system
Given the following post, respond as if you're commenting on Reddit:
human
How close does the energy of a photon have to be to the energy jump of an electron for it to absorb the photon?

If an electron can only absorb all or none of a photon and can only jump up to specific energy levels, the energy of the photon would have to be equal to the energy level of the electron. But, I am assuming that there can be some error, otherwise it would rarely happen. What is this error and why is there one?
gpt
The answer is if you are going to transition between two bound states (energy levels) the energy of the photon and energy of the transition must match *exactly* for non-scattering interactions.

That being said its not "rare" because we are typically measuring ensembles of many many atoms.  These ensembles have statistical broadening effects, as well as uncertainty effects in the light field that make them more probable.  For example the precision something can measure a frequency of light is going to be inversely proportional to the time it can interact with that light field.  Meaning most systems can only interact for a set amount of time before the light field is turned off.  This innately gives the light field some uncertainty in frequency.

These uncertainty effects give both the atom/molecule and the light field a distribution of available frequencies.  Now the probability that the light will interact (be absorbed) but the object will be proportional to the overlapping area of the two frequency distribution functions.  There are more factors at play here but thats the basic point.

Additionally you can have scattering events where only part of the photos energy is absorbed due to induced fields.