Consider the following decay process: π^+ →μ^++v. The mass of the pion (π^+) is 139.6 MeV / c^2,

Name: Problem 63, Chapter 26: College Physics
Uploaded: 2020-05-24T04:13:55-08:00
Duration: 2 min 20 s
Channel: Dading Chen
Description: Consider the following decay process: π^+ →μ^++v. The mass of the pion (π^+) is 139.6 MeV / c^2, the mass of the muon (μ^+) is 105.7 MeV / c^2, and the mass of the neutrino (v) is negligible. If the pion is initially at rest, what is the total kinetic energy of the decay products?

step 1 So from the decay process that was given the final question, we have such equation here, which i

Question

Consider the following decay process: $\pi^{+} \rightarrow \mu^{+}+v$. The mass of the pion $\left(\pi^{+}\right)$ is $139.6 \mathrm{MeV} / c^{2}$, the mass of the muon $\left(\mu^{+}\right)$ is $105.7 \mathrm{MeV} / c^{2}$, and the mass of the neutrino $(v)$ is negligible. If the pion is initially at rest, what is the total kinetic energy of the decay products?

   Consider the following decay process: $\pi^{+} \rightarrow \mu^{+}+v$. The mass of the pion $\left(\pi^{+}\right)$ is $139.6 \mathrm{MeV} / c^{2}$, the mass of the muon $\left(\mu^{+}\right)$ is $105.7 \mathrm{MeV} / c^{2}$, and the mass of the neutrino $(v)$ is negligible. If the pion is initially at rest, what is the total kinetic energy of the decay products?

College Physics

lan Giambattista,… 2nd Edition

Chapter 26, Problem 63

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Solved by Expert Dading Chen

05/24/2020

Step 1

First, we need to find the total energy of the decay products. Since the mass of the neutrino is negligible, the total energy of the decay products is the sum of the energies of the muon and the pion. Show more…

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Consider the following decay process: $\pi^{+} \rightarrow \mu^{+}+v$. The mass of the pion $\left(\pi^{+}\right)$ is $139.6 \mathrm{MeV} / c^{2}$, the mass of the muon $\left(\mu^{+}\right)$ is $105.7 \mathrm{MeV} / c^{2}$, and the mass of the neutrino $(v)$ is negligible. If the pion is initially at rest, what is the total kinetic energy of the decay products?

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Key Concepts

Conservation of Energy

This principle states that in any isolated system, the total energy remains constant. In particle decays, the rest energy of the original particle is redistributed as the sum of the rest energies and kinetic energies of the decay products.

Mass-Energy Equivalence

Expressed by Einstein's equation E=mc², this concept explains that mass can be converted to energy and vice versa. In decay processes, the difference in rest masses between the initial particle and the final state particles is what transforms into kinetic energy.

Relativistic Kinematics in Particle Decay

This concept involves using the principles of special relativity to analyze energy and momentum distributions in decay processes. In a two-body decay from an initial particle at rest, the conservation of energy and momentum determines how the available energy is shared between the decay products.

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