How can a non-resonant monochromatic light induce an atomic transition?

In summary, the author explains that energy eigenstates are only stable when ignored, and that adding an oscillating E&M field will cause the energy eigenstates to be mixed, resulting in a transition.
  • #1
Abu Abdallah
26
0
Hello
How can a monochromatic light induce a transition ( absorption ) between two energy levels whose energy difference doesn't match the frequency of the incident light ?? A treatment using time dependent perturbation theory shows that the transition will occur even when the incident radiation frequency and hence the energy of its photons is less than the difference between the two levels !
 
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  • #2
A transition like that could not happen. It'd violate conservation of energy. Maybe you've misunderstood something? From what exactly did you read this?
 
  • #3
It's been a long time since I've done this problem, but I believe that the OP is correct.

Let me try and remember, and please forgive me, it's been nearly 30 years...

The first thing one must note is that the "energy eigenstates" of an atom are only energy eigenstates in the absence of any interactions that might allow them to decay. That is, energy eigenstates are stable, but excited atoms are not. Excitations are only stable when you ignore the ways that they can decay. This all gets back to the dE dT > h-bar rule. Energy eigenstates implies that dE = 0, and therefore that dT = infinity, and thus you are considering states that have infinite lifetimes (i.e. states that are stable).

Of course that is only an approximation, but it can be a very good one.

Now consider what happens when you add a small oscillating E&M field to the system. (I.e. monochromatic light.) The effect is that the energy eigenstates that you had before are now going to be slightly mixed. The mixtures will give you the transition probabilities. As Abu Abdallah said, you don't have to have these energies exactly matched in order to have a positive probability of inducing a transition. Heck, if the energies always had to match exactly we'd never get anything done.

The thing to remember is that you are dealing with a transitory state, so it doesn't have to satisfy energy conservation exactly.

Carl
 
  • #4
Sure non-resonant transitions happen but you can't have a transition unless the photon's energy is atleast the difference between the energy levels of the atom. You can't get the K alpha out of molybednum unless you supply more than the 17 something keVs for example.
 

1. What is a non-resonant monochromatic light?

A non-resonant monochromatic light is a type of light that has a single wavelength or color and is not in resonance with the energy levels of the atoms it interacts with. This means that the energy of the light does not match the energy difference between the atomic energy levels, and therefore cannot induce an atomic transition.

2. How does a non-resonant monochromatic light interact with atoms?

A non-resonant monochromatic light can interact with atoms through scattering or absorption. In scattering, the light changes direction but does not transfer energy to the atoms. In absorption, the light is absorbed by the atoms and can cause them to transition to a higher energy level.

3. Can a non-resonant monochromatic light induce an atomic transition?

No, a non-resonant monochromatic light cannot induce an atomic transition. In order for an atomic transition to occur, the energy of the light must match the energy difference between the atomic energy levels. Since a non-resonant monochromatic light does not have the right energy, it cannot induce a transition.

4. What is the difference between a resonant and non-resonant monochromatic light?

The main difference between resonant and non-resonant monochromatic light is that resonant light has the right energy to induce an atomic transition, while non-resonant light does not. This means that resonant light can be absorbed by atoms and cause them to transition to a higher energy level, while non-resonant light cannot.

5. Why is it important to have a resonant monochromatic light for inducing atomic transitions?

Having a resonant monochromatic light is important for inducing atomic transitions because it allows for precise control over the energy of the light and the resulting atomic transitions. This is crucial in many scientific applications, such as spectroscopy, where the energy levels of atoms need to be accurately measured.

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