which frequencies of photons are allowed?

[lemur]

Is there a discrete number of photons possible and if not, what determines the range of discreet photons possible in a given system?

[ajb]

People have created single photon sources and used these in experiments. Do a quick google and I am sure you will find out lots more than I know.

[swansont]

If you mean energy states, there is no restriction on them in general. [math]E = h\nu[/math] and any frequency is possible in principle (there is a practical upper limit). The blackbody spectrum, for example, is continuous. The energy spectrum of a photon undergoing Compton scattering is continuous. Photon energies are discrete when looking at transitions within systems with quantized energy levels.

[lemur]

If you mean energy states, there is no restriction on them in general. [math]E = h\nu[/math] and any frequency is possible in principle (there is a practical upper limit). The blackbody spectrum, for example, is continuous. The energy spectrum of a photon undergoing Compton scattering is continuous. Photon energies are discrete when looking at transitions within systems with quantized energy levels.

 

It's odd to hear this after hearing so often that the basis for quantum physics and the notion that light is a particle as well as a wave is the discovery, made by Planck I think, that light-energy was always emitted and absorbed in whole 'packets' and that they could never emit or absorb partial packets. Now what you're saying is that this is not an essential characteristic of EM energy itself but of a given system that is absorbing/emitting it. Does this mean that systems are only absorption/emission compatible with other systems with precisely the same allowable frequencies? Are there not more common allowed frequencies that result in materials being more likely to absorb/emit than to be transparent or reflect?

 

Also, how strict are the allowable frequencies of a given system then? Can a system allow a certain frequency of red light yet completely disallow a similar frequency only slightly higher or lower in frequency, say red-orange?

Edited May 11, 2011 by lemur

[swansont]

It's odd to hear this after hearing so often that the basis for quantum physics and the notion that light is a particle as well as a wave is the discovery, made by Planck I think, that light-energy was always emitted and absorbed in whole 'packets' and that they could never emit or absorb partial packets. Now what you're saying is that this is not an essential characteristic of EM energy itself but of a given system that is absorbing/emitting it. Does this mean that systems are only absorption/emission compatible with other systems with precisely the same allowable frequencies? Are there not more common allowed frequencies that result in materials being more likely to absorb/emit than to be transparent or reflect?

 

Saying I can get any frequency/energy/wavelength for a photon, given access to an appropriate generator of photons still does not mean I could divide that photon up, or that the photon could be partially absorbed by a material. Discrete energy levels are the result of boundary conditions being applied. Free particles do not have such a restriction.

 

Also, how strict are the allowable frequencies of a given system then? Can a system allow a certain frequency of red light yet completely disallow a similar frequency only slightly higher or lower in frequency, say red-orange?

 

The energy (or frequency) width of a transition ([imath]\Gamma[/imath]) is related to the interaction time by the Heisenberg Uncertainty Principle. For example, the first excited state in most alkali atoms have lifetimes of a few tens of nanoseconds, and have transition widths of just under 10 MHz. [math]\Delta{\omega}\Delta{t} = \frac{1}{2}[/math]

e.g. 2 pi * 6 MHz * 25 nsec (roughly the values of Rubidium's transition at 780 nm)

 

Absorption and emission profile has the shape of a Cauchy-Lorentzian function

http://en.wikipedia.org/wiki/Cauchy_distribution

 

An atom can absorb or emit light that is off resonance by a few linewidths, but the probability drops off with the square of the detuning. The lineshape can be modified if the atom is interacting (e.g. it can be broadened via collisions)