Question

Muons are particles created about 10 km above Earth's surface when cosmic rays interact with nuclei in atmospheric molecules. If Special Relativity did not exist, these muons which are traveling 99.7% the speed of light, would only go about 0.660 km before decaying (their lifetime is 2.2 microseconds). But Special Relativity does apply in our Universe. How far do the muons travel before decaying (at 99.7% the speed of light and created 10 km above the Earth)? The muon flux at Earth's surface can and has been measured and is a result of relativistic time dilation.

a. 1.50 km

b. 6.00 km

c. 10 km

d. 8.50 km

Answer 1

Saludin ting the formula of time dialation t' rito 1 V where to is half life in rest frame it half life measured at surface velocity c2 Here given v = 99,7% of velocity of light V = 99.7% of c. U 3x108 m/s = 2.99 1 x 108 mis х V= 99.7 100 to = 2.2 MS = 2.2 X10 second -6 -6 2.2810 12.9 1968 2.2X10 V- (0.99702 -6 28.42312 X 10 sec second Ñ 28.4 x 10-6 second t At this half life distance traveled by moon is d = speed x time. 0.9978 3x10 x 28.48 107 6 d = d = 8 ugu.uu ~ 8500 meters. 8.50 km This is option & The distance traveled by muons are 8.50 km