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Hells_Kitchen

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**1. Problem Statement**What is the wavelength of each of the two photons produced when a particle pair of a positron and electron accelerated at 25GeV collide? Can the net result of this annihilation be only ONE single photon? Why or why Not?

## Homework Equations

Etotal(initial) = Etotal(final)

Ptotal(initial)=Ptotal(final)

Qtotal(initial)=Qtotal(final)

**3. My attempt to the solution has been based on the three conservation laws which I mathematically described above, i only need a confirmation if correct.**

Etotal(initial) = E(e+) + E(e-)= [mc^2 + K+] + [mc^2 + K-] = 50GeV + 2mc^2 =50 GeV + 1.022 MeV =5.0001022 × 10^10 eV

Etotal(final) = hf_1 +h_f_2 = 2hf ==> f=6.0451*10^24 Hz; lambda=c/f =4.959*10^-17 meters

Each photon will have a wavelength of 4.959*10^-17 meters.

One photon cannot result from this particle annihilation because in this case momentum would not be conserved. Since momentum is a vector quantity and after the collision all that remains is energy which is scalar there is no reasonable way that the P_initial vector be conserved. When there are two or more photons the net resultant vector of all momenta from

**each photon**must add to zero. (is this explanation plausiable ... is there any math that can be shown???) What happens if the net P_initial is zero??? In this case the total initial momentum is probably zero since both particles are accelerated with the same energy and in opposite directions their velocity vectors sum adds to zero. Any thoughts???

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