Not exact but yes closer than Bill G's answer, I would have accepted it. That is why I picked on Bill G not you.
As stated the problem is the emission when measured definitely contains photons which will perplex your answer.
I wouldn't for example use "continuous building and falling" the charged particles are just moving and colliding randomly the emission reflects that. You correctly got it as heat but missed converting that to kinetic energy.
Your question is how and why does the kinetic energy get quantized in the collisions. There is no obvious answer for you, it's not what you see in classical physic collisions. Which is why I suspect you will try to deny the fact rather than deal with the fact and why I am staying out of this discussion.
For all that I am never right
So don't use me as a reference ... but you now have the terms and a start reference.
I am sorry I had to interject, but you should see why, I hate butchered science .... I will now leave you both with it.
