The pion is an elementary particle that decays with a meanlifetime in its rest f

Question

The pion is an elementary particle that decays with a meanlifetime in its rest frame of 2.6x10^(-8) seconds. A beam ofpions has a speed of 0.79c. a) In the reference frame of the pion, how far does thelaboratory travel in one mean lifetime? b) What is the distance in the laboratory's frame? The pion is an elementary particle that decays with a meanlifetime in its rest frame of 2.6x10^(-8) seconds. A beam ofpions has a speed of 0.79c. a) In the reference frame of the pion, how far does thelaboratory travel in one mean lifetime? b) What is the distance in the laboratory's frame?

Explanation / Answer

mean lifetime in its rest frame   t = 2.6x10^(-8) seconds
speed of pion v = 0.79c a) mean lifetime in pion's reference frame t ' = t /[ 1-( v / c ) ^ 2 ]                                                                   = ( 2 * 10 ^ -8 ) / [ 1-( 0.79 c / c ) ^ 2 ]                                                                   = 3.262 * 10 ^ -8 s (b). Distance in the laboratory frame S = v * t '                                                            = 0.79 c * 3.262 * 10 ^ -8                                                           = 0.79 * 3 * 10 ^ 8 * 3.262 * 10 ^ -8 m                                                           = 7.731 m

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