The Cosmic Ray Detector's Muon Mystery · AI Generator #GEN-CEE1BFC9

Physics · modern-physics

Problem

A cosmic ray detector on a mountain peak consists of two parallel scintillation plates separated by a vertical distance of

d = 2.4\;\text{m}

. The detector is designed to measure muons created when cosmic rays interact with the atmosphere at an altitude of

h = 15\;\text{km}

above the detector. Muons have a rest mass

m_\mu = 106\;\text{MeV}/c^2

and a proper lifetime of

\tau_0 = 2.2 \times 10^{-6}\;\text{s}

. A particular muon is created with kinetic energy

K = 1.5\;\text{GeV}

and travels vertically downward. (a) What is the Lorentz factor

\gamma

of this muon? (b) What is the probability that this muon will survive to trigger the top plate of the detector (i.e., travel the full

15\;\text{km}

distance)? (c) Given that the muon triggers the top plate, what is the probability it will also trigger the bottom plate (i.e., survive the additional

2.4\;\text{m}

journey between the plates)? Use

c = 3.0 \times 10^8\;\text{m/s}

and assume the muon travels at constant velocity in a straight line.

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