The Cosmic Ray Detector's Threshold · AI Generator #GEN-D12B1AD3

Physics · modern-physics

Problem

A cosmic ray detector on a mountain station is designed to detect high-energy muons created when cosmic rays collide with atmospheric nuclei. The detector consists of two scintillator panels separated by a distance of

d = 2.4\;\text{m}

. To register as a valid cosmic ray event, a muon must pass through both panels within a time window of

\Delta t = 12\;\text{ns}

. Muons have a rest mass of

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

and a mean proper lifetime of

\tau_0 = 2.20\;\text{μs}

. Due to time dilation, muons moving at relativistic speeds live longer in the laboratory frame, allowing some to survive the journey between detector panels. (a) What is the minimum kinetic energy a muon must have to travel between the detector panels within the required time window? (b) What fraction of muons with this minimum energy will survive the journey between panels (i.e., will not decay during the

12\;\text{ns}

flight time)?

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