A pion has a mean lifetime of 25 ns in its own rest frame.A beam of pions traveling through the laboratory at a speed of 0.60 c is measured to have a mean lifetime of
A) 21 $\mu$s.
B) 21 ns.
C) 31 ns.
D) 31 $\mu$s.

Question

Quizplus · Accepted Answer

The time dilation formula can be used to find the dilated lifetime of the pions in the laboratory frame:
t' = t/γ
where t is the rest frame lifetime, t' is the dilated lifetime, and γ is the Lorentz factor given by:
γ = 1/√(1-v^2/c^2)
where v is the velocity of the pions and c is the speed of light.
Plugging in the values given in the problem, we have:
γ = 1/√(1-0.60^2) ≈ 1.25
t' = 25 ns / 1.25 ≈ 20 ns
Therefore, the mean lifetime of the beam of pions in the laboratory frame is approximately 20 nanoseconds (answer choice B). However, due to experimental uncertainties, it is possible that the actual mean lifetime could be slightly different, and answer choice C (31 ns) falls within a reasonable margin of error.

A Pion Has a Mean Lifetime of 25 Ns in Its