Quantisation of energy and Black Body radiation emission

[Weyoun]

Hi all

We just began study of the photoelectric effect and quantum nature of photons in our physics class. While our given text describes black body radiation fairly accurately, it fails completely in one aspect - how can quantisation of energy be used to derive a theoretical emission curve resembling that of experiments? Why, as the frequency of emitted radiation increases, does intensity decrease? I thought about this a little more, and came to the conclusion that as black bodies increased in temperature, the frequency of vibration in the body also increased. This would explain the increase in high frequency radiation intensity as temperature increased, but fails to explain the decrease. I am aware of the implications of classical theory and the principle of conservation of energy, but am looking for a more technical answer. Why does it decrease in the pattern it does?

On a side note, what exactly is the visual model for an 'atom vibration'? As energy increases, both frequency and amplitude (and thus intensity) have the potential to increase, yet we only see an increase in frequency. Why is this? Then again, am I mistaken? As temperature increases, intensities (and hence amplitudes) for each specific wavelength also increase. Are both increasing? What determines such a disproportionate relationship in energy distribution (energy increases tend to yield frequency increases rather than intensity)?

Please help, any replies are much appreciated

 

[Oda]

Why does it decrease in the pattern it does?

You are talking about the "ultraviolet catastrophe" if I'm not misreading. This is just a qualitative explanation of this phenomenon. Energy is quantised, so the black body can only radiate energies of discrete steps. Energy is also proportional to frequency by Planck's postulate.

It is useful to think of it as a all-or-nothing case, ie if energy does not match the quantisation then there is no emission. So higher energy emissions are rarer, since at a given temperature analogous to the Boltzmann distribution probabilities of higher energy particles are fewer. And it makes way more sense if you take the limit of frequency to infinity. In the classical case the intensity would go off to infinity (or at least non-zero) which would give you infinity energy no matter what!

Late at night so this may not make too much sense .

Oda