Understanding Real-World Emission Spectra: Are Solids Similar to Blackbodies?

[Alexander83]

Hi all,

I've got two questions about the emissions spectrum from solids.

Question #1:

I feel like I have a reasonable understanding of line absorption and emission spectrum of low density gases based on transitions of electrons between discrete allowed energy levels in a gas.

I'm trying to understand the production of a continuum emission spectrum from a hot solid. I understand that a key difference between the two cases is that the quantum mechanical effects of many atoms in close proximity to one another is to split electron energy levels and in solids energy levels can form bands where the spacing between energy levels is so close that the energy levels in practice form essentially a continuum.

Is it still valid to think about the emission spectrum of a solid as essentially resulting from electrons dropping from higher to lower energy levels, as they would in a gas, just with essentially a continuous set of energy transitions open to the electron? Is this a reasonably correct model, or am I missing something fundamental here.

Question #2

Often when the continuum spectrum of solids is introduced in textbooks, the next step is to introduce the blackbody spectrum. I understand that blackbodies are theoretical objects which we can only approximate in practice and that the blackbody spectrum is only strictly valid under these ideal theoretical conditions. Yet, I also know that the spectrum of many solids is often approximated by the blackbody spectrum (or a blackbody spectrum modified by including an emissivity factor).

I'm wondering under what conditions it's valid to treat the spectrum of a solid as if it behaved like a blackbody. It seems like something that's done fairly frequently in practice (e.g. infrared thermometers, for example, seem to implicitely assume that blackbody-type radiation flux-temperature relations can apply to real world objects).

Any insight would be greatly appreciated.

Alex.

 

[Andy Resnick]

The Handbook of Optics, vol II has several chapters about this. Thermal emission from condensed matter is a lot easier in terms of a continuum model: Kramers-Kronig relations, for example. Quantum behavior can be incorporated into a model of the dielectric function (which has been done in fair detail for semiconductor materials).

As for the blackbody spectrum, it's actually better to think of it as the spectral distribution of an electromagnetic field at thermal equilibrium, rather than to attach it to 'thermal emission'.

Does this help?

 

[Alexander83]

Hi Andy,
Thanks for the reply. I'm still a little confused about the distinction between blackbody radiation and 'thermal emission'. I understand that the blackbody spectrum is formally determined as the spectral distribution of an EM field at thermal equilibrium. However, I was under the impression, perhaps erroneous, that the blackbody spectrum is often used as a model to approximate thermal emissions from real objects. E.g. that certain aspects of blackbody radiation like Wien's Law that describes a colour-temperature relation could also be roughly applied to explain the changes in colour of objects as they are heated, or that you could measure changes in the IR flux off of an object to infer its temperature. This seems to imply a similarity in behaviour between the more idealized blackbody radiation spectrum and the actual spectrum of warm, real-world objects.

My question was essentially - is it reasonable to think of the spectrum of a real object (e.g. a stove element, a lightbulb filament) as similar in spectral distribution and temperature-dependence to a blackbody curve and if so, under what circumstances.

Maybe I'm also mis-using the term 'thermal radiation' - I'm thinking of it as radiation emitted by an object because the object is warm (above 0K) and has random molecular motions associated with this non-zero temperature.

Alex.