Question
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Q.302. A relativistic particle with rest mass m collides with a stationary particle of mass M and activates a reaction leading to formation of new particles: m + M →m1 +m2 . ..,where the rest masses of newly formed particles are written on the right-hand side. Making use of the invariance of the quantity , demonstrate that the threshold kinetic energy of the particle m required for this reaction is defined by Eq. (6.7c).
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With particle masses standing for the names of the particles, the reaction is
On R.H.S. let the energy momenta be etc. On the left the energy momentum of the particle m is and that of the other particle is 'where, of course, the usual relations
etc
hold. From the conservation of energy momentum we see that
Left hand side is
We evaluate the R.H.S. in the frame where (CM frame of the decay product).
Then R.H.S.
because all energies are . Therefore we have the result
or since , we see that where
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Question Text | Q.302. A relativistic particle with rest mass m collides with a stationary particle of mass M and activates a reaction leading to formation of new particles: m + M →m1 +m2 . ..,where the rest masses of newly formed particles are written on the right-hand side. Making use of the invariance of the quantity , demonstrate that the threshold kinetic energy of the particle m required for this reaction is defined by Eq. (6.7c). |
Topic | Atoms |
Subject | Physics |
Class | Class 12 |
Answer Type | Text solution:1 |
Upvotes | 89 |