How Far Will Muon Beams Travel Before Halving in Intensity?

[Ayame17]

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!

 

[malawi_glenn]

Use half life and time dilation.

 

[Ayame17]

Where does the intensity come into it though?

 

[malawi_glenn]

intensity is number of particles per area, so what is reducing the intensity is the decay of the particles.

 

[Ayame17]

Ah, I see...you work out gamma via $$E=\gamma*mc^{2}$$...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.

 

[malawi_glenn]

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.

 

[Ayame17]

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!

 

[malawi_glenn]

Ok, great. good luck then.