Question

Find the proper lifetime of this muon.

Answer 1

Given : $v=0.99c$ $l=3km=3000m$

In the frame K, lifetime of muon $t=\frac{l}{v}$

$\therefore$ Proper life time of muon $\tau =t\sqrt{1-v^2/c^2}$

$\therefore$ $\tau =\frac{3000}{0.99\times 3\times {10}^8}\times \sqrt{1-(0.99{)}^2}=1.42\times {10}^{-6}$ s

$⟹$ Proper lifetime of muon is $1.42\mu s$