# Maximum speed for absorbing photons?

1. Aug 26, 2013

### Helices

1. The problem statement, all variables and given/known data
A ray of photons coming from a laser with a wavelenght of 589.59nm meets a ray of sodium atoms (A=23) coming from the opposite direction.

What is the maximum speed the sodium atoms can have in order to absorb photons?

3. The attempt at a solution
I thought about viewing this as a kind of photo-electric effect, the work function of sodium being 2.46 eV, but then I realised the problem is about absorbing photons, not about emitting photo-electrons.

The energy of the photons seems relevant: E = hc/λ = 3.369*10^-19 J
As this is less than the work function for sodium, I am pretty convinced I shouldn't be viewing this as a photo-electric effect problem.

I was also thinking the clue might be relativistic energy, viewing the sodium atoms and the photons as two frames of reference. Is there perhaps a kind of maximum (kinetic) energy a sodium atom can have if it wants to absorb a photon?
Am I perhaps supposed to bring into account different energy levels of sodium with different quantum numbers?

2. Aug 26, 2013

### Staff: Mentor

A ray of sodium atoms is not a metal, you don't have the photoelectric effect. You can excite electrons in the atoms, or ionize them.

That is a strange question, as the compton effect and pair production have no upper energy limit.
I guess the question asks for absorption via the D line. Do you know its wavelength? How fast do sodium atoms travel if they see incoming light at that wavelength?

3. Aug 26, 2013

### Helices

Thanks for the reply.

Absorption via the D-line for sodium occurs at 589.0 and 589.6 nm, though these numbers were not given with the problem.
I worked it out, taking 589.3 nm as the average wavelength for absorption.

I used the relativistic Doppler-effect to determine the velocity of the sodium atoms, which would equal 5.64*10^5 m/s.
That seems like quite a decent speed, but I'm still wondering about some things.

Why take absorption via the D-line? Is that the lowest possible wavelenght (and thus highest possible energy) at which absorption can occur? Or did you just suggest it because the D-lines are very characteristic for sodium?

As I understand it, in this approach, we're saying the sodium atoms "see" the approaching fotons at a (slightly) higher wavelength because the sodium atoms are themselves moving fast. The question is thus: "How fast can the sodium atoms move, in order to still observe the photons below a threshold wavelength of 589.3 nm?"
What bothers me is why this D-line absorption should be the threshold at all...

4. Aug 27, 2013

### Staff: Mentor

There is no upper limit. The wavelength given in the problem statement is basically the D-line, so I guessed that you are supposed to use this line.
Higher frequency, shorter wavelength, not "higher wavelength".

Well, above that line there is no allowed transition for a while*, until the energy is sufficient for the next line*.

*not perfectly true, as spectral lines are not single frequencies, and their distribution has an infinite width.

5. Aug 27, 2013

### vela

Staff Emeritus
But would those processes be considered absorption?

6. Aug 28, 2013

### Staff: Mentor

The initial photon is destroyed. If you don't like that: ionization stays possible too, and does not have to produce new particles.

7. Aug 28, 2013

### vela

Staff Emeritus
I would interpret absorption to mean that the end state is just an excited atom. There's no second photon, and the electron stays bound to the atom.