1. Aug 31, 2010

### fluidistic

To make my question simpler, assume that there's a black body at 0K or very close to it (if we can't assume there's a body at 0K).
Say I have a monochromatic source of photons which sends 1 photon on the black body. The wavelength of the photon is 500 nm so around green. If I understood well how a black body behaves, it will absorb the photon and re-emit a continuum spectra of light. In other words, it will radiate an infinity of photons. Obviously the black body can't emit another 500 nm photon otherwise it would emit only 1 photon (due to conservation of energy) and not a continuum spectra. I realize that in a realistic case the black body cannot emits an infinity of photons, but it doesn't matter for my question.
How can I know what will be the spectra of a black body, knowing that I send a photon of wavelength $$\lambda$$?
So after all, the "continuum spectra" can be very limited in wavelength range? I'm interested in knowing how to determine for example what would be the most energetic photon that will be emitted in my previous example.
By the way it's not a homework question so any reply of the form "look at Planck's Law" or any other Law satisfies me. Explanations are welcome too.

2. Aug 31, 2010

### zhermes

The black-body spectrum is a statistical effect which only corresponds to average properties. What happens to a single photon requires a solid state analysis.

3. Aug 31, 2010

### fluidistic

Hmm interesting. Even in an idealization of a black body? I.e. absorbs all incident light and re-emits a continuum spectra.

4. Aug 31, 2010

### cjl

The continuum spectrum it emits will be exclusively dependent on its temperature. So, that depends on how much it heats up due to the single incident photon. If it were to remain at 0K, it would not emit any spectrum at all.

5. Aug 31, 2010

### fluidistic

Ok I see. It can't remain at 0K (it's not infinite in size) since it absorbs a photon. I think I could use Stefan-Boltzmann's law to calculate the gain of temperature due to the absorption of 1 photon. Say it gives me it heats up to 0.1K. What formula can I use to see the black body radiation at this temperature?
I'm really curious if there's at least 1 photon with a close to 500 nm wavelength. It's almost impossible.

6. Sep 1, 2010

### zhermes

The reason why a black-body behaves the way it does is because of statistics and averaged quantities. It was all of the boltzmann distribution, einstein's quantization that pieced it together.

I don't know exactly what a perfect black-body, starting in the ground state, would do after being hit by a single photon.... but its definitely not going to produce black-body, continuum emission. Whatever results will most likely be purely quantum mechanical.... maybe just re-emit a photon with the same wavelength? More likely a probabilistic function would decrease the probability of producing some combination of 'n' photons, and whatever combinations of frequencies (the sum of which equal the initial frequency)? Anyone out there have specifics?

EDIT: another guess, the blackbody intensity distribution might describe the probability with which a photon, of energy less than or equal to that available, is emitted.