Cosmic ray muons are created in Earth's upper atmosphere at an altitude of approximately 15km. These muons have a proper lifetime of τ0=2.2×10−6s and travel toward Earth's surface at 98% the speed of light.
A physicist sets up a detector array with two stations: Station A at altitude 12km and Station B at sea level. She observes that 1000 muons pass through Station A in a given time interval.
(a) How many muons would reach Station B if there were no time dilation effects?
(b) How many muons actually reach Station B when relativistic effects are properly accounted for?
(c) The energy of each muon is measured to be E=1.5GeV. Using this information and the known muon rest mass mμc2=106MeV, calculate the expected number of muons reaching Station B and compare with your answer from part (b).
Use c=3.0×108m/s and assume the muon flux remains constant during the measurement period.