Question

Find the mean path travelled by pions whose kinetic energy exceeds their rest energy η = 1.2 times. The mean lifetime of very slow pions is τ₀ = 25.5 ns.

Answer 1

Energy of pions is (1 + η) m₀ c² so

Here β = v/c of pion. Hence time dilation factor is 1 + η and the distance traversed by the pion in its lifetime will be

on substituting the values of various quantities. (Note. The factor  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).