Cosmic Ray Muon Underground Detection · AI Generator #GEN-9EE62230
Physics · modern-physics
Problem
High-energy cosmic rays striking Earth's upper atmosphere create muons that travel toward the surface at approximately 0.98c. A physics research team sets up muon detectors at two locations: one at sea level and another in an underground laboratory at depth d=2.1km below the surface. The muons have a proper lifetime of τ0=2.2×10−6s and are created at an altitude of h=15km above sea level.
The research team observes that the underground detector registers muons, even though classical physics would predict that all muons should have decayed before reaching that depth. Calculate the fraction of muons that reach the underground detector compared to those detected at sea level, accounting for relativistic time dilation.