# where does the photon go after scattering?

My question is about photo electric but it could be applied to other daily routine phenomenon. As we know rest mass of photon is zero. When a photon strikes the metal surface it transfers its energy to the electrons. Whether electron will be emitted or not, it depends upon work function. But my question is about that photon which was hit on metal surface. Does that photon vanished? Does that photon turned into nothing? where does it go after scattering? When I study this I only find the story about the emitted electrons but not about photons after collision. Am i missing some basic concept?

• Where does the flame go after you blow out a candle? Where does the sound of someone's voice go after it has reached your ears? When something disappears in one location, you have to think carefully about whether or not it's reasonable to infer that it must have gone somewhere else (as opposed to being gone altogether). The intuition that "all things must be somewhere, so if it's not here then it must be somewhere else" is justified by the various physical conservation laws (mass, energy, momentum, charge, etc.) and spatiotemporal continuity. (1/2) Feb 19 '14 at 18:52
• The law of conservation of mass tells us that the amount of mass of a closed system is constant; mass can neither be created nor destroyed. Suppose you weigh a pot of water before and after boiling it for some time. You'll notice that it weighs less afterwards. From the law of conservation of mass, you can infer that since the mass of the missing water couldn't have simply been destroyed, and that the missing mass will be found if we look in the right place (collect and weight the water vapor). (2/3) Feb 19 '14 at 19:27
• Another process where mass is conversed is the electrolysis of water, i.e. the conversion of water into oxygen and hydrogen: $2\text{H}_2\text{O}\rightarrow2\text{H}_2+\text{O}_2$. The mass before and after the reaction is conserved, but the number of molecules is not. It makes no sense to ask "where did the H2O molecules go?" because after the reaction, the H2O molecules aren't anywhere. They're simply gone. In much the same way, photon number isn't conserved either. I apologize for the lengthy comments. Hopefully they'll still be helpful. Feb 19 '14 at 19:53

In particle interactions the total number of particles is not conserved. For example in a collision in the LHC two photons collide and many hundreds of particles are created in the collision.

There are still some conserved quantities, for example lepton number is still conserved so you cannot just create an electron. You need to create an electron and positron together so the total lepton number doesn't change (the electron has number +1 and the positron -1, so they add to zero).

However the number of photons is not conserved. Photons are bosons and they are their own antiparticle so no particle number conservation law is violated when you create a photon. Specifically an accelerating electron can emit any number of photons, and the corollary of this is that an electron can absorb photons and be accelerated. This is what happens in the photoelectric effect. An electron in the metal absorbs the photon and its energy is increased by the photon energy (so energy is conserved). The electron will in turn collide with other electrons in its vicinity, and in a small percentage of cases enough energy is transferred to another electron that it can escape from the surface.

Note that not every photon falling on the metal emits a photon. Far from it in fact as the quantum yield is usually around $10^{-5}$ i.e. only one photon in 100,000 manages to eject an electron. In the other 99,999 cases the energy of the photon just ends up heating the metal.

electrons are only dislodged by the photoelectric effect if light reaches or exceeds a threshold frequency, below which no electrons can be emitted from the metal regardless of the amplitude and temporal length of exposure of light. To make sense of the fact that light can eject electrons even if its intensity is low, Albert Einstein proposed that a beam of light is not a wave propagating through space, but rather a collection of discrete wave packets (photons), each with energy hf. This shed light on Max Planck's previous discovery of the Planck relation (E = hf) linking energy (E) and frequency (f) as arising from quantization of energy. The factor h is known as the Planck constant.1

In this formulation, the electron absorbs the total energy and momentum of the photon.

In non metals electrons are in bound states around the nuclei forming the stable atoms. A photon will interact with an electron and transfer its total energy and momentum if its energy matches a quantum energy difference in higher levels of the atoms potential well, or has enough energy to kick it completely out.

In metals, there exists the Fermi level and the fermi function which characterize the collective but still quantum mechanical behavior of the electrons which create the conductivity of metals. In this case it is easy for a photon to kick an electron out because the energy levels have a very small magnitude.

In both cases the photon disappears. There is no conservation of photons quantum number. It is a boson and many of them can exist in the same energy state and they also may give all their energy up to electronic and other transitions and disappear.

First: momentum is conserved, energy is conserved, electric charge is conserved, and a few other things.

Particles and particle number can, in some instances, flit into and out of existence.

The photon is absorbed by the electron. I.e. the photon ceases to exist, its energy and momentum have to go somewhere (the electron and the bulk material). In the photoelectric effect if the electron cannot absorb the energy of the photon (i.e. it cannot exist at that energy level because of atomic orbitals) then the photon just passes through without absorption. This is the case with glass, visible light does not have enough energy to excite an electron so it just passes through.

Does that photon vanished?

Basically yes, it ceases to exist, but some of its properties must be conserved.

Does that photon turned into nothing?

It's not nothing. It turns into the extra energy in an electron.