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A K meson (with a rest mass of 494 MeV) at rest decays into a muon (with a rest mass of 106 MeV) and a neutrino. Then energy of the neutrino, which can be taken to be massless. (In MeV).
Correct answer is '236'. Can you explain this answer?
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A K meson (with a rest mass of 494 MeV) at rest decays into a muon (wi...
Ev = 236 MeV
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A K meson (with a rest mass of 494 MeV) at rest decays into a muon (wi...
Given:
- Rest mass of K meson (mK) = 494 MeV
- Rest mass of muon (mμ) = 106 MeV
- Neutrino is considered massless
To Find:
- Energy of the neutrino produced in the decay of the K meson
Explanation:
The decay process is described as follows:
K0 → μ+ + ν
Step 1: Calculate the total energy before the decay
The total energy before the decay is equal to the rest mass energy of the K meson.
Total energy before decay (Ei) = mKc2
Given:
mK = 494 MeV
c2 = (3 × 108)2 m2/s2 = 9 × 1016 m2/s2
Ei = mKc2
Ei = 494 MeV × 9 × 1016 m2/s2
Step 2: Calculate the total energy after the decay
The total energy after the decay is equal to the sum of the rest mass energy of the muon and the energy of the neutrino.
Total energy after decay (Ef) = (mμc2) + (Eν)
Given:
mμ = 106 MeV
Ef = (mμc2) + (Eν)
Ef = (106 MeV × 9 × 1016 m2/s2) + (Eν)
Step 3: Conservation of energy
According to the law of conservation of energy, the total energy before the decay must be equal to the total energy after the decay.
Ei = Ef
Therefore, we can equate the two expressions for the total energy to solve for the energy of the neutrino.
mKc2 = (106 MeV × 9 × 1016 m2/s2) + (Eν)
Solving for Eν:
Eν = mKc2 - (106 MeV × 9 × 1016 m
- Rest mass of K meson (mK) = 494 MeV
- Rest mass of muon (mμ) = 106 MeV
- Neutrino is considered massless
To Find:
- Energy of the neutrino produced in the decay of the K meson
Explanation:
The decay process is described as follows:
K0 → μ+ + ν
Step 1: Calculate the total energy before the decay
The total energy before the decay is equal to the rest mass energy of the K meson.
Total energy before decay (Ei) = mKc2
Given:
mK = 494 MeV
c2 = (3 × 108)2 m2/s2 = 9 × 1016 m2/s2
Ei = mKc2
Ei = 494 MeV × 9 × 1016 m2/s2
Step 2: Calculate the total energy after the decay
The total energy after the decay is equal to the sum of the rest mass energy of the muon and the energy of the neutrino.
Total energy after decay (Ef) = (mμc2) + (Eν)
Given:
mμ = 106 MeV
Ef = (mμc2) + (Eν)
Ef = (106 MeV × 9 × 1016 m2/s2) + (Eν)
Step 3: Conservation of energy
According to the law of conservation of energy, the total energy before the decay must be equal to the total energy after the decay.
Ei = Ef
Therefore, we can equate the two expressions for the total energy to solve for the energy of the neutrino.
mKc2 = (106 MeV × 9 × 1016 m2/s2) + (Eν)
Solving for Eν:
Eν = mKc2 - (106 MeV × 9 × 1016 m
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A K meson (with a rest mass of 494 MeV) at rest decays into a muon (with a rest mass of 106 MeV) and a neutrino. Then energy of the neutrino, which can be taken to be massless. (In MeV).Correct answer is '236'. Can you explain this answer?
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Solutions for A K meson (with a rest mass of 494 MeV) at rest decays into a muon (with a rest mass of 106 MeV) and a neutrino. Then energy of the neutrino, which can be taken to be massless. (In MeV).Correct answer is '236'. Can you explain this answer? in English & in Hindi are available as part of our courses for Physics.
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