Determine the Energy of Electromagnetic Radiation After Particle Collision

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SUMMARY

The energy of electromagnetic radiation produced from the collision of an electron and a positron, each with a rest mass of 9.11 x 10-31 kg and moving at 0.20c, is calculated to be 1.67 x 10-13 J. This value is derived using the total energy equation for particles, resulting in a combined energy of 1.67 x 10-13 J for both particles. The discussion highlights a common error in calculations, specifically the importance of squaring the speed of light (c) in the energy equation. The textbook's value of 0.615 MeV (9.84 x 10-14 J) is questioned, indicating potential inaccuracies in the textbook.

PREREQUISITES
  • Understanding of relativistic energy equations, specifically E=mc2
  • Knowledge of particle physics, particularly electron and positron properties
  • Familiarity with the concept of relativistic speeds (e.g., 0.20c)
  • Basic proficiency in unit conversions between joules and electronvolts (eV)
NEXT STEPS
  • Study the derivation and applications of the relativistic energy equation E=mc2
  • Learn about particle-antiparticle annihilation and its implications in physics
  • Explore the conversion of energy units from joules to electronvolts (eV) and MeV
  • Investigate common calculation errors in relativistic physics and how to avoid them
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Students and educators in physics, particularly those focusing on particle physics and energy calculations, as well as anyone involved in experimental physics and energy conversion processes.

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Homework Statement


The positron and the electron each have a rest mass of 9.11 x 10-31 kg. In a certain experiment, an electron and a positron collide and vanish, leaving only electromagnetic radiation after the interaction. Each particle is moving at a speed of 0.20c relative to the laboratory before the collision. Determine the energy of the electromagnetic radiation.

Homework Equations


Total energy of a particle:

sqrt-1-v2-c2-mc2-over-e.png


The Attempt at a Solution



Using the equation:

(9.11 x 10-31)c2 / sqrt[1 - (0.2c)2/c2]
= 8.37 x 10-14 J
This is the total energy of one electron or positron. Since two particles are colliding, the total energy of the system is 8.37x10-14 x 2 = 1.67 x 10-13 J
When the particles vanish, all the energy is converted to electromagnetic radiation, so the energy of the electromagnetic radiation is 1.67 x 10-13 J
However, the answer in my textbook says 0.615 MeV, which is 9.84 x 10-14 J. My textbook is known to have mistakes, so I am checking if this is my mistake or the textbook's mistake.
 
Last edited:
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Ok, a quick check. The energy must be E>mc^2. Mass is m = 2*9.1e-31kg, c = 3e8m/s, so E > 1.6e-13J
So it's possible both you and your book is wrong...
 


Sorry, I made a calculation error. I forgot to square c.
I edited my previous post. Now my answer is 1.67 x 10-13 J
 

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