Feynman writes, from beyond the grave:
You are of course correct, Feynman, but I am also, modulo some miscommunication on our part. I mistakenly took the words “higher energy quantum step” in SuaSponte’s post to mean the energy levels of an electron in an atom, which is not the main source of radiation in blackbody radiation. Atoms or molecules that are vibrating like weights on a spring due to thermal energy also have ‘quantum states’, but they are not so well defined or quantized as the atomic energy levels.
There are two types of quantum energy levels that are being confused (by me) here.
[ul][li]Electron energy levels in an atom/molecule. The amount of energy an electron can have above its ‘ground state’ in an atom is quantized. The ‘ground state’ is the lowest energy state an electron can have in an atom.[/li]
The size of the quantization depends on many factors, chief among them the number of protons in the atom, how many other electrons are present in the atom, and how highly energized the electron already is. To excite the electron from the ground state to the next available state takes quite a bit of energy - to go from that state to the next state takes less, and so on. The energy it takes to get the electron all the way off the atom is the ionization energy, and if you added up all the steps of energy to go from the ground state to the Nth state, as N approaches infinity the total energy approaches the ionization energy. Does that make sense?
In short, in this type of quantum state change, only photons of specific wavelengths may be emitted because there are specific energy levels of the atom to be observed.
[li]Electron/other particle energy levels in general. A photon can carry no less than hv energy, where v is the frequency, so any particle that reduces its energy must emit a photon in the amount of energy appropriate for the reduction in energy. However, there is no restriction on what energy level the particle can go into, because a photon of any energy from near zero up to the entire energy the particle has can be emitted.[/li]
This is the bit of quantum theory that saved us from the ultraviolet catastrophy. This part of quantum theory does not involve electrons jumping levels in atoms, but instead involves electrons acting like pendula that must slow down by emitting a photon. The pendulum can move at any speed between zero and the original speed before photon emission.
[/ul]
So, when an electron goes from one quantum level in an atom to a lower state, it has a limited number of choices of which state to jump into, and must emit a specific photon. But, when an atom goes from one quantum state to another by radiating a photon, it can emit any frequency it chooses up to an upper limit of the total amount of energy it has.
The confusion comes from the ‘jumping levels’ terminology. I was using it in the sense of the levels of an electron in an atom, the first sense of quantization. Feynman, I believe you are using it to describe the second. I don’t really think of atoms that are emitting quanta of blackbody radiation to be ‘jumping quantum energy levels’, because they can go to any energy state less than what they currently have. They are changing from one quantum state to another, but I didn’t consider “energy level” to refer to that because there is no definite energy difference between one and the next. Mea culpa.
In summary, the energy levels you are talking about are just any energy an atom or molecule vibrating in a blackbody can have, and the energy levels I’m talking about are the different ‘orbits’ (chemistry term) of electrons in an atom. Two very different things, but both are quantum states.
Thank you for keeping me honest.
A good quick explanation of the evolution of blackbody radiation theory can be found at http://theory.uwinnipeg.ca/physics/quant/node2.html .