Energy of resulting Gamma Rays after particle annihilation

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SUMMARY

The discussion centers on calculating the energy of gamma rays produced from the annihilation of an electron and a positron moving at 0.50c. The relevant equation used is (mc² + K+) + (mc² + K-) = E1 + E2, where mc² is 0.511 MeV and K is calculated as 79.1 keV. The final energies of the resulting photons are E1 = 0.885 MeV in the +x direction and E2 = 0.295 MeV in the -x direction. The solution emphasizes the need for conservation of momentum to resolve the two unknowns in the energy equations.

PREREQUISITES
  • Understanding of special relativity concepts, particularly energy-momentum relations.
  • Familiarity with the principles of particle physics, specifically electron-positron annihilation.
  • Knowledge of the equation E = mc² and kinetic energy calculations.
  • Experience with conservation laws in physics, including conservation of momentum.
NEXT STEPS
  • Study the conservation of momentum in particle collisions to understand how to apply it in annihilation scenarios.
  • Learn about photon energy calculations using the equation E = hc/λ.
  • Explore advanced topics in special relativity, focusing on relativistic kinetic energy.
  • Review examples of particle-antiparticle annihilation to solidify understanding of resulting energy distributions.
USEFUL FOR

This discussion is beneficial for physics students, educators, and anyone interested in particle physics and energy calculations related to particle interactions.

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Homework Statement


An electron and a positron are moving side by side in the +x direction at 0.50c when they annihilate each other creating two gamma rays. What is the energy of each photon?


Homework Equations


(mc2 + K+) + (mc2 + K-) = E1 + E2


The Attempt at a Solution



I solved out that K = mc2 = 0.511MeV ( \gamma - 1 ) where \gamma = 1.155. Therefore K should equal 79.1keV. Plug this into the equation up in that "relevant equations" section and I get E1 + E2 = 1.18MeV.

I know the answer is E1 = .885 MeV in the +x direction and E2 = .295 MeV in the -x direction as my prof gave us the answers. These values verify that the calculations I performed earlier are correct.

However, I don't know how to obtain the answers. It seems like it should be stupidly simple, but I just can't figure it out. I tried using hc/\lambda = E to solve for wavelength and then tried plugging stuff in again to get energy but that doesn't work. And even if it did, how would I know direction? If anyone can just give me that slight push in the right direction I'd be very grateful!
 
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You have one equation and two unknowns (E_1, E_2). So you might want to use conservation of momentum to help solve for both unknowns.
 

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