Cosmic Ray Muon Detection · AI Generator #GEN-F45DB9B5

Physics · modern-physics

Problem

A cosmic ray muon detector on a mountaintop records muons with kinetic energy

K = 1.5 \times 10^{11}\;\text{eV}

. These muons are produced when cosmic rays collide with atmospheric particles at an altitude of

15\;\text{km}

above the detector. The muon rest mass is

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

. Due to relativistic time dilation, these high-energy muons can reach the detector before decaying, even though their proper lifetime is only

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

. (a) Calculate the Lorentz factor

\gamma

for these muons. (b) What is the dilated lifetime of the muons as measured in the Earth's reference frame? (c) How far would these muons travel at their relativistic speed before decaying (on average) in the Earth frame?

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