A neutral pion has a rest energy of 135 MeV and a mean life of . It is produced with an initial kinetic energy of 80 MeV and it decays after one mean lifetime. We have to find the longest possible track that this particle could leave in a bubble chamber.

Solution:             Click For PDF Version

The kinetic energy K, the rest mass energy and the Lorentz factor are related as

Therefore, the Lorentz factor of the pion of rest mass energy 135 MeV and kinetic energy of 80 MeV will be

The speed of the pion will therefore be

The mean lifetime of neutral pion measured in its rest frame is . Therefore, the lifetime measured in the laboratory frame with speed v will be given by the relativistic formula

Therefore, the longest possible track that this particle can leave in a bubble chamber will be