# Do photon apply a force to the electron ?

1. Jan 25, 2016

### big_bounce

Hello PF members,

In Newtonian perspective, applying a force to a object like ball causes it starts to moving and getting more speed and more energy.

Do photon apply a force to the electron when it interacts with the atom and electron absorbs it?

It seems electron gets more energy and goes to higher level energy without any force that could doing work on it. Is it compatible with Newtonian perspective?

Last edited: Jan 25, 2016
2. Jan 25, 2016

### jfizzix

When the electron absorbs a photon, the total momentum of electron plus photon is conserved.

When the photon is absorbed, its momentum is transfered to the electron, changing it.

Since the photon causes a change in the electron's momentum, one could imagine this as the photon imparting a force on the electron, but understanding things in terms of momentum is easier to understand.

At the atomic scale, the Newtonian picture is often inaccurate in describing individual atomic events, but energy and momentum conservation still largely hold.
That being said, Ehrenfest's theorem shows that the average statistics built out of many atomic events obey Newtonian equations of motion.

3. Jan 25, 2016

### big_bounce

Okay. My question could change to : How the momentum transfer occurred ? In Newtonian perspective applying a force times time could change the momentum. this is a mechanism that would understood.

But in photon's absorbs phenomena seems changing in momentum and energy level of electron is instantaneous without any explanation without any force that could do these. This transfer is like "ghost phenomena".

In general, for me this is clearly incompatible with Newtonian Laws of Motion. No force but changing in motion,energy,momentum and state of a electron!

4. Jan 25, 2016

### bhobba

The explanation is in Quantum Field Theory - but its nothing like classical explanations.

Thanks
Bill

5. Jan 26, 2016

### Staff: Mentor

Sorry to be pedantic, but this is a pet peeve of mine. It is not the electron that absorbs the photon, it is the system nucleus+electron. In this case, it is clear that it is the total momentum of the atom that changes, not just that of the electron. See radiation pressure and laser cooling.

6. Jan 26, 2016

### Staff: Mentor

Neither a photon nor an electron is an object like a ball (an electron may act enough like one to tempt us into that error, but a photon seldom even comes close). Thus, there's no particular reason to expect them to act like balls.

The electromagnetic interaction does transfer momentum between the electron and the photon but it's not described by Newton's $F=ma$. The $a$ in that equation is acceleration, acceleration is defined as change in velocity, velocity is defined as change in position, and that's fine for objects like balls that have a position - but it's not going to work for electrons and photons which don't have a classical position.

7. Jan 26, 2016

### jfizzix

I was imagining a free electron. Momentum conservation of the electron plus photon only works if there are no external interactions with the electron plus photon system, like a nucleus.

8. Jan 26, 2016

### Staff: Mentor

But a free electron can't absorb a photon...

9. Jan 26, 2016

### ZapperZ

Staff Emeritus
It is only "incompatible" if you learn Newton's laws or classical mechanics up to F=ma. You are forgetting (or maybe you never knew) that classical mechanics can also be formulated via the Lagrangian/Hamiltonian picture whereby the concept of "force" is virtually non-existent! So the first problem in your question is the fact that you somehow believe that "Force" is a necessary and fundamental concept.

The second problem has been addressed by DrClaude, and it is also one of my pet-peeve. The existence of the discrete energy states in an atom is NOT just due to the electron. It is due to the nucleus and electron system. Without the nucleus central charge, these states will not exist (try to find such states for a free electron). When a photon is absorbed by an atom, what has changed in an atomic transition is the energy and momentum of the entire atom, not the electron! While this change is manifested by the electron changing state, it is the entire atom (which includes that electron) that is involved in the process.

Zz.

10. Jan 26, 2016

### jfizzix

Really? How do you figure?

Free electrons might have a continuous energy spectrum instead of discrete energy levels, but what would keep them from absorbing photons?

"free" electrons can at the very least gain and lose energy due to electromagnetic interactions

11. Jan 26, 2016

### Staff: Mentor

The interaction won't conserve momentum. You need either a bound electron (so that the rest of the system can soak up the excess momentum) or a scattering interaction in which a photon and an electron come in and then come out with different energies.

12. Jan 26, 2016

### ZapperZ

Staff Emeritus
See solution to Problem 3:

http://web.mit.edu/jlee08/Public/7.91/8.04/sol2.pdf

Zz.