Understanding Blackbody Radiation in Quantum Mechanics

[Raman Choudhary]

I'm trying to start understanding quantum mechanics, and the first thing I've come across that needs to be understood are black bodies. But I've hit a roadblock at the very first paragraphs. :( According toWikipedia:
A black body (also, blackbody) is an idealized physical body that absorbs all incident electromagnetic radiation, regardless of frequency or angle of incidence.
OK, that's nice. It's an object that absorbs (takes in itself and stores/annihilates forever) any electromagnetic radiation that happens to hit it. An object that always looks totally black, no matter under what light you view it. Good. But then it follows with:
A black body in thermal equilibrium (that is, at a constant temperature) emits electromagnetic radiation called black-body radiation.
Say what? Which part of "absorbs" does this go with? How can it absorb anything if it just spits it right back out, even if modified? That's not a black body, that's a pretty white body if you ask me. Or a colored one, depending on how it transforms the incoming waves.

What am I missing here?

 

[Geofleur]

The term "blackbody" is perhaps not very good, because a blackbody does not have to look black. The sun, for example, absorbs almost all of the radiation incident upon it, but it certainly doesn't look black! A blackbody absorbs radiation, but it emits radiation of its own in response. If it didn't, its temperature would keep on rising and rising forever! The radiation emitted is not "the same" as what is absorbed. For example, the wavelengths of the emitted radiation are usually quite different from those of the absorbed radiation. When the temperature of the blackbody reaches steady state, the energy absorbed per unit time will equal the energy emitted.

 

[256bits]

A black body in thermal equilibrium (that is, at a constant temperature) emits electromagnetic radiation called black-body radiation.
Say what? Which part of "absorbs" does this go with? How can it absorb anything if it just spits it right back out, even if modified? That's not a black body, that's a pretty white body if you ask me. Or a colored one, depending on how it transforms the incoming waves.

( A white body is that which reflects all incident light upon it ( with scattering ) so that term is already taken. )

One has to distinguish that which how a body can interact with incomming radiation,
1. it can transmit.
2. it can reflect .
3. it can absorb.

Outgoing radiation can be,
1. transmittied radiation.
2. reflected radiation.
3. emitted radiation.

For all 3 cases, the theoretical range can be 0% to 100% of the incomming radiation, or outgoing radiation.

Then to analyze, one notes the following,
Transmission - easy analysis, the radiation and body do not interact, so there is no energy exchange, for all frequencies of radiation.
Reflection - again easy, no interaction, no energy exchange, for all frequencies.
absorption - interaction, the body gains all energy.
Emittance - the body loses energy.

Hence, the interesting cases seem to be the absortion and emmitance of radiation.
Question is, how much energy is gained, or lost. What is the relationship with the temperature of the body? How is thermal equilibrium reached between objects using radiation as a means of energy transfer? Is a perfect radiator ( another term of a body interacting with radiation ) both a perfect absorber and a perfect emitter?

So, one would naturally ( ? ) come to think of what happens when all 100 % radiation is absorbed, and deal with that case. In other words, we will assume there is such a thing as an ideal or perfect absorber of radiation and see to where that leads. Another question comes to mind, is that, Is a perfect radiator ( another term of a body interacting with radiation ) both a perfect absorber and a perfect emitter?

Gustav Kirchhoff, 19th century, was one of the guys thinking of this problem, and it is he ( 1860 ) who coined the term "blackbody" - that which neither reflects, transmitts, but absorbs wholly all incomming radiation. You can look up https://www.physicsforums.com/wiki/Kirchhoff%27s_law_of_thermal_radiation , as being just one of his contributions to science. Perhaps a piece of carbon black infuenced his choice of words.

Note that, from https://en.wikipedia.org/wiki/Kirchhoff's_law_of_thermal_radiation,
Opaque bodies, Planck was interested in black bodies,

Bodies that are opaque to thermal radiation that falls on them are valuable in the study of heat radiation. Planck analyzed such bodies with the approximation that they be considered topologically to have an https://www.physicsforums.com/wiki/Interior_(topology) and to share an https://www.physicsforums.com/wiki/Boundary_(topology) . They share the interface with their contiguous medium, which may be rarefied material such as air, or transparent material, through which observations can be made. The interface is not a material body and can neither emit nor absorb. It is a mathematical surface belonging jointly to the two media that touch it. It is the site of refraction of radiation that penetrates it and of reflection of radiation that does not. As such it obeys the https://www.physicsforums.com/wiki/Helmholtz_reciprocity principle. The opaque body is considered to have a material interior that absorbs all and scatters or transmits none of the radiation that reaches it through refraction at the interface. In this sense the material of the opaque body is black to radiation that reaches it, while the whole phenomenon, including the interior and the interface, does not show perfect blackness. In Planck's model, perfectly black bodies, which he noted do not exist in nature, besides their opaque interior, have interfaces that are perfectly transmitting and non-reflective

Some historical terms we just have to accept as being so commonly used, that anyone is immediately understood.

 

[davenn]

@256bits
great explanation and reference cheers
Dave

 

[256bits]

@256bits
great explanation and reference cheers
Dave

Thanks. Much appreciated.