explaination to black-body radiation and planck (1 Viewer)

[Danny11]

i just thought this would be useful to the people (i think most people who does physics) who doesn't quite understand the planck and black body radiation curve. i don't think any one has explained it properly, the text books are just waffling cause the explaination is beyond hsc physics and math. the explaination why the curve drops when it reaches a max, is in terms of decreasing probability of higher frequency:


Why does the Planck radiation curve fall below the classical Rayleigh-Jeans Law? The origin of the drop involves the probability of higher frequency (higher energy) modes being occupied. It may be helpful to compare to the probability for higher energies in an ideal gas as given by the Maxwell distribution. Given an energy on the order of the thermal energy, what is the probability that the system could be found at multiples of that energy?

The classical view treats all electromagnetic modes of the cavity as equally likely because you can add an infinitesmal amount of energy to any mode. The quantum view expressed in the Planck hypothesis is that you either add the energy of a whole photon, or you don't add any at all. Since the excitation of a high frequency photon takes an energy high above the average thermal energy, it is therefore less likely. Thus the radiation curve falls progressively further below the classical expectation.

from:http://hyperphysics.phy-astr.gsu.edu/hbase/mod7.html#c2

 

[mojako]

>> i don't think any one has explained it properly, the text books are just waffling cause the explaination is beyond hsc physics and math. <<
its not "beyond"...
maybe no books use the word "probability" and list the numerical statistics or go into such depth.
my basic understanding (and perhaps it's a little distorted):

Classical physics theory predicted, for some reason that you don't really need to know but is explained in hyperphysics, that the intensity gets larger for shorter wavelengths or higher frequencies. Basically it's because there are more "modes" (which is a kind of combination or arrangement... of something...) for the shorter wavelengths.
This is a problem for the conservation of energy.

Planck proposed that the radiation is given out by atomic oscillators which can only emit (and absorb) energy in lumps called quanta. The size of a quantum is proportional to the frequency (E=hf).

When the wavelength is really short the frequency is really high so the quantum is large and it's harder or less probable for an individual atomic oscillator to have possessed this large amount of energy.

When the wavelength is long, frequency is low and quantum is small so there are a reasonable amount of atomic oscillators which can emit energy at the size of the required quantum. But each quantum has a small amount of energy so even though there are a reasonable amount of them the total energy isn't really great.
Also if the wavelength is really long there are fewer modes.

In the middle of the curve there is a kind of compromise between the number of quanta emitted and the size of the energy of the quanta. The total energy or intensity is maximum.

any correction?

 

[Steven12]

do we really need to know this?

i thought the curve has a limiting output because each oscillating charge vibrate at certain frequency, thus limiting the output if energy give e=hf. hf1 hf2 hf3...
is this a okay explaination?

 

[mojako]

do we really need to know this?

i thought the curve has a limiting output because each oscillating charge vibrate at certain frequency, thus limiting the output if energy give e=hf. hf1 hf2 hf3...
is this a okay explaination?

but there are more than 1 oscillating charge that emits quanta for each frequency. you need to say something about the oscillating charges being less probable to possess energy in the size of the quanta (or multiples of it) for the high frequencies or long wavelengths

 

[Steven12]

when you mentioned atomic oscillator, is it the electron?

 

[mojako]

when you mentioned atomic oscillator, is it the electron?

hmm.. I think it is.. not 100% sure.
But Planck didn't know it was electron.