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Find the mean path travelled by pions whose kinetic energy exceeds their rest energy eta= 1.2 time s. The mean lifetime of very slow pions is tau_(0)= 25.5 ns. |
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Answer» Solution :Energy of poins is `(1+ETA)m_(0)c^(2)` so `(1+eta)m_(0)c^(2) = (m_(0)c^(2))/(sqrt(1-beta^(2)))` Hence `(1)/(sqrt(1-beta^(2)))=1+eta or beta =sqrt(eta(2+eta))/(1+eta)` Here `beta=(V)/(c )` of pion. Hence time dilation factor is `1+eta` and the distance traversed by the pion in its lifetime will be `(cbetatau_(0))/(sqrt(1-beta^(2)))=ctao_(0)sqrt(eta(2+eta))=15.0` metres on substituting the values of various quantities (Note The factor `(1)/(sqrt(1-beta^(2)))` can be looked at as a time dilation effect in the laboratory frame or as length contraction factor brought to outside in the PROPER frame of the pion. |
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