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An unstable particle of rest energy 1000 MeV decays into a μ-meson and a neutrino, with a mean life time of 10-8 sec, when at rest. The mean decay distance in meters, when the particle has a momentum of 1000 MeV/C is ____.
Correct answer is '2.12'. Can you explain this answer?
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An unstable particle of rest energy 1000 MeV decays into a μ-meson ...
We know that relativistic energy and momentum is related as
E2 = (PC)2 + (m0C2)2
Here we have
P = 1000 MeV/C
PC = 1000 MeV
m0C2 = (1000) MeV
Energy
But by Einstein mass-energy relation
Total distance = time x velocity =
E2 = (PC)2 + (m0C2)2
Here we have
P = 1000 MeV/C
PC = 1000 MeV
m0C2 = (1000) MeV
Energy
But by Einstein mass-energy relation
Total distance = time x velocity =
Most Upvoted Answer
An unstable particle of rest energy 1000 MeV decays into a μ-meson ...
Stable particle of rest energy 400 MeV and a photon. What is the energy of the photon?
To solve this problem, we can use the conservation of energy and momentum. The total energy before the decay must be equal to the total energy after the decay. Since the initial particle is at rest, its momentum is zero.
Let's denote the energy of the photon as E_photon. The energy of the stable particle can be calculated by subtracting the rest energy of the unstable particle (1000 MeV) from the total energy before the decay:
E_stable = Total energy before decay - Rest energy of unstable particle
= E_total - 1000 MeV
Since the initial particle is at rest, the total energy before the decay is equal to its rest energy:
E_total = Rest energy of unstable particle
= 1000 MeV
Substituting this into the equation for E_stable:
E_stable = 1000 MeV - 1000 MeV
= 0 MeV
Now, using the conservation of energy, we can write the equation:
E_total = E_stable + E_photon
Since E_total is 1000 MeV and E_stable is 0 MeV, we can solve for E_photon:
1000 MeV = 0 MeV + E_photon
E_photon = 1000 MeV
Therefore, the energy of the photon is 1000 MeV.
To solve this problem, we can use the conservation of energy and momentum. The total energy before the decay must be equal to the total energy after the decay. Since the initial particle is at rest, its momentum is zero.
Let's denote the energy of the photon as E_photon. The energy of the stable particle can be calculated by subtracting the rest energy of the unstable particle (1000 MeV) from the total energy before the decay:
E_stable = Total energy before decay - Rest energy of unstable particle
= E_total - 1000 MeV
Since the initial particle is at rest, the total energy before the decay is equal to its rest energy:
E_total = Rest energy of unstable particle
= 1000 MeV
Substituting this into the equation for E_stable:
E_stable = 1000 MeV - 1000 MeV
= 0 MeV
Now, using the conservation of energy, we can write the equation:
E_total = E_stable + E_photon
Since E_total is 1000 MeV and E_stable is 0 MeV, we can solve for E_photon:
1000 MeV = 0 MeV + E_photon
E_photon = 1000 MeV
Therefore, the energy of the photon is 1000 MeV.
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Community Answer
An unstable particle of rest energy 1000 MeV decays into a μ-meson ...
We know that relativistic energy and momentum is related as
E2 = (PC)2 + (m0C2)2
Here we have
P = 1000 MeV/C
PC = 1000 MeV
m0C2 = (1000) MeV
Energy
But by Einstein mass-energy relation
Total distance = time x velocity =
E2 = (PC)2 + (m0C2)2
Here we have
P = 1000 MeV/C
PC = 1000 MeV
m0C2 = (1000) MeV
Energy
But by Einstein mass-energy relation
Total distance = time x velocity =
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An unstable particle of rest energy 1000 MeV decays into a μ-meson and a neutrino, with a mean life time of 10-8 sec, when at rest. The mean decay distance in meters, when the particle has a momentum of 1000 MeV/C is ____.Correct answer is '2.12'. Can you explain this answer?
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