Continuous Spectrum and Energy levels of Electrons (Energy Bands)

[ktmsud]

TL;DR Summary

How can we get continuous spectrum from a heated object? Can it be explained on the basis of electronic transition among various energy level?

My book says that emission spectra are produced when an electron in excited state jump from excited to lower energy states. It also states that solids and liquids produce continuous spectra and it depends upon temperature only (is this black body radiation?).

I know, Electrons around a nucleus in an atom can only have discrete energy level and in case of solids these energy level form continuous bands due to interactions. These energy bands have certain space between them, right?(e.g. in case of insulator there is forbidden gap between conduction band and valance band).Also electron very far from nucleus can have any energy. An electron can jump inside a band from one energy value to another or from one band to another band but it cannot have energy value of forbidden band. In this way there should be forbidden wavelength band.

So it confuses me, how a conductor and insulator can have similar emission spectrum at same temperature?

 

[Charles Link]

The theoretical blackbody emission applies to a cavity, where basically you have a box with an aperture, and you measure what emerges from the aperture. From the outside surface of the box, the radiated spectrum can be very much dependent on the material, and there is an emissivity that is less than unity and it can also be spectrally dependent. Meanwhile the radiative characteristics of the cavity (coming out of the aperture) are such that a small aperture will result in an emissivity that is very nearly unity, because by Kirchhoff's law the absorbance of the aperture is the same as the emissivity. Meanwhile light that enters the aperture can make many reflections on the interior walls and ultimately gets absorbed, regardless of the material of the interior walls.

There are materials that do have an emissivity that is nearly unity, but most materials don't have this property.

It might interest you that the theoretical blackbody calculation is done by counting the modes in the cavity assuming periodic boundary conditions, and assigning average occupancy numbers for a given temperature for the Bose states. This gives the photon density, and with an effusion type calculation, the rate of emergence of photons from the aperture is computed. See https://www.physicsforums.com/threa...-density-of-a-black-body.956343/#post-6063569
and
https://www.physicsforums.com/threa...erivation-of-plancks-law.958747/#post-6079472

 

[ktmsud]

But my interest is not on how a theoritical black body works, i am interested to know can radiation from a heated object be explained sililarly as in the case of atomic spectra(electronic transition)?

 

[Charles Link]

But my interest is not on how a theoritical black body works, i am interested to know can radiation from a heated object be explained sililarly as in the case of atomic spectra(electronic transition)?

It's not nearly as simple (as atomic spectra), but when you have a non-zero emissivity, you necessarily have some kind of process going on such as vibration modes and/or electronic transitions or electronic bands. Otherwise you may find the solid to be nearly transparent with an emissivity much closer to zero than to unity.

Edit: I should also mention the metals, which are non-transparent, but have a high reflectivity, and thereby low emissivity. Here the material properties are such that they can reflect an electromagnetic wave with little loss of energy.

 

[rude man]

Summary:: How can we get continuous spectrum from a heated object? Can it be explained on the basis of electronic transition among various energy level?

My book says that emission spectra are produced when an electron in excited state jump from excited to lower energy states. It also states that solids and liquids produce continuous spectra and it depends upon temperature only (is this black body radiation?).

I know, Electrons around a nucleus in an atom can only have discrete energy level and in case of solids these energy level form continuous bands due to interactions. These energy bands have certain space between them, right?(e.g. in case of insulator there is forbidden gap between conduction band and valance band).Also electron very far from nucleus can have any energy. An electron can jump inside a band from one energy value to another or from one band to another band but it cannot have energy value of forbidden band. In this way there should be forbidden wavelength band.

So it confuses me, how a conductor and insulator can have similar emission spectrum at same temperature?

I think the answer is that there are umpteen gazillion discrete energy drops from many Bohr orbits to other orbits, each with a definite energy transition or drop E. Each drop generates a photon with a definite frequency $\nu$ and energy $h \nu = \Delta E$.. Together they form a practical continuum of frequencies.

Classical physics could not and cannot explain the now infamous "ultraviolet catastrophe" until Max Planck postulated these finite energy quanta later shown to be emitted photons.

 

[PeterDonis]

My book

What book?

 

[PeterDonis]

Electrons around a nucleus in an atom can only have discrete energy level

But the radiation from solids and liquids is not just due to transitions of electrons between energy levels in atoms. Solids and liquids are not just single atoms; they are huge conglomerations of molecules (in some cases, a solid object is basically just one huge molecule), and there are many more energy levels present than just the ones that would be present for a single atom: for example, different energy levels due to the vibrations of the atoms or molecules. There will be a wide enough range of such energy levels, with close enough spacing, that the emission spectrum is effectively continuous.

how a conductor and insulator can have similar emission spectrum at same temperature?

Because the emission spectrum has virtually nothing to do with whether or not the material is a conductor or an insulator. A conductor, such as a metal, might have a range of energies for electrons (the conduction band) which actually is continuous, but even outside that range, as above, there will be a large enough number of energy levels with close enough spacing that the spectrum will be effectively continuous. An insulator, even though it lacks the conduction band, will still have the same general property.

 

[PeterDonis]

I think the answer is that there are umpteen gazillion discrete energy drops from many Bohr orbits to other orbits

"Bohr orbits" of individual atoms alone would not be enough; there are not "umpteen gazillion" different ones of these covering a wide range of energies. To get that, you need the additional energy levels due to things like vibrations of atoms within molecules or larger structures.