I am trying to understand the absorption of different energies/frequencies of light by electrons, and I have a few questions (I am relatively new to quantum mechanics, and may have some fundamental misconceptions).
As I understand it, photons can exist at a continuum of frequencies and therefore energies. For an electron to absorb a photon and jump to a higher energy level, it needs to absorb a photon whose energy is the difference in energy between the 2 energy levels. Does the photon need to be that exact frequency/energy to be absorbed, or is there a narrow range of frequencies/energies that will be absorbed?
If the photon needs to be the exact frequency, it seems to me that the chance of any photon would have a minimal probability of having the specific frequency required, due to the energy/frequency of photons ranging over a continuum. My instinct for this case would be that due to the uncertainty principle, photons would not have exactly defined energies/frequencies, and photons with frequencies around the correct value would have a probability of being absorbed. Is this idea correct?
If the photons can be in a range of frequencies around the correct energy, this would explain why photons have a non-0 chance of being absorbed, and also why the bands on absorption/emission spectra have varying thicknesses, but if so, what happens to the minute difference in energy between the energy of the photon and the actual value?
Which, if any of these thoughts are correct? if none, what is the correct case?