contestada

A muon is a type of subatomic particle. If a muon is at rest in the laboratory, it will decay into an electron after about 2 microseconds. Suppose an observer watches a muon travel through the atmosphere at 90% of the speed of light. How does the lifetime of the moving muon compare to the laboratory muon for an observer at rest with respect to the lab

Respuesta :

Answer:

 [tex]\frac{t}{t_p}[/tex] = 2.29

Explanation:

For this exercise as the muon goes at speeds close to the speed of light we must use relativists

          t =[tex]\frac{t_p}{\sqrt{1- (\frac{v}{c})^2 } }[/tex]

The proper time is the decay time in the reference frame where the muon is fixed ( laboratory), t_p = 2 10⁻⁶ s and the relation

            v / c = 0.90

let's calculate

          t = [tex]\frac{2 \ 10^{-6} }{\sqrt{1 \ - \ 0.9^2 } }[/tex]2 10-6 / Ra (1 - 0.9²)

          t = 4.59 10⁻⁶ s

the ralation is

          [tex]\frac{t}{t_p} = \frac{4.59 \ 10^{-6}}{ 2 \ 10^{-6}}\\[/tex]

          [tex]\frac{t}{t_p}[/tex] = 2.29