Question

A pion lives 1.50 x 10-16 s as measured in the laboratory, and 0.90 x 10-16 s when at rest relative to an observer.

i) Determine the speed of the pion.
ii) Calculate the kinetic energy in MeV of the particle, given its rest mass energy is 139.6 MeV?

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Answer 1

i)

$$\tau=\frac{\tau_0}{\sqrt{1-\frac{v^2}{c^2}}}\to 1.5=\frac{0.9}{\sqrt{1-\frac{v^2}{(3\cdot10^8)^2}}}$$

$$v=1.92\cdot10^8\frac{m}{s}$$

ii)

$$K=\frac{E_0}{\sqrt{1-\frac{v^2}{c^2}}}-E_0\to \\K=\frac{139.6}{\sqrt{1-\frac{1.92^2}{3^2}}}-139.6=42.1\ MeV$$