Why do electrons drop energy levels?

1. Apr 8, 2014

jonland82

I understand that a photon can be 'absorbed' by an electron resulting in the electron jumping to a higher energy level within an atom. I also understand that a photon is emitted when an electron jumps to a lower energy level within an atom.

It seems that in the case of jumping to a higher energy level, there is a cause - a photon interacts with the electron. But I am not able to wrap my head around what causes the opposite - jumping to a lower energy level and emitting a photon.

If a lone atom was sitting in an isolated system in an excited state, would it eventually decay to the ground state?

2. Apr 8, 2014

BruceW

yeah. welcome to physicsforums! :) I think the proper answer requires quantum field theory. In the standard quantum mechanics, with an electron around the atom, the electron simply stays at the same energy. But once you do the second quantization (i.e. quantum field theory), it will show that the electron can spontaneously emit a photon.

p.s. I am still very new to quantum field theory, so I probably won't be able to answer any follow-up questions. haha. But yeah, I think that is the basic idea. You quantize the EM field, and then it all makes sense. Even when the EM field contains zero photons initially, as long as you have quantized the EM field, the physics will predict that photons can be emitted.

3. Apr 8, 2014

jonland82

Thanks for the info. I was thinking that an atom in an excited state might spontaneously decay due to quantum uncertainty.

For a more of a specific example though - I was wondering what happens, say, for example when a light beam hits a blue sheet of paper. The red end of the spectrum is absorbed by the atoms in the paper. The atoms are now in an excited state. The blue light is reflected back hence making the paper appear blue. But if the light continues to hit the paper - it stays blue right (at least for a while)?

So doesn't that mean that at some point the atoms in the paper are no longer in an excited state and are thus able to continue absorbing (red) photons so that the paper continues to appear blue?

If so, what is the decay mechanism? The spontaneous decay? Or something to do with the interaction of the atoms in the paper?

Or is the sheer number of atoms so large that it doesn't matter and it will stay blue until all the atoms are in an excited state some time in the far future?

4. Apr 8, 2014

Staff: Mentor

Consider a more mundane example of energy levels: A ball rolling around on an uneven surface. A ball on top of one of the hills is at a higher energy level (has more gravitational potential energy) than when it's down in one of the valleys.

You can push the ball uphill to a higher energy level; that's the cause you mentioned, adding energy to push the ball uphill just as the photon pushes the electron to a higher energy level. But it takes really steady hands to get the ball balanced exactly on top of the hill, and even then the tiniest disturbance is likely to allow the ball to roll back downhill.
Yes, just as this rock is eventually going to return to its ground state if we just leave it alone for long enough.

Last edited: Apr 8, 2014
5. Apr 8, 2014

6. Apr 8, 2014

MisterX

Indeed "spontaneous emission" does not happen in the theory where the electromagnetic field is not quantized. If we have the electromagnetic field be a classical entity which exists in the Hamiltonian for the for the atom, then we can set, for example $\mathbf{A} = 0$, and then we get the Hamiltonian as if the external field was absent. In this case, all the energy states are perfectly stable, that is, the energy level won't change unless something external comes along and makes it change.

However when the electromagnetic field is quantized, we may calculate non-zero decay rates from excited states, even when no photons are present initially. With Gaussian units, and ignoring spin

$$H_{EM} = -q\frac{\mathbf{p} \cdot \mathbf{A} + \mathbf{A} \cdot \mathbf{p}}{2mc} + \frac{q^2A^2}{2mc^2}$$

When the first term acts on the electromagnetic field state, it can change the photon number by $\pm 1$, and the second term can change the photon number by $0$ or $\pm 2$. So it is possible to have nonzero matrix elements of $H_{EM}$ when the initial state has no photons. This means the decay rate from an excited state can be nonzero even when there are no photons present initially.

7. Apr 9, 2014

WannabeNewton

Sure but that which has been demonstrated amounts to saying "therefore yes it can happen" and not "this is why it happens", the latter of the two being what the OP was concerned with (see the two links above and references therein).

8. Apr 9, 2014

BruceW

I'm not 100% sure what your question is. But (I think) it is something like "when a brick wall absorbs a photon, this is causing an atom to go into an excited state. So if the wall has light shone on it for a long time, eventually all it's atoms will be in excited state and we will essentially have a completely different material" Well I think the answer is that when these atoms go into an excited state, they will also drop back down, but instead of just releasing the same photon to go away from the wall, the photon can be emitted inside the wall, and after a while this photon will just end up having increased the KE of the atoms and molecules. So, the atoms and molecules don't all end up in an excited state.

So anyway, I think that's how it works. The photon's energy is used to cause the molecules to bounce around more, rather than causing all the atoms to be permanently in an excited state.

9. Apr 9, 2014

jonland82

I meant that if there was no decay/spontaneous emission of photons and there was a light beam shining constantly on the blue piece of paper - the blue piece of paper would no longer appear to be blue. All the atoms in the paper would be in an excited state and none of the incoming (red) photons would get absorbed. Therefore it seems the paper should appear to be white after a while. But, in nature that doesn't seem to be the case. So is spontaneous emission the only cause of atoms to go back to the ground state? Or is it some interaction with the other atoms in the paper itself? Either way, in order for the paper to continue to appear blue, wouldn't a transition back to the ground state for the atoms in the paper be necessary?

10. Apr 10, 2014

BruceW

yeah, that's what I thought you meant. Thanks for clarifying. In my last post, I give what I think is the answer. The atoms (or molecules) will re-emit the photon inside the solid structure, and eventually the energy of this photon will be used to give extra KE to the molecules. So this causes the solid to be warmed, due to the incident photons. (and the solid won't end up saturated with excited atoms). Also, I guess the photon would be emitted by spontaneous emission some of the time. But also, the atoms are all jostling around. So I'm hesitant to say it is only purely spontaneous emission. I don't know a lot of solid state physics. Do phonons affect the probability of the excited atom to drop down to ground state? and are there other photons in the solid, which would mean that the excited atom would not be emitting its photon by purely spontaneous emission.

11. Apr 10, 2014

Staff: Mentor

My understanding is that the atoms in bulk materials are bound into molecules, which means that they have very different energy states than single atoms. Many of these can absorb energy from a photon and lead to a vibration or other type of motion instead of an electronic transition of an electron to a higher energy state. The net effect is that photons are absorbed and their energy is transformed into heat instead of being re-emitted back as photons. Note that just because something absorbs a photon does not mean that it must emit a photon back out to get rid of that energy. That's only true in cases where there is literally no other means of getting rid of said energy. Even single atoms can absorb a photon and then collide with another atom, giving up that energy to the other atom instead of emitting a photon back out.

12. Apr 10, 2014

UltrafastPED

Phonons are a major pathway - they can be emitted or absorbed, or scattered elastically or inelastically. There are other quasi-particles that can make an appearance as well.

When considering photons we all of the above behaviors - thus a photon can be scattered and either gain or lose energy (Raman scattering), or it can undergo elastic scattering and merely change direction.