I am trying to understand radiative transport of thermal energy in materials from first (or close to first) principles. I do not understand the systematics/statistics of how photons are emitted and absorbed in a medium. How is it that photons can be emitted at so many wavelengths and atoms can absorb photons at these different wavelengths (http://panda.unm.edu/Courses/Finley/P262/ThermalRad/PlanckRadHotT.gif) when we know from spectroscopy that photons are emitted and absorbed only at very specific wavelengths (http://www.astro.cornell.edu/share/sharvari/websiteV7/images/absorption.gif). Is it the case that this emission and absorption changes with kinetic energy (thermal energy) of each individual atom? Does an absorbing atom have to have exactly the same thermal energy as the emitter? If there are so many quantized energy levels, how is it not made statistically impossible for a randomly emitted photon to encounter an atom at a temperature necessary to absorb it? As you can see my understanding is muddled. Let me know what you think.