Concept explainers
The kinetic energies (in the lab frame) of the neutron and pion after decay.
Answer to Problem 92P
The kinetic energy (in the lab frame) of the neutron after decay is
Explanation of Solution
Write the expression for the relativistic energy of a particle.
Here,
Write the expression for the relativistic energy of a neutron.
Here,
Write the expression for the relativistic energy of a pion.
Here,
Since lambda hyperon is at rest in the lab frame, by conservation of momentum
Equate equation (I) and (II).
Thus, total energy of the system is conserved. Apply conservation of energy for the decay process.
Here,
Rearrange above equation to get
Here,
Rearrange the equation
Substitute
Substitute
Solve above equation to get
Substitute
Conclusion:
Substitute
Substitute
Therefore, the kinetic energy (in the lab frame) of the neutron after decay is
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