photons, so less intensity. Probability of having a 'middle' energy photon is high, so more photons, so more intensity!