Trying to understand emission and absorption

[nabeel17]

I cannot wrap my head around this stuff. Sorry if long post.

I understand that emission lines come from a higher energy state dropping to a lower state. This happens at discrete energy levels, which should correspond to discrete frequencies. And the same atom should be able to absorb photons at those same energy/frequency. Yet when you look at an absorption or emission profile you see a curve (looks Gaussian) rather then delta functions. I can't understand this? Is there a probability that the atom will absorb or emit photons not at that discrete frequency?

Also recombination produces emission and do those photons have energy = to the ionization energy? Will this also be a spectrum rather then a delta function?

I also don't understand the idea of line radiation and continuum radiation. Say I have some line and it travels through a gas cloud. The cloud can absorb some of it or emit and add to it. I saw in class that there's a line absorption profile and a continuum profile. The line profile is the gaussian looking shape and the continuum profile is a constant (or practically constant). What are these? Sorry if this is a little vague

 

[Zarqon]

There's more than one broadening mechanism. The most fundamental one is due to the fact that the atom only spend a finite amount of time in the excited state. The quantization of the energies happen because the wavefunction (naively speaking) are circling around the nucleus and "bites itself in the tail". For all radii where it does not evenly come full circle you have destructive interference and consequently no stable orbits. However, it takes a finite amount of time to resolve the destructive intereference, and the closer two frequency components are the longer time it takes. Thus given a certain lifetime of the excited state, it must also have a certain frequency width ascociated with it where Δf ~ 1/Δt. This is the natural lineshape and has the shape of a lorentzian (not gaussian).

In addition to that, there are also several other line broadening mechanism on top of that. For gases, one of the most common ones is doppler broadening, which is an inhomogeneous effect (different for each atom) and looks like a broadening only when you observe an entire ensemble. This broadening does have a gaussian shape.