How do I write a nuclear equation for the annihilation of a positron?

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SUMMARY

The nuclear equation for the annihilation of a positron with an electron results in the production of two photons, each with an energy of 511 keV. This process conserves both energy and momentum, as the photons are emitted in opposite directions. The equation does not simply cancel out the particles; instead, it represents the transformation of mass into energy, adhering to the principles of conservation in nuclear reactions.

PREREQUISITES
  • Understanding of nuclear equations
  • Knowledge of particle physics, specifically positrons and electrons
  • Familiarity with energy-momentum conservation laws
  • Basic principles of photon emission and energy quantization
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  • Study the principles of mass-energy equivalence as described by Einstein's equation E=mc²
  • Learn about photon interactions in particle physics
  • Explore the concept of center of mass in nuclear reactions
  • Investigate the role of conservation laws in particle annihilation processes
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Students and professionals in physics, particularly those focused on particle physics, nuclear reactions, and energy conservation principles.

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How do I write a nuclear equation representing the annihilation of a positron with an electron?

Do they just cancel out? or do I write energy on the left hand side of the equation?
 
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When an electron and a positron annihilate each other, they produce a pair of photons. The photons conserve energy, and by having two of them, they conserve the momentum of the initial particles as well.
 
When you work in the center of mass sytem, you will get a pair of 511 kev photons going off in opposite directions - the direction is otherwise free.
 

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