Electron/Positron Annihilation

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In summary, The textbook states that when a positron collides with an electron, the energy of each photon is equal to the sum of one particle's rest and kinetic energy. This can be represented by the equation E = m_o*c^2 + K. However, the question arises as to why the energy of each photon is not twice the mass and kinetic energy of each particle, since the ratio is 2:1. The answer is that two photons are created as a result of the collision, with each photon having an energy equal to the sum of the mass and kinetic energy of the colliding particles. This is due to the conservation of momentum and energy.
  • #1
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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  • #2
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?
 
  • #3
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.
 
  • #4
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.
 
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Oh right! Thanks!
 

FAQ: Electron/Positron Annihilation

1. What is electron/positron annihilation?

Electron/positron annihilation is a process in which an electron and a positron collide and annihilate each other, resulting in the production of gamma rays.

2. How does electron/positron annihilation occur?

Electron/positron annihilation occurs when the two particles come into close proximity to each other, causing them to interact and convert their mass into energy. This energy is released in the form of gamma rays.

3. What is the significance of electron/positron annihilation in science?

Electron/positron annihilation plays a significant role in understanding the fundamental properties of matter and energy. It is used in various fields of science, such as particle physics, astrophysics, and medical imaging.

4. Can electron/positron annihilation be observed?

Yes, electron/positron annihilation can be observed through the detection of gamma rays. This process has been observed in particle accelerators and in natural phenomena, such as gamma-ray bursts.

5. How is electron/positron annihilation used in medical imaging?

In medical imaging, electron/positron annihilation is used in a technique called positron emission tomography (PET). A small amount of a radioactive substance is injected into the body, which emits positrons that annihilate with electrons in the body. The resulting gamma rays are detected and used to create images of the body's tissues and organs.

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