Unraveling the mysteries of thermal radiation within quantum mechanics

[Hydr0matic]

The quanta first appeared in modern physics when investigating the nature of thermal radiation, or blackbody radiation. In a sense, it was the beginning of QM. Yet, even though I've read a lot about both BB radiation and quantum theory, I can't really tell you exactly how BB radiation fit into QMs description of radiation.

If you read any basic QM text today you'd probably first read about Planck and how he solved the problem with BB radiation by introducing the quanta. You'd probably also read about the Bohr model and schrödinger waves and how photons are emitted when electrons shift energy levels. What I've noticed about these texts though, is that they never make any connecting between these two types of radiation. It's as though they were two separate phenomena.
Many texts also give you the impression that blackbody radiation is something unreal, not present in nature. They don't clarify that it's the blackbody that's ideal and unnatural, not the radiation. The fact that BB radiation is emitted by all matter is always left out.

I think this is intentional though, not to confuse the reader. Because, to be honest, I'd be confused when first reading how all matter emit continous spectra of radiation, and then reading about atoms and how all matter emit discrete spectra of radiation.

Please enlighten me - how does thermal radiation, a phenomena so abundant in nature, fit into QMs desciption of radiation ?

 

[TeV]

Please enlighten me - how does thermal radiation, a phenomena so abundant in nature, fit into QMs desciption of radiation ?

WithOut too much oversimplfying,I'd advise you to remember that Planck constant is so small and there are so many levels of E=nh that these almost enumarable chunks of energy levels as fundamental steps make in macroscopic apperance thermodynamic spectra to look smooth and continious...

 

[jcsd]

For most (but not all purposes), blackbody radiation can be thought of as em radiation and therefore it's quanta are photons (generally speaking that is, as there's no reason to confine all blackbody radiation to the em spectrum).

 

[Hydr0matic]

WithOut too much oversimplfying,I'd advise you to remember that Planck constant is so small and there are so many levels of E=nh that these almost enumarable chunks of energy levels as fundamental steps make in macroscopic apperance thermodynamic spectra to look smooth and continious...

I'm not questioning wheather the thermal radiation spectra is truly continuous or not. My question is... what's the source of this (truly or not) continuous thermal spectra ? ... Take a piece of Lithium for example.. the atoms in such a piece emit rather few discrete spectral lines, yet.. it also emits a continuous thermal radiation spectrum... where do those photons come from ?

 

[TeV]

Hydr0matic,
In all the cases EM radiation origin is in sudden movement/shifting of charge.
But there is a difference in origin between discrete radiation (strict spectral lines ) in say excited gasses (electron transition from one "orbit" energy level to another in strict energy) property inherent to a single atom energy (that serve as fingertip indetification for elements),and "continuos" thermal radiation of atom gas colisions due to the entropy of whole system of atoms/molecules gas elements.

P.S.Erratum for my first post :"=" to be interpreted as proportionality "~"

 

[TeV]

Even more preceise on thermal energy,radiation associated with,entropy etc.

When photons with a given energy equilibirates with bulk of matter,the termal energy of atoms,molecules ,whichever matter parts, is comparable with the energy of the photons.A body in equilibrium is called a BB,and the wavelenght at which BB with temperature T has the greatest radiant power is given by Wien's law (albeit whole EM spectra contributes )
Of course,absolute equilibrium can be never established (thermodinamic laws wieved through the entropy concept) and BB is just an idealization.

 

[Hydr0matic]

So you're saying that the origin of the thermal radiation is the general movement/acceleration of the atoms/charges in the system (for example a gas) .. correct ?

That's the point of my original question - the origin of this radiation is very classical in nature... just accelerating charges emitting EM waves..

It just seems so incompatible with QM ..

Follow-up question... How does QM explain the distribution of this thermal radiation ?
I have read tons about Planck and BB radiation, but in real life, the things that emit this radiation are nothing like blackbodies, nor are they ovens with SMH-oscillator-walls...

 

[Hydr0matic]

When photons with a given energy equilibirates with bulk of matter,the termal energy of atoms,molecules ,whichever matter parts, is comparable with the energy of the photons.

Yes, but why ? What kind of process is taking place here, and how does this result in thermal radiation distributed like that of a BB ?

Like I just said, a real particle system (any piece of matter) is nothing like the system from which Planck derived his law...

 

[TeV]

Yes, but why ? What kind of process is taking place here, and how does this result in thermal radiation distributed like that of a BB ?

Like I just said, a real particle system (any piece of matter) is nothing like the system from which Planck derived his law...

1.Emitting and absorbing,emiting and reasorbing..That's the mechanism and it is quantum mechanical one.Only discrete amounts of E=nhf are excepted or emited.
2.You must agree that both in classical and quantum model thermal energy must be finite. For given temperature for extra high frequencies energy that corresponds to intensity goes unrealisticaly higher and higher in classical theory.That's the moment when Planck with his model came in and derived the Planck law of radiation of BB.
3.Not true.Every system in nature is finitely energy level quantizied

 

[Hydr0matic]

1. And what if the thermal radiation photons don't match the discrete energy levels within the atoms ? Practically none of the TR will be part of this process ...- TR is continuous, atomic is discrete.

2,3. Did I suggest Reyleigh-Jeans was the answer ? Did I suggest anything at all ? ... "classical" implies continuity, not infinite energy.

It appears my question went right over your head ...

 

[TeV]

1. And what if the thermal radiation photons don't match the discrete energy levels within the atoms ? Practically none of the TR will be part of this process ...- TR is continuous, atomic is discrete.

...

Is the matter at certain intrisic energy level (characteristic of temperature) constitued only of constantly unionized atoms or.. are there perhaps ions ,or electron gas in metals,or mixture of ANY egzotic particle mixes in nature if you want, that interchange energies and move so vigorously that actualy interaction via photons occurs mainly in ping-pong manner? Is there perhaps law of conservation of momentum satisfied when photon and electron and atom interact?Is there possibility that in some cases vast energy contribution in thermodynamic state in bulk of material is due to dynamics of free electrons in interspaces?Can high energy level among atoms in order to satisfy energy conservation be interchanged even among nucleoses via photon of adjanced atoms?Finaly ,are there such thermodynamic levels where nucleos exhibit mass defect according to Einstein relation in order to release energy?
And all these proceses (and more of them not mentioned here) if radiate energy ,radiate it by Planck law ?Amazing ha?
More ultraviolet "Jeans" to ponder about.

regards

 

[Hydr0matic]

Is the matter at certain intrisic energy level (characteristic of temperature) constitued only of constantly unionized atoms or.. are there perhaps ions ,or electron gas in metals,or mixture of ANY egzotic particle mixes in nature if you want, that interchange energies and move so vigorously that actualy interaction via photons occurs mainly in ping-pong manner? Is there perhaps law of conservation of momentum satisfied when photon and electron and atom interact?Is there possibility that in some cases vast ... *snip*

Now you changed your answer ... But anyway, you're basically talking about compton scattering.. and perhaps thermal bremsstrahlung, and similar processes right ? .. Well, I don't buy it.

Scattering processes occur only when photon wavelength matches the de broglie of the subatomic particles, and this isn't naturally the case with thermal radiation. At normal temperatures TR is in the long wavelength spectrum, and scattering with subatomic particles occur with X-rays and UV light. So I can't really see how there's any "ping-pong" action goin' on. And this isn't a radiative process anyway so I don't see why Planck should apply to it. In fact, you haven't mentioned any process which Planck should apply to.

I could be wrong though, but even if I was... the process still isn't anything like the one Planck derived his law from, so I don't see why it's applicable.

But as you can see, there's a lot of stuff I don't see .. so I'm probably wrong ...

And all these proceses (and more of them not mentioned here) if radiate energy ,radiate it by Planck law ?

Why ? .. What you mentioned may explain why the spectrum is continuous, but I can't see how it explains the intensity distribution.

 

[TeV]

. Because, to be honest, I'd be confused when first reading how all matter emit continous spectra of radiation, and then reading about atoms and how all matter emit discrete spectra of radiation.

Please enlighten me - how does thermal radiation, a phenomena so abundant in nature, fit into QMs desciption of radiation ?

This is extrated from your first post ,and maybe here lays a stumbling block of your confusion.Seems I have completely oversaw the possibility that you miss something quite fundamental :the point that Planck's law is derived from observing radiating intensity from SOLID bodies (objects).This is emphasized in almost every textbox on the subject.I thought you understood that?
Again,rereading gives me now the impression you may be reffering to difference in radiating spectra of very rarified gases (like interstelar one) of incomparably smaller DENSITY than those of the bodies.
If that turns be the case,than expanation is quite elementar.So,my last shot:The radiation of BB differs significantly from radiation of highly rarified gases.Every gas of such density,as already said before radiates dominantely in certain wavelenght regions-spectral lines and stripes characteristic for each chemical element like fingertip prints in humans.
On other hand,all other firm bodies radiate continious spectrum like BB.This is due to comparably higher density,where each body particle affects the radiation of other particles of large number particle system.(The only parameter desirable to know would be density,not a chemical structure nor details of the process in each separate case.)To get general grasp of treating ALL solid objects systes regardless of details and energy processes, desirable is to use Fermi quantum statistics.So,to repeat :Planck's law of radiation is of continious spectra for all the bodies under these terms and the shape of intensity curve against wavelenght graph has the same character like that of BB.
Now,if anything else is bothering you,let someone else try to "enlighten" you.
I can't do any more.Most definitely you will not make me write Fermi statistics expressions here.

regards


derived for all objects

 

[Hydr0matic]

I've been aware of your issue:Planck derived the law of BB radiation while knowing how the intesity curve for given T vs. waveleght distribution looked like

No, that's not my "issue". I was wondering why Planck's law is applicable to all solid bodies, given the fact that the derivation involved some very specific circumstances - An oven in thermal equilibrium with SMH oscillators in the walls constrained in emitting capabilities. These specific criterias are not found in an arbitrary solid body, so why does PL apply to it ?

If I were to figure out some sort of theory on the social structure of African lions, I can not apply this theory on cats, or birds ... [ A very bad analogy I know, but I'm desperate here ]

My point was this - a general law like Planck's, that applies to basically all matter, should be derived from an equally general model ...

NOW, I know - since you told me - this can be achieved with Fermi functions (Fermi-Dirac distribution?) and I'm longer wondering about this.


On the other hand, here's another question ... All these statistical distribution functions - http://ece-www.colorado.edu/~bart/book/book/chapter2/ch2_5.htm#2_5_1

... they also seem very classical in nature. With this statistical derivation, is quantization really necessary ? I quess my question is - could one derive a classical law describing BB radiation with the help of statistical distribution functions ?

Seems I have completely oversaw the possibility that you miss something quite fundamental :the point that Planck's law is derived from observing radiating intensity from SOLID bodies (objects).This is emphasized in almost every textbox on the subject.I thought you understood that?

Hey, it was you who brought up the gas, not me ...

But there is a difference in origin between discrete radiation (strict spectral lines ) in say excited gasses (electron transition from one "orbit" energy level to another in strict energy) property inherent to a single atom energy (that serve as fingertip indetification for elements),and "continuos" thermal radiation of atom gas colisions due to the entropy of whole system of atoms/molecules gas elements.

I, on the other hand, gave a SOLID body example ..

Take a piece of Lithium for example..

 

[TeV]

O.K.,me overworked,in many cases too quick in going through somebody elses' texts..
Important thing is you have better feelling now about the problem.
Yup,"gasses" word used in many ways in the posts:rarefied gasses,then as phraseology of electron gass in metals ,and at one stage I was even reffering to fussion process of nuclous ala Sun spectrum ( that still obey Planck's law quite well despite being called gasseous giant and having nonlinear temperature distribution)

regards