# Photon momentum vs hf?

i was learning about laser cooling in thermodynamics, and my professor said that as the photon gets absorbed by the electron, the electron gets excited and re-emits the energy in the form of a photon, and that this process was continuous since it's getting hit by a continuous laser beam and that the emission process emitted the photons in no preferred direction so the average reaction momentum (the kickback momentum from emitting the photon one way) is zero. He said that the atom moved when absorbing the photon since the photon has momentum and it is this momentum that is being absorbed that moves the atom. (we were just talking about what happened for a single atom in a vacuum being hit by a continuous laser beam of the appropriate wavelength)

we have went back and forth various times now via email and i am still completely lost. The photon has energy hf. This gets absorbed by the electron so this particular quantity went into exciting the electron into a higher potential orbital. But now there is a momentum component that gets transferred.

What???

i thought the energy of a photon was hf. and all of this went into exciting the photon. if the acceleration/propelling of the atom came from the photon, the photon MUST have an additional energy component, because it takes energy to do so. I'm trying to avoid using momentum and i'm trying to put everything in terms of energy; it's just easier for me to keep track of everything when all the stuff i'm dealing with are in the same forms (energy) (yes i understand i'm not dealing with just a single energy form, i was just referring to the fact that i don't have a mix of an energy term, amomentum term, a torque term, a moment of inertia term, etc etc etc...). So my professor said that there is a momentum component that gives rise to the acceleration of the atom. I tried converting this 'momentum piece' in terms of energy and i asked him if then, the TRUE energy of a photon is hf+(1/2)pc

and he replied that it was not. I am still at a loss... where is the energy to accelerate the atom coming from? If all of the hf did go into exciting the electron, then there must be another/more energy term/s that i am not aware of. What are they?

thanks

mfb
Mentor
the electron gets excited
A single electron cannot get excited. An atom with electrons can.
and that this process was continuous
Well, it happens frequently.

But now there is a momentum component that gets transferred.
A photon has energy E=hf and momentum p=E/c = hf/c.

and all of this went into exciting the photon.
The atom?
Depending on the velocity of the atom, the photon appears a bit red- or blueshifted for the atom. Therefore, its energy is not exactly the same. Anyway, energy is not the relevant quantity here. You can just consider momentum, this is easier.

where is the energy to accelerate the atom coming from?
The emitted radiation does not have to have the same frequency as your laser beam. This depends on the motion of the atom and the direction of the emitted radiation. Doppler effect...

i mentioned that we were only dealing with a single atom in an ideal vacuum because i wanted an ideal scenario. I guess i left out one piece; I will also mention that i will be ignoring doppler shifting and just considering an initially stationary atom relative to the container. (i'm trying to get an ideal scenario because i want to understand the fundamental mechanism before i start considering six laser beams and the doppler shift.)

i was told that the average momentum from the emitted radiation just cancels out because the electron radiates in all directions equally; if this is true then i am not concerned with the emitted radiation.

I am only concerned with the mechanism of propagation of the atom from the photon. ie the 'momentum' transfer. And i am still confused as to where exactly the energy that went into moving the atom came from if the total energy of the photon is hf. i cannot say that "p=hf/c therefore the momentum transferred is hf/c". otherwise i would be violating energy conservation wouldn't i? i already used "hf" to excite the electron (in the atom....). and as i've said if i have any more energy to something into motion, then the total energy of a photon should be something more than just hf.

Anyway, energy is not the relevant quantity here. You can just consider momentum, this is easier.

if i am considering a stationary atom, and not considering doppler shift, is energy still irrelevant? if so, why? whenever something has momentum it has to have kinetic energy doesn't it?

Dale
Mentor
2020 Award
A photon has both energy and momentum, and so does an atom. When an atom absorbs a photon both the energy and the momentum are conserved together. The atom's final energy equals the total energy of the initial atom and the photon together. The atom's final momentum equals the vector sum of the momenta of the initial atom and photon.

K^2