# Special relativity and muons

1. Nov 12, 2009

### bon

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. Nov 13, 2009

### clamtrox

I think mean lifetime is $$1/\lambda$$

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

$$\langle t \rangle = \int_0^{\infty} t e^{-\lambda t} dt$$

3. Nov 13, 2009

### bon

Great! Thanks