# Electrons absorb exact energy photons so how is Ek possible

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1. Apr 2, 2015

### CAH

Hello!
I've read that electrons can only absorb photons of exactly the right amount of energy to move to a higher energy level, if its to little or too much then it doesnt absorb it at all, so my question:
How can electrons be liberated from an atom with Kinetic energy when they cant absorb any 'extra' energy?

Thanks!

2. Apr 2, 2015

### gleem

Actually it is the atom that absorbs the photon.. Since the orbital electrons exist in discrete energy states they can only change states if the absorbed photon has the exact energy to move them . This energy is equal to the difference in energies of the initial and final states. As the final state becomes higher and higher the final states have energies that are closer and closer until the difference becomes infinitesimal. At this point the electron in free or unbound. The difference in energy between the initial state and the unbound state is called the binding energy. If the exciting photon has energy equal to or greater that the binding energy of a bound electron the electron is totally removed from the atom . Any energy in excess of the binding energy go into the kinetic energy of that electron.

3. Apr 2, 2015

### CAH

So an electron/atom can only absorb 'extra' photon energy if it is in the final energy level, and only then? If so, i can see that it would make sence since there is not more discrete levels above it..?
Thanks so much!

4. Apr 2, 2015

### gleem

The electron can only be moved to a higher energy state within the atom unless the photon has the exact energy equal to the difference between the initial and the final state. If the final state is outside the atoms influence then any energy above that which just gets it out goes into kinetic energy.

5. Apr 2, 2015

### CAH

If the photon has MORE than enough energy to free the electron then the electron will be liberated with kinetic energy but only if it can overcome the particular work function for the specific electron?

6. Apr 2, 2015

### gleem

The work function applies to the liberation of an electron from he conduction band of bulk matter i.e. metal plate not from a given atom. The work function is of the order of a few eV. the binding energy of atomic electrons can be many KeV.

7. Apr 2, 2015

### echaniot

I think that the extra energy goes to the whole atom:
If (e,g) you have a hydrogen atom with an electron in the ground state n=1 (E1=-13.6 eV), then to take it to the first excited state n=2 (E2 = -3.4 eV), you need to provide it with 10.2 eV of energy. To take it to the third from the second you need an extra 2.3 eV of energy.
So if we suppose that you have the electron in the ground state , and fire a photon with energy W = 10.3 eV, your question is where will the 0.1 eV surplus go.
or in numbers: Ein = Efin => E1 + W = E2 + 0.1 eV

I believe that the extra energy goes to the recoil of the atom as a whole, since the gamma+electron process alone for a bound electron has to conserve momentum.

8. Apr 2, 2015

### sophiecentaur

There is a degree of confusing terms here. For the simple case of an atom in a gas, the well known rules of QM apply (as in the hydrogen atom we all know and love). A very high energy photon can cause an electron to be lost (ionisation) completely (with any value of surplus KE). For lower photon energies, only appropriate frequencies will interact with the atom and be absorbed. The simple rules only apply when initial and final states are 'bound'.
"Work Function" is a term that applies to metals, in which the electrons are not in "orbitals" but have a continuum of energy levels within the structure (energy bands and not levels). The Work Function corresponds to the minimum energy that can cause a photo-electron to be emitted from the metal surface. Any extra photon energy will go into the KE of the electron.

I should also mention that Momentum has to be conserved, too.

9. Apr 2, 2015

### CAH

What I'm getting at is how can electrons be ionised with any kinetic energy at all when books/Internet specifically says that electrons can only absorb photons of the exact amount of energy to move up to higher energy level/state, if this is true then how can an electron absorb obviously more than it needs to be ionised because it is liberated with Ek.

Is it because an orbital electron can't have excess energy since there are discrete energy levels so will only absorb the exact amount. However if an incident photon has enough energy to ionize the electron (and the electron 'knows' this) then the orbital electron will absorb the photon (of which is NOT an exact amount of energy the electron would need to move between levels) and have excess energy as Ek?

10. Apr 2, 2015

### sophiecentaur

Those rules only apply for jumps between Bound States. For energies greater than ionisation energy, any photon can be absorbed.

11. Apr 3, 2015

### echaniot

So , sophiecentaur what you suggest is that if we bombard a hydrogen atom in its ground state with 10.3 eV photons, it will not absorb them (and thus be excited) , because they don't have the correct energy (10.2 eV sharp) to jump to the first excited state?

12. Apr 3, 2015

### sophiecentaur

Not at all. What did I write in my post 10? Read it carefully and also my previous, more detailed post.

13. Apr 3, 2015

### echaniot

Yes, but here we don't speak of energies greater than the ionisation energy

You say:
-----------------------------------------------------------------------
For the simple case of an atom in a gas, the well known rules of QM apply (as in the hydrogen atom we all know and love). A very high energy photon can cause an electron to be lost (ionisation) completely (with any value of surplus KE). For lower photon energies, only appropriate frequencies will interact with the atom and be absorbed.
-----------------------------------------------------------------------

In terms of energy, to ionise hydrogen you need 13.6 eV, while in order to take it from the fundamental to the first excited state, you need 10.2 eV.
So the question is what happens if you send it a 10.3 eV photon.
I believe that there will be excitation, and the 0.1 eV of surplus energy will be provided to the nucleus which will recoil, or a lower energy photon will be emitted to conserve momentum.

14. Apr 3, 2015

### sophiecentaur

Actually, that's exactly what were are speaking of, here. The fact is that, the inverse law that the potential follows means that the solutions to the wave equation get closer and closer together, once the quantum numbers get high. You can more or less treat it as a classical situation 'near' ionisation energy.

There will always be conservation of momentum, of course, and you can't only think of it applying when the residue of energy is small.

15. Apr 3, 2015

### echaniot

Agreed, but in the case between the fundamental and the first excited state we are not (yet) in the high quantum numbers realm.
In this part, the energy difference between the different states is of order 0.1 eV or less, whereas here we are dealing with ~1 eV differences.

The conservation of momentum of course applies everywhere and we agree on that.
Yet, I apologize to repeat the same question here.
If an electron is in its fundamental state :E1 = -13.6 eV
If the first excited state has an energy of : E2 = -3.4 eV and the second has E3 = -1.51 eV
If I fire a photon with energy which can span from : 10.3 to 11.9 eV , what is the effect that I will observe and why?

16. Apr 3, 2015

### DrDu

There is not one final energy level. Below E=0, there are discrete energy levels and above E=0, there is a continuum of states, so that there is a state for any energy>0. These continuum states correspond to unbound electrons and can be labelled with the momentum p the particle has at suffient distance from the atom.

17. Apr 3, 2015

### sophiecentaur

One of the main results of QM is the formation of Absorption Lines, which implies that only certain frequencies are absorbed. A number of statements made in this thread seem to ignore the basic theory of how EM interacts with atoms. If there is not a transition corresponding to the incident wave's frequency then the atom will absorb nothing.

18. Apr 3, 2015

### Staff: Mentor

My understanding was that since 10.3 eV photons are not of the correct frequency to excite an electron from N=1 to N=2, and also since 10.3 eV is not enough to ionize the atom, they would not be absorbed. I don't see how that contradicts your previous posts, Sophie. That seems to be exactly what you are saying.

19. Apr 4, 2015

### sophiecentaur

Yes. You are right because that's the whole basis of QM and the H atom is the first example we're all given. Sorry, I don't know why I disagreed with that post. I think I mis-read the numbers. But I really hate numerical examples because specific examples can fail to show the basic situation. The word "equals" is far more useful than an example of two 'unequal' numbers. I think we have to agree that getting an understand of Physics - especially QM and beyond - just has to involve using some proper symbolic maths. Arithmetic is just not enough.

20. Apr 6, 2015

### echaniot

This means for example that we cannot observe Raman scattering (which has negligible yet not zero cross section) from the 10.3 eV photons when we shoot them at hydrogen?

21. Apr 6, 2015

### sophiecentaur

Does it? Could you explain, please?