Under certain circumstances, a photon moving through a material can interact with the
nucleus of an atom of the material to produce an electron and a positron.

Photons whose wavelength exceeds a certain value will not cause this process.

Why is this??

Because everything is energy and everything interacts with everything.

When you move your arm you are interacting with the sun.

Evern when you think you are using neurons which are creating and moving electrical pulses and so you are interacting with a very distant galaxy or say the whole universe.

How would one calculate the maximum wavelength possible for an electron-positron pair production?

i think momentum comes into play, too, here but its explainable without referring to it

since e=mc^2 tells you the energy of mass at rest, assuming the formed electron and positron are at rest, there is a minimum amount of energy needed for the photon to produce mass equivalent to a positron and an electron.

you get the energy of a photon from e=hf, where f=c/λ --> e=hc/λ
h = planck constant
f = frequency
c = speed of light
λ = wavelength

the energy is inversely propotional to wavelength, therefore for a given minimum of energy, there is a maximum of wavelength, since h and c are constants.

however like i said in the beginning, there is also momentum involved so the particles MUST have kinetic energy, too. You get the momentum of light from λ=h/p, and this would be the combined momenta of the produced particles. Of course, these are unrelativistic formulae so you would most probably need to include the Lorentz factor in calculations and calculate total relativistic energy instead of only resting energy (mass).

This post was edited by Ocen on Aug 24 2012 09:46am

Thanks, this has helped me a lot.

Just another question I was curious about, what is the relation charge and energy have? For example can energy be used to give an electron charge, or does the electron acquire it some other way?

no, charge is a quantity that's conserved just as energy, and momentum, etc.

it's actually the reason you get a positron-electron pair, because the +1 charge on the positron cancels the -1 charge on the electron, so you will have a net charge of 0, as was the original case (photon).

oh and as to why is there charge... well i cant say any more than (according to my knowledge) its one of the fundamental properties of particles. I think it's just a given just like the fact this world has gravity is a given. However keep in mind that electromagnetic force (related to charge), weak force and strong force are all the same (more fundamental) force that manifests differently due to low energies, so even charge might not be the most fundamental property. See Grand Unified Theory from google or wikipedia for more, it might give some insight.

This post was edited by Ocen on Aug 24 2012 11:27am

The reason I asked about energy being converted into charge is because I'm reading a mark scheme for a test paper question and in the question, it is stated that the energy required for pair production is 1.02MeV. It then says: Photons whose wavelength exceeds a certain value will not cause this process. Calculate the maximum wavelength for the process to occur stating your answer to an appropriate number of significant figures.

So anyway, in the marking scheme it shows these calculations:

E = (1.02 × 1.6 × 10–^-13) = 1.63 × 10^-–13 ---- I figured that 1.6 x 10^-13 was 1.6 x 10^-19 before they multiplied it with the 1.02MeV in standard form, right? And 1.6 x 10^-19 is the charge of an electron, so this would say that the initial energy of the photon = (amount of energy to create e- and e+) x (charge of electron)?

1.63 × 10^-1–3 = 6.63 × 10^-–34 × 3.00 × 10^8/λ

λ = 6.63 × 10^-–34 × 3.00 × 10^8/1.63 × 10^-–13 = 1.22 × 10^-–12

I really hope you can clear this up for me, I've just been zonking at my screen for the past hour trying to work my way around this looool

An electron-Volt (eV) is a unit of energy, not of charge. It's the amount of energy an electron would gain from moving through a region of space with an end-to-end potential difference (voltage) of 1 Volt. The charge of an electron/proton isn't important in this problem.

So, what you have is 1,020,000 eV of energy required for this reaction to take place. So if a photon hits the nucleus with too low of an energy, it won't take place. Low energy electrons have longer wavelengths, which is why there is a maximum wavelength where this reaction can take place.

E = h*f --> Planck's constant multiplied by the frequency.

The speed of a wave is equal to the frequency multiplied by its wavelength, i.e. v = f * lambda, and since photons travel at the speed of light, c = f*lambda. Solve for f and you get f = c / lambda. Plug this into the above equation and you get

E = h * c / lambda.

Solve for lambda and you will find that the maximum wavelength is

lambda = h * c / E