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

Answer:

19.2*10^6 s

Explanation:

The equation for time dilation is:

$t = \frac{t'}{\sqrt{1-\frac{v^2}{c^2}}}$

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

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

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