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Special relativity and muons

  1. Nov 12, 2009 #1

    bon

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    1. The problem statement, all variables and given/known data

    a burst of muons is produced by a cosmic ray interacting in the upper atmosphere. They travel towards the Earth's surface with an average speed of 0.99c. If 1% survive to reach ground level, estimate the height of the burst.

    muon mean lifetime is 2.2 x 10^-6 s



    3. The attempt at a solution

    well i guess the mean lifetime is given in the muon frame..

    therefore mean lifetime in labf = 2.2 x 10^-6 x 1/lorentz factor

    then i continue, using A = Ao e^-lambda t

    where lambda = ln2/T(1/2)

    where T(1/2) is the half life, i.e. half of the mean lifetime i calculated above..

    then when i found the time, i just used dist = speed x time where speed = 0.99c to calculate the distance..but it didnt come up with the right answer..

    where am i going wrong?

    thanks
     
  2. jcsd
  3. Nov 13, 2009 #2
    I think mean lifetime is [tex] 1/\lambda [/tex]

    You can check by calculating the mean from the probability distribution,

    [tex] \langle t \rangle = \int_0^{\infty} t e^{-\lambda t} dt [/tex]
     
  4. Nov 13, 2009 #3

    bon

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    Great! Thanks
     
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