The Cosmic Ray Muon Detector · AI Generator #GEN-D4A7E12D

Physics · modern-physics

Problem

A research team is studying cosmic ray muons using a simple detector consisting of two scintillator plates separated by a vertical distance of

h = 15.0\;\text{m}

. When a muon passes through both plates within a time window of

\Delta t = 200\;\text{ns}

, it triggers the detector. Muons are created in the upper atmosphere at an altitude of approximately

15\;\text{km}

and travel vertically downward at

v = 0.98c

. Free muons have a proper lifetime of

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

. The detector is calibrated such that it only registers muons that would have decayed if time dilation effects were not present. What is the minimum kinetic energy in MeV that a muon must have to be detected by this system? The rest mass energy of a muon is

m_\mu c^2 = 105.7\;\text{MeV}

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