The half-life of a muon is 2.2 μs. How fast is it moving relative to an observer who says its half-life is 4.4 μs?
A) 0.87 c
B) 0.75 c
C) 0.97 c
D) 0.72 c
E) 0.50 c

Question

Quizplus · Accepted Answer

The observed half-life of the muon is 4.4 μs, which is twice its rest half-life of 2.2 μs. This indicates time dilation is occurring, which is a relativistic effect described by the theory of special relativity. The formula relating time dilation to velocity is $t' = \frac{t_0}{\sqrt{1 - \frac{v^2}{c^2}}}$, where $t'$ is the dilated time (4.4 μs), $t_0$ is the proper time (2.2 μs), $v$ is the velocity of the object, and $c$ is the speed of light. Solving for $v/c$ gives a value close to 0.87, indicating the muon is moving at 87% the speed of light relative to the observer.

The Half-Life of a Muon Is 2