[Particle physics] An electron and a positron undergo pair annihilation, producing two gamma ray photons:

e- + e+ → 2γ

If they had approximately zero kinetic energy before the annihilation, what is the wavelength of each γ ?

Question

[Particle physics] An electron and a positron undergo pair annihilation, producing two gamma ray photons: 

e- + e+ → 2γ

If they had approximately zero kinetic energy before the annihilation, what is the wavelength of each γ ?

anonymous · Answer

Mass - Energy Equivalence

anonymous · Answer

Initial rest energy:
$$E_{0} = 2(m_{0})c^2 = 1.022 \frac{ MeV }{ c^2 } = 1.637244 \times10^{-13} J$$
$$E=hf=\frac{ hc }{ \lambda }$$
$$\lambda = \frac{ hc }{ E } = \frac{ (4.136 \times10^{-15})(3\times10^{8}) }{ (1.637244\times10^{-13}) }$$

anonymous · Answer

I thought I was on to something but the answer was ridiculously high. I'm not sure what I've done wrong.

anonymous · Answer

your method is right.. your planks constant is wrong :P

and also that energy is not of one photon, but of two photons together

anonymous · Answer

$$h = 6.63 \times 10^{-34} Js$$

anonymous · Answer

Thanks! I'll have another go.

anonymous · Answer

Awesome, I got the answer out after I divided the energy by 2. Thanks for your help!

anonymous · Answer

no problem :)