How Far Will Muon Beams Travel Before Halving in Intensity?

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Homework Help Overview

The discussion revolves around calculating the distance a beam of muons will travel in empty space before its intensity is halved, given specific kinetic energies. The subject area includes concepts from particle physics and relativistic effects.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the relationship between muon decay and intensity reduction, questioning how intensity is defined in this context. There is discussion about using half-life and time dilation to approach the problem, with some participants suggesting the need to calculate speed from the gamma factor.

Discussion Status

Participants are actively engaging with the problem, offering guidance on relevant concepts such as half-life and time dilation. Some have verified their understanding of the necessary calculations, while others are still seeking clarity on how to apply these concepts effectively.

Contextual Notes

There is a noted constraint regarding the timing of relevant material being taught, which affects the participants' ability to fully engage with the problem. Additionally, the half-life of the muon is mentioned as a given piece of information that aids in the discussion.

Ayame17
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Homework Statement



How far will a beam of muons with kinetic energy (a) 1 MeV, (b) 100 GeV travel in empty space before its intensity is reduced by half?

Homework Equations



See below

The Attempt at a Solution



My main problem with this is that it looks like we won't be taught the relevant material until the day before the work is due in. I could wait, but I'd rather get it sorted beforehand. I'm not asking for the answer, but if someone could give me some kind of relevant equation to get started, I would be very grateful!
 
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Use half life and time dilation.
 
Where does the intensity come into it though?
 
intensity is number of particles per area, so what is reducing the intensity is the decay of the particles.
 
Ah, I see...you work out gamma via [tex]E=\gamma*mc^{2}[/tex]...since you need the speed to calculate the distance, I'm assuming you calculate the speed from the gamma factor...it certainly seems to work okay.
 
Yes, that is correct. Also take into account the time dilation, the higher energy the beam has, the longer life time the particles will have in the frame in which they are traveling in.

The life time of the muon is 2.2 micro seconds, and is the time it gets for a sample of particles to be reduced by the factor of 1/e. So you need to find the "half life" of the muon.
 
Thankfully we'd already been given the half-life, and we figured we'd have to calculate the speed from gamma...thanks for verifying, you've been a great help!
 
Ok, great. good luck then.
 

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