Energy conservation in heating by irradiation

[FredMadison]

Hi all!

I've been thinking of something lately.

When an atom absorbs an incoming photon, the atom must gain some momentum in order to conserve linear momentum, right? Sort of like a totally inelastic collision? This momentum corresponds to some amount of kinetic energy and thus a raise in temperature of the gas, liquid or bulk of which the atom is a part.

This is how I've understood heating by irradiation, please correct me if I'm wrong.

Now the atom, having absorbed a photon, is in an excited electronic state. By means of spontaneous emission it will again return to its ground state by emitting a photon. But what about the energy that is dissipated throughout the material? In a gas, for example, suppose the atom transfers some of its kinetic energy to another atom before emitting a photon and returning to its ground state, there seems to me to have somehow entered extra energy?
Like this:

photon energy in (E) = photon energy out (E) + heating of gas (Q)

Since the photon energies are the same, where does Q come from?
Surely I'm missing something in my very primitive analysis, but where do I go wrong?

 

[Mapes]

The photon is not re-emitted at the same energy level; some energy is transferred to the surrounding atoms first.

 

[FredMadison]

Transferred how? By collision or by radiation?

 

[Mapes]

By collision.

 

[FredMadison]

So, in the collision, there is an electronic transition to a lower state without photon emission?

 

[Mapes]

Yes, I believe this is modeled as a phonon emission into the surrounding material. But I'm not sure if translational or rotational energy modes come into the picture also. Perhaps the QM experts could enlighten us.

 

[Cthugha]

When an atom absorbs an incoming photon, the atom must gain some momentum in order to conserve linear momentum, right? Sort of like a totally inelastic collision? This momentum corresponds to some amount of kinetic energy and thus a raise in temperature of the gas, liquid or bulk of which the atom is a part.

This is how I've understood heating by irradiation, please correct me if I'm wrong.

Now the atom, having absorbed a photon, is in an excited electronic state. By means of spontaneous emission it will again return to its ground state by emitting a photon. But what about the energy that is dissipated throughout the material? In a gas, for example, suppose the atom transfers some of its kinetic energy to another atom before emitting a photon and returning to its ground state, there seems to me to have somehow entered extra energy?
Like this:

photon energy in (E) = photon energy out (E) + heating of gas (Q)

Since the photon energies are the same, where does Q come from?
Surely I'm missing something in my very primitive analysis, but where do I go wrong?

Mapes already told you the answers, but I would like to stress, that you are mixing two different cases here. There is the case of the excitation and emission of a single atom and the excitation and emission of a whole system of emitters.

The single atom has discrete energies and can only absorb or emit photons at one of these energies. As we do only consider a single atom, there won't be any energy transfer to other atoms.

On the other hand, there are whole systems of emitters, for example bulk material like metals or semiconductors. Here you have allowed energy bands for the electron energy and therefore also a wider range of allowed transitions. So it is possible, that an electron, which was excited to the conduction band, interacts with the system, for example by emission of phonons, which changes the momentum and energy of the electron, and afterwards still undergoes an transition back to the valence band at an energy, which is lower than the excitation energy was. Note that in this case the electron is not considered as belonging to one special single atom anymore.