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Unstable pions are produced as a beam in a nuclear reaction experiment . The pions leave the target at a speed of 0.995c. The intensity of the beam reduces to half its original value as the beamtravelsa distance of 39 m . Find the half - life of pions (a) in the laboratory frame, (b) in their rest frame. |
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Answer» Solution :(a) The INTENSITY of the pion beam reduces to half its original value in one half - life. The half - life of the pions as measured in the laboratory is ` t_(1/2) = 39 m / 0995c = 39 m / 0.995 xx 3 xx 10 ^(8) m s^(-1)` `= 1.3 xx 10^(-7).`(B) The events -a pion leaving the target and its DECAYING - OCCUR at the same place in the pion - frame . thus, the time measured in the pion - frame is the proper time and is the smallest. It is equal to ` t'_(1/2) = t_(1/2) (sqrt 1 - v^(2) / C^(2)) = (1.3 xx 10^(-7) s ) (sqrt 1- (0.995)^(2)` `= 1.3 xx 10^(-8) s.` |
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