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A pion at rest decays into a muon and a neutrino. Find the energy of the outgoing muon (E) in of the mass of the pion im) and the mass of muen) (m?
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A pion at rest decays into a muon and a neutrino. Find the energy of t...
- **Given data:**
- Mass of pion (mπ) = mπ
- Mass of muon (mμ) = mμ
- **Conservation of energy:**
When the pion decays into a muon and a neutrino, the total energy before the decay is equal to the total energy after the decay.
- Therefore, the energy of the incoming pion (Eπ) is equal to the sum of the energies of the outgoing muon (Eμ) and the neutrino.
- **Energy of the pion:**
Eπ = √(p2 + mπ2)
- **Momentum conservation:**
Since the pion is at rest, its initial momentum is zero. Therefore, the momentum of the muon and neutrino after the decay must cancel out to zero.
- **Energy of the muon:**
Eμ = Eπ - Eν
Eμ = Eπ - √(p2 + mν2)
- **Substitute the values:**
Eμ = √(mπ2) - √(p2 + mν2)
- **Simplify the expression using the masses of muon and neutrino:**
Eμ = mμ - √(p2 + mν2)
- **This is the energy of the outgoing muon after the decay of the pion.**
- Mass of pion (mπ) = mπ
- Mass of muon (mμ) = mμ
- **Conservation of energy:**
When the pion decays into a muon and a neutrino, the total energy before the decay is equal to the total energy after the decay.
- Therefore, the energy of the incoming pion (Eπ) is equal to the sum of the energies of the outgoing muon (Eμ) and the neutrino.
- **Energy of the pion:**
Eπ = √(p2 + mπ2)
- **Momentum conservation:**
Since the pion is at rest, its initial momentum is zero. Therefore, the momentum of the muon and neutrino after the decay must cancel out to zero.
- **Energy of the muon:**
Eμ = Eπ - Eν
Eμ = Eπ - √(p2 + mν2)
- **Substitute the values:**
Eμ = √(mπ2) - √(p2 + mν2)
- **Simplify the expression using the masses of muon and neutrino:**
Eμ = mμ - √(p2 + mν2)
- **This is the energy of the outgoing muon after the decay of the pion.**
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A pion at rest decays into a muon and a neutrino. Find the energy of the outgoing muon (E) in of the mass of the pion im) and the mass of muen) (m?
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A pion at rest decays into a muon and a neutrino. Find the energy of the outgoing muon (E) in of the mass of the pion im) and the mass of muen) (m? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about A pion at rest decays into a muon and a neutrino. Find the energy of the outgoing muon (E) in of the mass of the pion im) and the mass of muen) (m? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A pion at rest decays into a muon and a neutrino. Find the energy of the outgoing muon (E) in of the mass of the pion im) and the mass of muen) (m?.
A pion at rest decays into a muon and a neutrino. Find the energy of the outgoing muon (E) in of the mass of the pion im) and the mass of muen) (m? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about A pion at rest decays into a muon and a neutrino. Find the energy of the outgoing muon (E) in of the mass of the pion im) and the mass of muen) (m? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A pion at rest decays into a muon and a neutrino. Find the energy of the outgoing muon (E) in of the mass of the pion im) and the mass of muen) (m?.
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