I Black body radiation -- Some basic questions to aid my understanding

[AhmedHesham]

Hi
I am currently taking a physics course and studying black body radiation.I have already seen a good number of books , but I have a lot of unanswered questions.

-What does the black body radiation, which is approximately the radiation of the sun, has to do with standing waves inside a cavity . They say the radiation of the sun and then say consider a cavity.There is no apparent relation between the two situations .I understand it as follows .the radiation of the sun reach us after escaping from the interatomic spaces of the sun and so it's analogous to hot cavity,but I am not sure about this understanding

-secondly ,if the hole is a perfect absorber how does it follow immediately that the hole is a perfect emitter .

-I am tired of writing

I am seeking a deeper understanding of the subject.
Thanks

 

[Dale]

What does the black body radiation, which is approximately the radiation of the sun, has to do with standing waves inside a cavity

You get black body radiation whenever your system has internal energy only at discrete energy levels. Standing waves in a cavity are an easy classical example of such a system.

-I am tired of writing

I am not sure why. You didn’t write much and you proofread even less. Maybe it is a medical issue.

 

[AhmedHesham]

Thanks for replying
I understand it now a little better .
Could you please recommend some books for a deeper understanding of blackbody radiation .
You didn't tell me whether the way I understand it is correct or not ..ie,the waves escape from interatomic spaces .

 

[hutchphd]

-secondly ,if the hole is a perfect absorber how does it follow immediately that the hole is a perfect emitter .

This one is easy. The absorption and spontaneous emission at any frequency have to be identical at a given temperature. Otherwise stuff would spontaneously get hotter or colder than their environment.

.There is no apparent relation between the two situations

It is not too difficult to see. Matter is made of charged particles in motion. These are therefore always creating and absorbing light. Energies associated with this "gas of photons" is characteristic of the temperature of the material. This will also be true at equilibrium for an empty cavity enclosed in the material, and so that cavity is easier to think about ...a box of photons with a characteristic temperature and a small hole for access. It is a very good model for many hot chunks of matter: get them hot and they will glow.

 

[WernerQH]

The radiation of the sun reach us after escaping from the interatomic spaces of the sun and so it's analogous to hot cavity,but I am not sure about this understanding

No, it's the atoms that do the radiating. In equilibrium, the space between the atoms is filled with radiation that depends only on the temperature, independent of the stuff that is radiating. Whether an atoms radiates strongly or weakly at a particular frequency, in equilibrium the amount of energy emitted is always exactly compensated by the radiation absorbed. Already in the 19th century Kirchhoff deduced that the absorption coefficient of a substance must be strictly related to its emissivity by a universal function of temperature and frequency. Only decades later Planck was able to write that function down.

Of course the sun is not perfectly black, and (radiating into empty space) it is not in equilibrium. At different frequencies we can see into different layers of the photosphere that are at different temperatures. In the Fraunhofer lines we receive light only from the uppermost, cooler layers, and see a reduced intensity.

 

[AhmedHesham]

Ok
Thanks

 

[vanhees71]

"Black-Body Radiation" is electromagnetic radiation in thermal equilibrium, i.e., the electromagnetic field in thermal contact of any kind of matter. The classical measurement is indeed that of such thermal radiation in a cavity. Here the walls of the cavity have to be kept at some given constant temperature. The charged particles making up the wall are in thermal motion, i.e., all the time colliding somehow with each other (for a gas or the conduction electrons within a metal) or they are vibrating around their mechanical equilibrium positions (for bound molecules/atoms/electrons in a solid) and thus are radiating off electromagnetic waves. The electromagnetic waves within the cavity are now also interacting with the charged particles in the wall, and they can thereby also be absorbed. After a while, when the walls of the cavity are long enough at a certain constant temperature, there's as much radiation energy emitted from as is absorbed by the walls per unit time, and that's what characterizes thermal equilibrium between the cavity walls and the em. radiation within the cavity. That this must happen follows from the kinetic theory describing the absorption and emission of radiation (as a quantum mechanical process).

Now in such a cavity you have a discrete spectrum of frequencies of the em. waves, but if the temperature is not too law, the typical wavelengths of the radiation are small compared to the extension of the cavity and thus you can describe the equilibrium state in the socalled thermodynamic limit, i.e., you can consider the cavity as "infinitely big" while keeping the energy density of the radiation constant. In this limit you get a continuous spectrum of the black-body radiation, and taking into account all the quantum mechanical processes, i.e., absorption and both induced and spontaneous emission of photons (the latter phenomenon is only explainable via quantum theory, or more precisely quantum field theory, i.e., that's the phenomenon which clearly shows that you need to quantize the electromagnetic field).

In the Sun it's not so much different. There you have, of course, not some cavity in the literal sense, but a photon produced somewhere within the Sun it takes on average around 100000 years to get out, i.e., the radiation is pretty well in thermal equilibrium and that's why the solar spectrum is close to a black-body spectrum modulo some absorption lines (Fraunhofer lines).

 

[AhmedHesham]

"Black-Body Radiation" is electromagnetic radiation in thermal equilibrium, i.e., the electromagnetic field in thermal contact of any kind of matter. The classical measurement is indeed that of such thermal radiation in a cavity. Here the walls of the cavity have to be kept at some given constant temperature. The charged particles making up the wall are in thermal motion, i.e., all the time colliding somehow with each other (for a gas or the conduction electrons within a metal) or they are vibrating around their mechanical equilibrium positions (for bound molecules/atoms/electrons in a solid) and thus are radiating off electromagnetic waves. The electromagnetic waves within the cavity are now also interacting with the charged particles in the wall, and they can thereby also be absorbed. After a while, when the walls of the cavity are long enough at a certain constant temperature, there's as much radiation energy emitted from as is absorbed by the walls per unit time, and that's what characterizes thermal equilibrium between the cavity walls and the em. radiation within the cavity. That this must happen follows from the kinetic theory describing the absorption and emission of radiation (as a quantum mechanical process).

Now in such a cavity you have a discrete spectrum of frequencies of the em. waves, but if the temperature is not too law, the typical wavelengths of the radiation are small compared to the extension of the cavity and thus you can describe the equilibrium state in the socalled thermodynamic limit, i.e., you can consider the cavity as "infinitely big" while keeping the energy density of the radiation constant. In this limit you get a continuous spectrum of the black-body radiation, and taking into account all the quantum mechanical processes, i.e., absorption and both induced and spontaneous emission of photons (the latter phenomenon is only explainable via quantum theory, or more precisely quantum field theory, i.e., that's the phenomenon which clearly shows that you need to quantize the electromagnetic field).

In the Sun it's not so much different. There you have, of course, not some cavity in the literal sense, but a photon produced somewhere within the Sun it takes on average around 100000 years to get out, i.e., the radiation is pretty well in thermal equilibrium and that's why the solar spectrum is close to a black-body spectrum modulo some absorption lines (Fraunhofer lines).

So the way I understand it is correct.The photons escape out of the sun as if the they escape from the hole of a hot cavity after being trapped inside.