A particle physicist observes cosmic rays creating a new particle high in the atmosphere,and the speed of this particle is measured at 99.7% the speed of light.It is unstable,and is observed to decay in an average 37.0 μs.If this particle were at rest in the laboratory,what would be its average lifetime?
A)2.9 µs
B)18 µs
C)5.3 µs
D)12 µs
E)4.3 µs

Question

Quizplus · Accepted Answer

The observed lifetime of 37.0 μs is the dilated lifetime due to the particle's high speed. To find the rest lifetime, we use time dilation: $ t_0 = t / \gamma $, where $ \gamma = 1/\sqrt{1-v^2/c^2} $. For v = 0.997c, $ \gamma \approx 12.4 $. Thus, $ t_0 = 37.0 \, \mu s / 12.4 \approx 2.9 \, \mu s $.

A Particle Physicist Observes Cosmic Rays Creating a New Particle