What causes the shape of the blackbody radiation graph?

[manenbu]

Hello, I got a question about this famous graph of the spectrum given by a heated body, showing the classical line (which goes up) and Planck's line (which gives the hill shape).

How is this line continuous? Let's say my body is a lump of hydrogen, the only points on the graph should be the balmer, lyman, paschen etc wavelength. So I understand that the hotter the body is, the emission is more energetic and has shorter wavelength. But why it shows the entire spectrum and not only the allowed emission lines?

 

[NanakiXIII]

Thermal radiation has nothing to do with atoms or molecules absorbing and emitting light due to electron state transitions. Thermal radiation originates from the vibrating charges in a body, which is why it is dependent on temperature, since temperature corresponds to the strength of the vibrations of the particles in the body.

 

[dlgoff]

Another name for http://hyperphysics.phy-astr.gsu.edu/HBASE/bbcon.html" is "cavity radiation".

 

[alxm]

How is this line continuous? Let's say my body is a lump of hydrogen, the only points on the graph should be the balmer, lyman, paschen etc wavelength.

That would be true if your body was some hydrogen atoms, somehow suspended in vacuum. Quite a different thing from what you're actually made of.

The basic answer here is the same reason why you're opaque. The brief answer is that when atoms form molecules, they gain vibrational and rotational degrees of freedom, so you have these levels as well, in-between the electronic excitation levels. Condense the matter and you have additional modes caused by the interactions between molecules. Once you get to a solid, you end up with continuous bands of absorption across most of the visual/IR range, for most substances. (But you don't have the same amount of absorption in every region, hence things have colors)

Thermal radiation has nothing to do with atoms or molecules absorbing and emitting light due to electron state transitions. Thermal radiation originates from the vibrating charges in a body, which is why it is dependent on temperature, since temperature corresponds to the strength of the vibrations of the particles in the body.

No, temperature corresponds to all energy states (via the statistical-thermodynamical partition function), because these are coupled. It just doesn't correspond to electronic transitions in most substances at room temperature. At higher temperatures you end up with electronic transitions. At high enough temperatures you can even have ionization/X-rays in the blackbody curve (e.g. in the thermal radiation from exploding H-bombs, and from black hole accretion discs)

 

[NanakiXIII]

No, temperature corresponds to all energy states (via the statistical-thermodynamical partition function), because these are coupled. It just doesn't correspond to electronic transitions in most substances at room temperature. At higher temperatures you end up with electronic transitions. At high enough temperatures you can even have ionization/X-rays in the blackbody curve (e.g. in the thermal radiation from exploding H-bombs, and from black hole accretion discs)

I had never considered this, but you are right. Apologies to the original poster for giving an incomplete answer. Does the spectrum still have the same shape once you start adding these discrete lines, though?