Energy and Momenta of a muon? Relativity

In summary, the conversation discusses a pion spontaneously decaying into a muon and a muon antineutrino. Recent evidence suggests that the antineutrino's mass is no larger than 190 keV/c^2, and possibly zero. The energy and momentum for the muon and antineutrino are computed, assuming the decay occurs at rest in the laboratory. The solution involves using the formula E=mc^2 to calculate the energies and E=pc to calculate the momenta. Further discussion and help is requested for the accuracy of the solution.
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Homework Statement



A pion spontaneously decays into a muon and a muon antineutrino. Recent experimental evidence indicates that the mass m of the antineutrino is no larger than about 190 keV/c^2 and may be as small as zero. Assuming that the pion decays at rest in the laboratory, compute the energies and momenta of the muon and muon antineutrino (a) if the mass of the antineutrino were zero and (b) if its mass were 190keV/c^2.





The Attempt at a Solution


The mass of the pions is 139.56755MeV/c^2 and the mass of the muon is 105.65839MeV/c^2.
(a)

For the energy of the muon i simply used E=mc^2=105.65839MeV.
For the energy of the antineutrino i found the difference in mass before and mass after the decay which is m=33.90916MeV/c^2, and similarly applied the formula E=mc^2=33.90916MeV

For momenta of the antineutrino then i used the formula E=pc=> p=33.90916MeV/c.

I am thinking to do a simmilar thing for (b) also, but i have a strong feeling that (a) isn't even close to being correct.

Any help would be appreciated!
 
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Question 1: What is the energy of a muon?

The energy of a muon can be calculated using the equation E = mc^2, where m is the mass of the muon and c is the speed of light. The energy of a muon is also affected by its momentum and can be calculated using the equation E = √(p^2c^2 + m^2c^4), where p is the momentum of the muon.

Question 2: How does the energy of a muon change in relativity?

In relativity, the energy of a muon is affected by its velocity. As the muon's velocity increases, its energy also increases. This is due to the theory of special relativity, which states that the energy of a particle is directly proportional to its velocity.

Question 3: What is the momentum of a muon?

The momentum of a muon can be calculated using the equation p = mv, where m is the mass of the muon and v is its velocity. The momentum of a muon is also affected by its energy and can be calculated using the equation p = √(E^2/c^2 - m^2c^2), where E is the energy of the muon.

Question 4: How does the momentum of a muon change in relativity?

In relativity, the momentum of a muon is affected by its velocity. As the muon's velocity increases, its momentum also increases. This is due to the theory of special relativity, which states that the momentum of a particle is directly proportional to its velocity.

Question 5: How does the energy and momentum of a muon compare to other particles?

The energy and momentum of a muon are affected by its mass, velocity, and relativity, just like any other particle. However, muons are heavier than electrons but lighter than protons and neutrons. They also have a shorter lifespan, with an average decay time of 2.2 microseconds compared to the stability of protons and neutrons. In terms of energy and momentum, muons can have a wide range depending on their velocity and energy levels, making them a unique and versatile particle for scientific studies.

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