# Photons and hydrogen atom

lets say i have a hydrogen atom and i shoot a photon at it but the photon does not have enough energy to kick the electron to the next energy level , does the electron absorb the photon and if it does what happens ?

When light hits an atom but does not have sufficient energy for absorption to occur, the electrons oscillate in response to the applied field, and this causes the atom to re-radiate at the same frequency. This is what we call elastic scattering. If it's a beam of light, we will get most of the light continuing in a straight line unaffected, and some small amount of it scattered in other directions. But what if, like cragar said, it is a single photon? The field of the photon can make the charge oscillate, in which case it has to re-radiate, but you can't end up with more photons than you started with.

Is it simply the classical picture completely breaking down? I don't see what actually happens quantum mechanically.

The photon either goes by unaffected or is absorbed and reradiated by the elastic scattering process. This is exactly what happens when a photon hits the window. 4% of the time it scatters back away from the window. No electronic transitions (in glass anyway.)

The photon either goes by unaffected or is absorbed and re-radiated by the elastic scattering process. This is exactly what happens when a photon hits the window. 4% of the time it scatters back away from the window. No electronic transitions (in glass anyway.)
So the photon gets absorbed and re-emitted , but i thought scattering was different
than absorption an re-emission . When the electron absorbs the photon is it possible that the whole atom receives this energy and moves at a certain speed to conserve energy .

The photon either goes by unaffected or is absorbed and reradiated by the elastic scattering process. This is exactly what happens when a photon hits the window. 4% of the time it scatters back away from the window. No electronic transitions (in glass anyway.)

Sure, but is the picture of the electron oscillating in the E-field accurate? Because in that case, an observer in a number of orientations with respect to the electron could see a component of acceleration, therefore there must be a radiated field from the electron to the observer. Doesn't this require multiple photons to be scattered, when only one went in?

Last edited:
lets say i have a laser that is shining down , and then i shoot a beam of neon
atoms horizontally through the laser beam , the laser does not have enough energy to excite the neon atom to the next energy level , when the neon atom absorbs the photon , does the momentum of the photon transfer to the neon atom , I think it would . and will i get a diffraction pattern from the neon atoms , but if the laser has enough energy to kick the neon atom to the next excited state will we see a diffraction pattern ,

Last edited:

Born2bwire
Gold Member
Sure, but is the picture of the electron oscillating in the E-field accurate? Because in that case, an observer in a number of orientations with respect to the electron could see a component of acceleration, therefore there must be a radiated field from the electron to the observer. Doesn't this require multiple photons to be scattered, when only one went in?

That would only be true in a classical picture. For the same reason that the electron's accelerating orbit in the atomic orbital does not emit light, the reaction here would not do so as well. My recollection is as follows. It's easier to consider it as a multi-photon event treated quasi-classically. That is, you can assume that we have an incident electromagnetic wave on our quantum mechanical atom. The electric and magnetic fields will perturb the energy of the atom which causes the atomic orbitals to distort. The atom's electrons do not change their orbitals, but the energy levels can shift and/or the wavefunction will be affected. The proximity of the wave, if we imagine it to be localized in space, will affect the shift of the energy, behaving equivalently as a potential. In other words, the passage of the photon near an atom causes a potential perturbation to the system's Hamiltonian. We can then take that potential as the photon's Hamiltonian, as opposed to the free-space Hamiltonian that it would normally take. With this new Hamiltonian, you can calculate the resulting wavefunction and come up with the appropriate scattering cross-section. Removing the atom from the system here is probably a rough approximation but a good one in the case that it will only be minimally perturbed probably.

lets say i have a laser that is shining down , and then i shoot a beam of neon
atoms horizontally through the laser beam , the laser does not have enough energy to excite the neon atom to the next energy level , when the neon atom absorbs the photon , does the momentum of the photon transfer to the neon atom , I think it would . and will i get a diffraction pattern from the neon atoms , but if the laser has enough energy to kick the neon atom to the next excited state will we see a diffraction pattern ,

Yes, momentum is still transferred, this is how laser cooling works (with the snazzy addition of special relativity). And yes, part of the beam will diffract but only a small amount of energy depending on the number of atoms and so forth. The scattering usually referred to as the scattering cross-section. If the light is absorbed, I would expect you to still get a manner of scattering. Continued application of the beam would help stimulate the atom to emit the photon again, but I believe that the emission is random and so you would see a more uniform scattering pattern. Been a while since I thought about this.

For the same reason that the electron's accelerating orbit in the atomic orbital does not emit light, probably.

So let's see if I follow:

So in an atomic orbital, the electron is in an eigenstate, so there is no actual evolution of the system in time. And in the case of a perturbation, the wavefunctions are perturbed but we again say the electron is in an eigenstate and has no measurable time dependence, thus does not accelerate.

But when you bring large numbers of photons into it, do you come to agreement with the classical picture because, in these cases, it's no longer a simple perturbation and the electron DOES accelerate? Or in the quantum mechanical view, is it that the electron never accelerates at all, but the changing-Hamiltonian-perturbed-wavefunction picture can completely describe the observed radiation for any number of incident photons?

Born2bwire
Gold Member
So let's see if I follow:

So in an atomic orbital, the electron is in an eigenstate, so there is no actual evolution of the system in time. And in the case of a perturbation, the wavefunctions are perturbed but we again say the electron is in an eigenstate and has no measurable time dependence, thus does not accelerate.

But when you bring large numbers of photons into it, do you come to agreement with the classical picture because, in these cases, it's no longer a simple perturbation and the electron DOES accelerate? Or in the quantum mechanical view, is it that the electron never accelerates at all, but the changing-Hamiltonian-perturbed-wavefunction picture can completely describe the observed radiation for any number of incident photons?

In the classical sense, the electron is always accelerating in the atomic orbital. The wavefunction localizes the position of the electron about the atom. If you consider it classically this requires the electron to accelerate for it to remain moving within a bounded volume. The perturbation is time-dependent, however, such scattering problems are often simplified as static potentials in the free particle path. The behavior of these potentials results in different scattering behavior. This is easier to understand in the context of charged particles, like the electron. With other charged particles the scattering potential is coulombic. However with an atom, it will be similar to a coulombic potential because of the charge screening of th nucleus, perhaps a Yukawa potential, I can't remember. A lot of the resultant physics ends up being the same though because certain limiting cases give rise to similar behavior (i.e: hard or soft scattering).

With large numbers of photons, we can use more classical explanations. We can treat the perturbation of the electron cloud as an oscillating dipole moment (We can do this quantum mechanically for the atom as well in a quasi-quantum model. Indeed this is a rough treatment given in Griffiths for analyzing stimulated emission.). The problem though is that doing so can only give elastic scattering like Rayleigh or Mie. Raman scattering, for example, which incorporates absorption and emission, would not be correctly modeled in such a manner because there are frequency shifts.