The half-life of a muon is 2.20 μs as measured in a stationary reference frame. What is the half life of the muon (in μs) when it is moving with a speed of v = 0.800 c?
A) 8.13
B) 2.75
C) 3.67
D) 15.8
E) 1.32

Question

Quizplus · Accepted Answer

The half-life of a moving muon appears longer due to time dilation, a consequence of special relativity. The time dilation formula is $ t' = \frac{t_0}{\sqrt{1 - \frac{v^2}{c^2}}} $, where $ t' $ is the dilated time (observed half-life in this case), $ t_0 $ is the proper time (stationary half-life), $ v $ is the velocity of the object, and $ c $ is the speed of light. Plugging in the given values: $ t' = \frac{2.20}{\sqrt{1 - 0.800^2}} = 3.67 $ μs.

The Half-Life of a Muon Is 2