The positive muon an unstable particle lives on average 220

The positive muon , an unstable particle, lives on average 2.20x10^6s (measured in its own frame of reference) before decaying. Part A) If such a particle is moving, with respect to the laboratory, with a speed of 0.900c , what average lifetime is measured in the laboratory? Part B) What average distance, measured in the laboratory, does the particle move before decaying?

Solution

the average life time of decay measure in lab frame be t , to be the time in its own frame of reference

                                    t = to / sqrt (1-v^2 /c^2)

                                         = 2.20x10^-6s (1-0.9^2)

                                          =5.047 * 10^-6 sec

let the average distance covered by the particle before decaying be S

                                          and     S = v * t

                                                         = 0.9 *3*10^ 8 m/sec * 5.047 * 10^-6 sec

                                                          = 1362.729 m