How Do Neutral Atoms Emit Black-Body Radiation?

[exmarine]

None of my textbooks seem to “close the loop” with the quantum treatment of harmonic oscillators. They all start with Plank’s assumption of quantum oscillators to explain his excellent curve fit for the black-body radiation spectrum. Then they move on to Einstein’s explanation of the photo-electric effect and heat capacitance, I think, and then to Bohr, Summerfield, de Broglie, Heisenberg, Schrodinger, etc. Then they cover the solution of Schrodinger’s equation for some simple cases, and one of these shows that even harmonic oscillators are quantized. But they never go back and re-visit the black-body radiation spectrum in light of this discovery.

My question is this: How does the mechanical heat vibration of a NEUTRAL atom or molecule emit photons of B-B radiation, say down in the infrared range of the E-M spectrum? Do the inertial effects of the thermal vibrations cause relative motions and accelerations between the massive positive nucleus and the atomic electrons, and thus cause electrical dipole moments that radiate electro-magnetic waves?

My second question for today is how did they measure the B-B radiation spectrum back in 1900? They obviously didn’t have HP analyzers or whatever. For that matter, how do we measure that spectrum today in the lab?

Thanks,
BB

 

[Penn.6-5000]

1. How does the mechanical heat vibration of a NEUTRAL atom or molecule emit photons of B-B radiation, say down in the infrared range of the E-M spectrum? Do the inertial effects of the thermal vibrations cause relative motions and accelerations between the massive positive nucleus and the atomic electrons, and thus cause electrical dipole moments that radiate electro-magnetic waves?

Pretty much. You're safe if you stay at a low level of detail: Though the whole atom is neutral, atoms are composed of charged parts (electrons and the nucleus) that move around independently, and the thermal jiggling of these charged particles is what allows electromagnetic radiation to be generated. But don't get too caught up in the particulars of the accelerations and the dipole moments. A lot of the physical mechanisms that you're used to in classical mechanics work differently in quantum mechanics. An accelerating charge radiates in classical mechanics, eh? Well, in vanilla quantum mechanics, particles don't "accelerate." (That's good, because otherwise, electrons "orbiting" the nucleus would radiate all their energy away and fall in.) In quantum electrodynamics, a charged particle can emit (or absorb) an appropriately-polarized photon at any time and when it does its momentum will change. But that's not quite the acceleration you're used to; in this same theory, a photon can hit an electron so hard that the electron goes back in time. (That's not the best way to describe what happens, but it is by far the coolest.) So if understand too much of this stuff in terms of the mechanisms you think are working behind the scenes, you'll find yourself freaking out every time you learn a new quantum mechanism, because it'll make you wonder how many of the explanations you got used to won't work any more in light of the new information.

This sort of problem happens a lot in thermodynamics; we often need ways for heat to move from one object to another, or from an object to the electromagnetic field (as with blackbody radiation), or from one form of internal energy within an object to another (as in your microwave oven, where the microwaves cause water molecules to rotate, but eventually slow down as the "heat" moves from molecular rotations to a mixture of rotations and vibrations). But we can't cover these things directly because the rules in classical mechanics were confusing enough and their corresponding quantum equivalents are downright unmanageable. We usually sidestep it by arguing that as long as energy has *any* route from one place to another, no matter how circuitous it is, then given enough time those two places will eventually reach thermal equilibrium. In abstract discussions of thermodynamics, you say "these two systems are thermally coupled" with a wave of the hand and never think about it again; the phrase "thermally coupled" just means that there's a way for heat to move from one system to the other, and makes no statement about how the heat does it. So it generally isn't long before you get used to working with incomplete descriptions of everything.

2. How did they measure the B-B radiation spectrum back in 1900?

First you need a blackbody; it's been known for a long time that you can approximate one by drilling a small hole in the side of a large cavity; the hole looks back to you and if you did things carefully, it emits blackbody light, too.

Once you have blackbody radiation, the most natural thing to do would be to shine it through a prism to project a rainbow on the wall. Then you'd measure the intensity of the light by moving a dark thermometer up and down the rainbow; the warmer it gets in a particular color, the more light of that wavelength there must be. It turns out that this natural approach matches what Otto Lummer was doing toward the end of the 1800s when he was leading the world in this sort of research. Lummer actually used a diffraction grating instead of a prism (and after awhile he figured out how to use elaborate systems of mirrors made of fancy materials to reflect exactly the wavelengths he wanted into certain positions), and a gadget called a "bolometer" originally invented by Langley in place of a thermometer. But the principle was the same. A book called https://www.amazon.com/dp/0387951741/?tag=pfamazon01-20 is too expensive and too long for your interests but if you massage Google just right you can get a preview that includes pages 39-43, which were my start on this research. You could also try to chase down Lummer's papers, but they're mostly in German.

3. For that matter, how do we measure that spectrum today in the lab?

Modern devices called "spectrophotometers" and "spectographs" exist. I'm not experienced in this field so I don't know which devices are used in which situation, but they all seem to operate on the same basic principle: use a diffraction grating (and sometimes a couple of mirrors) to break the light out by frequency, and then measure the intensity with any suitable detector. Wikipedia says that photoresistors (used to turn on many streetlights) and CCDs (used in the pixels in modern cameras) are popular photon detectors nowadays.