Calculation of momentum of relativistic particles

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SUMMARY

The discussion focuses on calculating the momentum of relativistic particles resulting from the decay of a particle of mass M at rest into a massless particle and another particle of mass m. Key equations referenced include E = γmc² and p = γmv, highlighting the relationship between energy and momentum. The user struggles with applying the correct formulas, particularly the relationship E² = m²c⁴ + p²c² for massless particles. The conversation emphasizes the need for a clear understanding of relativistic momentum and energy conservation in particle decay scenarios.

PREREQUISITES
  • Understanding of relativistic mechanics
  • Familiarity with the concepts of energy and momentum in physics
  • Knowledge of the equations E = γmc² and p = γmv
  • Basic grasp of particle decay processes
NEXT STEPS
  • Study the relationship between energy and momentum for massless particles using E² = p²c²
  • Explore conservation of momentum in particle decay scenarios
  • Review relativistic energy-momentum diagrams
  • Practice problems involving decay of particles with varying masses
USEFUL FOR

This discussion is beneficial for physics students, particularly those preparing for entrance exams, as well as educators and anyone interested in understanding relativistic particle dynamics and decay processes.

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Homework Statement


A particle of mass M decays at rest into a massless particle and another particle of mass m. The magnitude of the momentum of each of these relativistic particles is:


Homework Equations



E = γmc2; p=γmv

The Attempt at a Solution


Pf-Pi = 0; but the particle is at rest, so pi = 0; and the momentum of massless particle = 0;
unable to start up with exact condition. Tried equating initial and final energies also, but not getting the right answer. Please help.
 
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physicsblr said:
and the momentum of massless particle = 0

This isn't correct. Look in your notes and/or text for the relationship between energy and momentum for a massless particle.
 
No, I tried the relation E2 = m2c4+p2c2 also, am not getting right answer. There are no explanations of this in my text graduation textbooks. These are pg level questions.

I did substitute E2 = M2c4 (initial energy) and onto r.h.s, p2c2+m2c4+p2c2 - p2c2 is the kinetic energy of the massless particle and m2c4+p2c2 for the particle of mass m.

Please give a solution if possible, am taking so much time to google n check. I am already running out of time for my entrance exam next week.
 

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