Electron/Positron Annihilation

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Homework Help Overview

The discussion revolves around the concept of electron-positron annihilation and the energy produced in the form of photons. Participants are exploring the relationship between the rest mass, kinetic energy of the particles involved, and the resulting energy of the photons emitted during the annihilation process.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are questioning the interpretation of the energy equation related to the annihilation process, particularly the reasoning behind the energy of the resulting photons. There is confusion regarding the ratio of energy and the number of photons produced during the collision.

Discussion Status

The discussion is active, with participants providing insights and clarifications regarding the number of photons produced and the conservation of momentum. Some participants are attempting to reconcile their intuitive understanding with the physical principles involved.

Contextual Notes

There appears to be a misunderstanding regarding the energy distribution and the conservation laws in the context of particle collisions, which is being examined in the discussion.

Von Neumann
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I recently read a textbook that stated without explanation "When a positron collides head on with an electron, the energy of each photon is the sum of one particle's rest and kinetic energy." So E = m_o*c^2 + K. However my question is, why isn't the energy of each photon twice the mass and kinetic energy of each particle since the ratio is 2:1? I know it's the incorrect answer, but that's just what I intuitively think. Any help?
 
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Von Neumann said:
I recently read a textbook that stated without explanation "When a positron collides head on with an electron, the energy of each photon is the sum of one particle's rest and kinetic energy." So E = m_o*c^2 + K. However my question is, why isn't the energy of each photon twice the mass and kinetic energy of each particle since the ratio is 2:1? I know it's the incorrect answer, but that's just what I intuitively think. Any help?

The total energy of the two photons is the same as the sum of the mass and kinetic energy of the colliding electron positron pair. Two photons, two particles. What's this 2:1 ratio of which you speak?
 
The way it's worded, to me it sounds as though one photon is created as the result of the pair colliding. Therefore the total kinetic energy of one photon being twice the energy of one colliding particle.
 
Von Neumann said:
The way it's worded, to me it sounds as though one photon is created as the result of the pair colliding. Therefore the total kinetic energy of one photon being twice the energy of one colliding particle.

One photon could not be created. There is zero momentum total if they collide head on. It couldn't conserve momentum and energy. You need two. I think "each photon" doesn't mean each single photon created by the collision. It means each of the two photons created by the collision.
 
Last edited:
Oh right! Thanks!
 

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