A muon has a mean lifetime of only 2.200 µs in its own rest frame.If it moves with a speed of v = 0.9994 c in a certain reference frame,what is its mean lifetime in that frame?

Question

Quizplus · Accepted Answer

The mean lifetime of a muon in a reference frame where it is moving can be calculated using the time dilation formula from special relativity: $ \tau' = \frac{\tau}{\sqrt{1 - v^2/c^2}} $, where $ \tau' $ is the dilated lifetime, $ \tau $ is the proper lifetime (2.200 µs in this case), $ v $ is the velocity of the muon, and $ c $ is the speed of light. Given $ v = 0.9994c $, the calculation yields a dilated lifetime significantly longer than the proper lifetime, which matches option D, 63.5 µs.

A Muon Has a Mean Lifetime of Only 2