Particle Annihilation: Electron-Positron & Photon Energies

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Homework Help Overview

The discussion revolves around the topic of particle annihilation, specifically focusing on the annihilation of an electron and positron at rest, which results in the production of two photons. Participants are exploring the principles of conservation of momentum and energy in this context.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to understand why the photons produced have equal energies and why two photons are necessary instead of one. Some participants suggest that conservation of momentum is a key factor, while others reference 4-momentum in their reasoning.

Discussion Status

The discussion is active, with participants engaging in clarifying the relationship between momentum and energy in the context of photon emission. There is an acknowledgment of the need for the photons to be emitted in opposite directions to satisfy momentum conservation.

Contextual Notes

The original poster is studying nuclear decays and is seeking a deeper understanding of the principles involved in particle annihilation, particularly in relation to momentum and energy conservation.

pyo
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Hey i am doing some studying and when it comes to the subject of nuclear decays it says that when an electron and positron annihilate at rest they produce two photons with equal energys. Can someone try to explain to me why the photons have equal energies and how come there must be two photons produced instead of one in this case? Is the conservation of momentum the answer here?
 
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Yep, its 4-momentum
 
Yes, since the initial system (electron and positron at rest) had no momentum, the final system must also have no momentum. Clearly this means that the pair of photons must be emitted in opposite directions and with equal magnitude for their momenta. Now, how is the energy of a photon related to its momentum?
 
Great thanks !
 

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