Assume a photon is produced by an atomic electron making a transition down from a certain energy level to another.
Can that photon only be absorbed by another atomic electron making exactly the opposite transition?
Is there any chance that the photon could be absorbed by an atomic electron undergoing a transition with a slightly different energy difference?
short answer is yes
from a certain energy level to another.
it's not that certain, every photon will have slightly different energy. it's a long story, but excited state of the atom is influenced by the vacuum around, so the spectral peak will always have some width. look at this spectrum
this is gas inside the lamp. each peak has a width. when the atoms are inside the liquid or solids, the line width becomes really wide.
so, no the energy of a photon is not certain, and it will be absorbed by other atoms
There is an intrinsic width to the spectrum of lines around an atom that can be measured and calculated by solving the quantum mechanical equations. This is connected with the Heisenberg uncertainty principle, and will exist even in vacuum.
This width is visible, for example in this photo of hydrogen lines:
One can see that for these specific atoms, the emitted photons can be absorbed again only by the same line , since there is no overlap. There exist though very many atomic structures with similar energy levels and large enough width to be excited by the above photons even if the central energy of the line will be different within the width.
In the study of transitions in atomic spectra, and indeed in any type of spectroscopy, one must be aware that those transitions are not precisely "sharp". There is always a finite width to the observed spectral lines.
One source of broadening is the "natural line width" which arises from the uncertainty in energy of the states involved in the transition. This source of broadening is important in nuclear spectra, such as Mossbauer spectra, but is rarely significant in atomic spectroscopy. A typical lifetime for an atomic energy state is about 10-8 seconds, corresponding to a natural linewidth of about 6.6 x 10-8 eV.
For atomic spectra in the visible and uv, the limit on resolution is often set by Doppler broadening. With the thermal motion of the atoms, those atoms traveling toward the detector with a velocity v will have transition frequencies which differ from those of atoms at rest by the Doppler shift. The distribution of velocities can be found from the Boltzmann distribution.
As the other answer states the fields around the atoms will also have an influence by changing the boundary conditions for the solutions.
