Maximum speed for absorbing photons?

[Helices]

Homework Statement

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?

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 realized 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?

 

[mfb]

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.

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

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?

 

[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...

 

[mfb]

Why take absorption via the D-line? Is that the lowest possible wavelenght (and thus highest possible energy) at which absorption can occur?

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.

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.

Higher frequency, shorter wavelength, not "higher wavelength".

What bothers me is why this D-line absorption should be the threshold at all...

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.

 

[vela]

That is a strange question, as the compton effect and pair production have no upper energy limit.

But would those processes be considered absorption?

 

[mfb]

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

 

[vela]

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.