Question

A π⁺ meson at rest decays into a μ⁺ meson and a neutrino in 2.5 × 10⁻⁸ s. Assuming that the π⁺ meson has kinetic energy equal to its rest energy. What distance would the meson travel before decaying as seen by an observer at rest?

Answer 1

(γ − 1)M = M 

Or γ = 2 

β = (γ² − 1)^1/2/γ = (2² − 1)^1/2/2 = √3/2 

The dilated time T = γ T₀ = 2 × 2.5 × 10⁻⁸ = 5 × 10⁻⁸ s 

The distance traveled before decaying is 

d = vT = β cT = √3/2 × 3 × 10⁸ × 5 × 10⁻⁸ = 13m