Question

The average lifetime of μ-mesons with a speed of 0.95c is measured to be 6 x 10^6 s. Find the average lifetime of μ-mesons in a system in which they are at rest?

Answer 1

19.2*10^6 s

Step-by-step explanation:

The equation for time dilation is:

`t = \frac{t'}{\sqrt{1-(v^2)/(c^2)}}`

Then, if it is observed to have a life of 6*10^6 s, and it travels at 0.95 c:

`t = \frac{6*10^6}{\sqrt{1-((0.95c)^2)/(c^2)}} = 19.2*10^6 s`

It has a lifetime of 19.2*10^6 s when observed from a frame of reference in which the particle is at rest.