# Average lifetime of a Muon

1. May 15, 2013

### lmstaples

Consider a beam of positive Muons, of energy 0.3GeV in the laboratory.

(i) What is the apparent mean lifetime of the Muon as measured in the laboratory frame?

(ii) What is the mean distanced travelled by the Muon in the laboratory?

I first tried using the E = pc and working out speed of muon and then using relativity to work out time dilated lifetime but kept getting v > c.

So then I tried using uncertainty principle ΔEΔt ~ h
But gave a very small time.

This is a past exam question, not homework.

Cheers.

2. May 15, 2013

### SammyS

Staff Emeritus
Try using this for the kinetic energy $\displaystyle E_\text{k} = m \gamma c^2 - m c^2 = \frac{m c^2}{\sqrt{1 - v^2/c^2}} - m c^2 \ .$