What is the average lifetime of a Muon in the laboratory frame?

[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 traveled 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.

 

[SammyS]

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 traveled 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.

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