Negative points with kinetic energy `T=100 MeV` travel an average distance `l=11m` from origin to decay. Find the proper lifetime of these poins.

Negative points with kinetic energy `T=100 MeV` travel an average dist

1.	Negative points with kinetic energy `T=100 MeV` travel an average distance `l=11m` from origin to decay. Find the proper lifetime of these poins.
Answer» Energy of pions 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 `(c betatau_(0))/(sqrt(1-beta^(2)))=ctau_(0)sqrt(eta(2+eta))= 15.0 meters` 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 the other side in the proper frame of the pion).

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Negative points with kinetic energy `T=100 MeV` travel an average distance `l=11m` from origin to decay. Find the proper lifetime of these poins.

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