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### Re^2: I'm not a PhD but...

by why_bird (Pilgrim)
 on Feb 04, 2009 at 10:14 UTC ( #741227=note: print w/replies, xml ) Need Help??

in reply to Re: I'm not a PhD but...
in thread How many colors does a rainbow have?

Thanks for answering my post jdporter. You've let yourself in for it a bit though, as you've generated more questions :) If you or anyone else can help me understand this I'd be grateful. I realise it's hideously OT in terms of perl, so feel free to ignore me, but here goes(!)

Whilst I agree that without a definitive definition of 'colour' (or 'color' :P) we won't agree how many colours are in the rainbow, I am proposing that part of the definition of 'colour' should include 'wavelengths of light that humans can see'. By definition (at least any that I've ever seen) infra-red and ultra violet are outisde the visible spectrum. That's all :)

As to the rest of my post.. I am bad at expressing myself with physics! Let me try again.. for one it should have sounded more like a (series of?) question(s):

Firstly, am I right in thinking that a blackbody doesn't just require not to 'reflect or transmit' (I am not quite sure what you mean by this) any of it's radiation? It must also have a continuous spectrum which is dependent only on temperatue, and is determined by Planck's law? And it must be able to absorb and emit radiation at any (and all) wavelengths?

Given that the Sun is (approximately at least) a blackbody radiator, doesn't that mean that it's spectrum is continuous, and it (absorbs and) radiates EM waves at all frequencies? If the previous is correct, is the mechanism for the sun's radiation atomic exctitation/de-excitation? Or plasma recombination, I would've thought more likely.

If the main mode of EM emission by the sun is through atomic excitation/de-excitation, is that true of all black bodies? What other modes (if any) of photon emission are there from materials? (Thinking about it, the only other ones I know would be the acceleration of charged particles---relevant to a plasma? and annihiliation of matter-antimatter pairs---plausible in something pretty hot I would have thought). If so, how is it that a theoretical black body has a continuous spectrum, dependent only on temperature if the main mode of anything's EM emission is through de-excitation? Wouldn't you expect the spectrum to be concentrated around spectral lines?

It also appears that whatever "fuzzing out" is happening, it is not enough to completely smooth out the spectrum. Far from it!

My point is though, shouldn't it? If the main mode of EM emission from a black body is by atomic excitation/de-excitation, shouldn't black body theory take account of this, or use it as its starting point?

Thanks!
why_bird
........
Those are my principles. If you don't like them I have others.
-- Groucho Marx
.......

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Re^3: I'm not a PhD but... (models, approximations, Planck)
by moritz (Cardinal) on Feb 04, 2009 at 12:04 UTC
It must also have a continuous spectrum which is dependent only on temperatue, and is determined by Planck's law?

It must, but the "continuous" part is mis-leading.

Planck's perfect black body is - like everything in physics - just a model, and contains assumptions and approximations.

The assumptions are that if your body has a length L, then the wavelengths lambda all have the property L = n * lambda, where n is an integer, (and that all absorption and transmission happens between two sharp energy levels; not 100% about this one).

The simplification is that in order to calculate the spectral power distribution, one replaces a sum by an integral, and thus looses the quantization condition on the way.

So in the model of the Planck black body radiator the continuous spectrum is just an artifact of a mathematical approximation, not a physical property.

Note that there are other mechanism that take care of smoothing the spectrum. For example all particles in the sun move (brownian motion), so the radiation has a red- or blue shift. The second mechanism is that all processes - including those of photon emissions - take finite time, so that have (by virtue of the Heisenberg uncertainty principle) a non-sharp energy distribution (called "intrinsic" line width)

My point is though, shouldn't it? If the main mode of EM emission from a black body is by atomic excitation/de-excitation, shouldn't black body theory take account of this, or use it as its starting point?

I'm not too firm with the astronomy of our sun, so I could be wrong, but... I think the "black body" approximation holds true for the bulk of the sun, but not for the out regions (Corona, whatever), and these outer regions could be enough to filter all the spectral lines that you see when looking at the sun.

You're trying to mix two different models (atomic spectra vs. black body, a thermodynamic model), so you have to be very careful which part of which model still holds true in the mixed case.

++ physicists :)

I'll write a more comprehensive answer when I'm not at work :S

why_bird
........
Those are my principles. If you don't like them I have others.
-- Groucho Marx
.......

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