In the laboratory frame a particle with the speed v 099c tr

In the laboratory frame a particle with the speed v = 0.99c travels a distance of 1 mm before spontaneously decaying. What is the proper lifetime of the particle?

Solution

since the particle moves with near light speed so there is a time dilation

T = T0( 1 + v²/2c²)

where T0 is the original time v = velocity

T0 = 1x 10^-3/ 0.99 c = 0.3367 x  10^-11 s

T = 0.3367 x  10^-11 s( 1 + 0.99²/2) = 0.5 x 10^-11 s