If photon energies are continuous and atomic energy levels are discrete, how can atoms absorb photons? @user1104 I suppose I should clarify my comment. If you ask "why perpetual motion" is impossible? And someone answers "because it violates energy conservation" and you in turn ask "how exactly" the next answer will be "it depends on details". The same situation here. I gave you general answer and can not go into details if you want to stay general. The details of the level broadening depend on the details of the system. Most likely, it is interaction with the surrounding of the atom.