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Change in mass in the decay process

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Consider a decay process: A --> B + C, where the particle masses Ma, Mb, Mc are known. Let us go the rest frame of A particle, so that in this frame it is not moving. What is the energy of A in this frame? If particle B has a momentum p, what is the total energy of the outgoing particles? Can you now use conservation of energy to argue that in order for the decay to be possible Ma (greater or equal to) Mb + Mc.

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Solution Summary

In this solution, a mathematical proof is given for the fact that a particle's total mass is less than initial mass when it decays from one to two particles.

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By momentum law,
pA = pB + pC
but, pA = 0, and pB = p
Therefore,
pC = - p

By energy law,
mA c2 = ( (mB c2)2 + ...

Solution provided by:
Amrit Lal Ahuja, PhD (IP)
Education
  • BEng, Allahabad University, India
  • MSc , Pune University, India
  • PhD (IP), Pune University, India
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