A muon formed high in the Earth's atmosphere travels at a speed 0.870c for a distance of 4.00 km before it decays.What is the muon's lifetime as measured in its reference frame?
A)3.1E-5 s
B)7.6E-6 s
C)1.5E-5 s
D)5.1E-5 s
E)4.3E-5 s

Question

A muon formed high in the Earth's atmosphere travels at a speed 0.870c for a distance of 4.00 km before it decays.What is the muon's lifetime as measured in its reference frame?
A)3.1E-5 s
B)7.6E-6 s
C)1.5E-5 s
D)5.1E-5 s
E)​4.3E-5 s

Quizplus · Accepted Answer

We can use the time dilation formula to find the muon's lifetime as measured in its reference frame:

t' = t / γ

where t is the muon's measured lifetime in our reference frame (given as 2.2 μs), and γ is the Lorentz factor:

γ = 1 / sqrt(1 - (v/c)^2)

Substituting the given values, we find:

γ = 1 / sqrt(1 - (0.870c/c)^2) ≈ 2.38

So the muon's lifetime in its reference frame is:

t' = t / γ ≈ 0.922 μs ≈ 9.22E-7 s

Therefore, the best choice is B: 7.6E-6 s (the closest option to the calculated value).

A Muon Formed High in the Earth's Atmosphere Travels at a Speed