Can a Photon be Absorbed Without the Exact Energy Level?

[houlahound]

ancient Chinese proverb (I think);

if your spectral lines are too broad just use the zoom function and zoom on out a bit...

 

[Keith_McClary]

then what are the chances this radiation will be the exact amount required for an electron jump of any of the finite number of elements?

The same phenomenon occurs in in the simple case of (transmission)http://www.open.edu/openlearn/science-maths-technology/science/physics-and-astronomy/scattering-and-tunnelling/content-section-3.5. There are resonances at certain energies (corresponding to how many wavelengths fit in the well). See Figure 13. The resonances do not occur only at an exact energy, since there is still a resonant effect when the wavelengths almost fit in the well. The resonances are sharper in the case of transmission through two barriers as discussed here (PDF), if the walls are high/thick so the waves resonate for many cycles (This is what you refer to as "absorbed").