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Consider the following A-level physics question:

The transitions between energy levels shown in Fig. 1 can occur when electrons in the atom are excited. This can happen when a photon interacts with an electron in the atom or when free external electrons collide with electrons in the atom. Explain why the photon must have an exact amount of energy to cause a certain state change but the free electrons need only a minimum threshold level of energy.

The standard answer we all learn to spout is (something like) this:

  • Energy level transitions for electrons in the atom are quantised and can only occur for fixed energy values.
  • If the photon "gives up its energy" to the electron to excite it, it must (?) give up all its energy which is only possible if it has exactly the amount of energy required for the transition.
  • The free electrons can "give up" some of their kinetic energy to excite the electrons in the atom and still carry on with their remaining kinetic energy, so only a minimum amount is needed for this to occur.

I accept bullet points $1,3$. However, bullet point $2$ is causing me some problems. The way I see it, which is from a relatively very uneducated - in the context of this question - A-level physics background, a photon could surely transfer some minimum energy to excite an electron and then carry on, just at a lower frequency (sort of like a red-shift) and although this apparently won't work, I don't understand why.

This Quora post is adding to my confusion, since one answer states:

A photons loses energy by undergoing a collision with an electron, giving rise to the Compton Effect. When it collides, its energy decreases with decrease in frequency and increase in wavelength.

But another answer states:

How does a photon lose energy?

In just one way: It either loses all of its energy completely to an electron or positron, or it loses none of it at all.

The two answers appear to stand in contradiction; my physics exam board tends towards the latter answer (without explanation) but I feel very sure (without basis I must admit) that there must be examples of photons only losing some of their energy in a process.

So - which is it? Can photons lose partial amounts of their energy? If so, why is that forbidden in electron excitation?

Many thanks for any advice. Note that I will likely not follow any detailed quantum mechanical answers so if someone wants to answer in a mostly intuitive (but physically correct!) manner that's ok by me.

FShrike
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    This is just one of those oversimplifications propagated in high school physics. Often only part of a photon's energy is lost. Other times, you can absorb two photons at once in an atomic transition, with each photon contributing half the energy. Or one photon can be absorbed by two different atoms, splitting the energy between them. Completely absorption of one photon is just one scenario, though a particularly common one. – knzhou Apr 19 '22 at 19:20
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    Also, I think your first mistake was trusting anything written in Quora. ;) You know, most of their top contributors couldn't pass A levels themselves, so you really can't rely on them to know anything beyond A levels. – knzhou Apr 19 '22 at 19:22
  • @knzhou Interesting! Thank you. Is there a way to alternatively explain this notion of: “photons must have exactly the right amount of energy” or is this also a generally incorrect oversimplification – FShrike Apr 19 '22 at 19:23

1 Answers1

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The premise is untrue. Photons don't have to give up all their energy when interacting with electrons. You've mentioned the Compton effect. When the energy shift is constrained to bound electron energy levels, the process is known as the Raman effect.

John Doty
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  • What then is the alternative justification for “photons can only excite electrons if they have exactly the right amount of energy”? – FShrike Apr 19 '22 at 19:20
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    Whoever wrote that simplified the physics. "Exactly the right amount of energy" never happens. What's true is that resonant excitation by absorbing a photon of approximately the right energy is generally much more likely than Raman scattering, where the outgoing photon carries the energy difference. – John Doty Apr 19 '22 at 19:31
  • That is a helpful and digestible point, thank you. – FShrike Apr 19 '22 at 19:37
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    adding to John's comment, at the quantum level which is the one describing atoms and molecules, it all depends on probabilities of interaction, and if a photon is within the correct range of the energy level differences it has a very high probability of being absorbed, whereas Raman scattering has much lower probabilities due to the mathematical nature of QED interactions. – anna v Apr 20 '22 at 04:13
  • @annav thanks for that- NN – niels nielsen Apr 20 '22 at 04:44
  • @annav The mathematical nature of QED interactions is the result of matching the mathematics to the phenomena. It doesn't cause the phenomena, it models them. – John Doty Apr 20 '22 at 12:22
  • @JohnDoty sure , but up to now we know the model as very successful in fitting data and predictin new. – anna v Apr 20 '22 at 14:15
  • @annav The way you phrased it suggested that the phenomenon was controlled by the mathematics. But it's the other way around. Physics isn't mathematics. Mathematics is a (very useful) human invention, but it's not what drives the universe. – John Doty Apr 20 '22 at 14:21