The Cosmic Ray Decay Chamber · AI Generator #GEN-D237760B

Physics

Problem

A cosmic ray muon detector consists of two parallel detection plates separated by a distance d=2.4  kmd = 2.4\;\text{km} in the laboratory frame. High-energy muons from cosmic ray showers enter the detector moving vertically downward at speed v=0.95cv = 0.95c, where cc is the speed of light. In their rest frame, muons have a mean lifetime of τ0=2.2×10−6  s\tau_0 = 2.2 \times 10^{-6}\;\text{s} before decaying. A particular muon is detected at the top plate at t=0t = 0 in the lab frame. Calculate the probability that this muon will reach the bottom plate before decaying. Assume the muon travels in a straight line and that the decay follows an exponential probability distribution P(t)=e−t/τP(t) = e^{-t/\tau}, where τ\tau is the appropriate lifetime in the relevant reference frame. Give your answer as a decimal probability to three significant figures.

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