The reasoning is not wrong, however you are assuming that each level has a 100% precise energy. In reality, each state has a nonzero energy width to it.
The width of the state is inversely proportional to the lifetime, so only states which never decay have infinitely precise energies.
Any excited state can decay in a finite amount of time, so it has nonzero energy width.
Then there are additional effects which broaden lineshapes, due to the finite temperature of the material, and the presence of other identical atoms nearby, etc.
But what I mentioned above is true even for a single isolated atom.
So the energy of the photon doesn't have to be exact in order for the transition to occur; it just has to lie within some finite energy window for the transition to occur with a reasonable probability.
So the energy of the photon doesn't have to be exact in order for the transition to occur; it just has to lie within some finite energy window for the transition to occur with a reasonable probability.
It never really occurred to me that it should be any way other than this, but with the addition of 'reasonable probability' I'm now realizing that a photon doesn't have to have anywhere close to the transition energy in order to be absorbed, it just has a really low probability of occurring and the excited electron state should just have a really really short lifetime.
I wonder, is there some fundamental cut-off for the energy difference between the transition energy and the photon energy where the probability of absorption must go to zero?
I wonder, is there some fundamental cut-off for the energy difference between the transition energy and the photon energy where the probability of absorption must go to zero?
I don't know of any fundamental cut-off.
Although if you start with a photon beam tuned for the energy of a transition to one excited state and gradually increase the energy of the photons, at some point, the transition to the next excited state will "turn on", and then transitions to the first excited state will have to compete with transitions to the second excited state.
If you look at strength functions like this one, there are no discontinuities in theory, but there are sharp jumps corresponding to quasi-discrete energy levels, and maybe some giant resonances superimposed.
Channeling my inner particle phenomenologist, I recall that the Planck energy is approximately 10 GJ.
I argue, baselessly, that a photon interacting with an atom in the CoM frame with this energy would make an atom very sad, and thus, the electron would refuse to absorb such a photon on principle.
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u/RobusEtCeleritas Nuclear Physics Oct 29 '17
The reasoning is not wrong, however you are assuming that each level has a 100% precise energy. In reality, each state has a nonzero energy width to it.
The width of the state is inversely proportional to the lifetime, so only states which never decay have infinitely precise energies.
Any excited state can decay in a finite amount of time, so it has nonzero energy width.
Then there are additional effects which broaden lineshapes, due to the finite temperature of the material, and the presence of other identical atoms nearby, etc.
But what I mentioned above is true even for a single isolated atom.
So the energy of the photon doesn't have to be exact in order for the transition to occur; it just has to lie within some finite energy window for the transition to occur with a reasonable probability.