5. Considering Muon Lifetimes. Muons are subatomic particles that have a mean lifetime 2μs (2 microseconds). They are pr

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5. Considering Muon Lifetimes. Muons are subatomic particles that have a mean lifetime 2μs (2 microseconds). They are produced in the upper atmosphere as cosmic-ray secondaries, about 10 km above the earth's surface (you'll learn more about how this happens when you get into particle physics). a. First, model a muon with classical physics (i.e., no special relativity). Calculate the mean distance traveled by a muon traveling at v=0.999c. b. Again using classical physics, what fraction of muons would be able to travel 10km? For a group of particles undergoing exponential decay we can express their quantity as a function of time, N(t) = N₁e7, where t is the mean lifetime and No is the quantity at time t=0. c. Now, taking into account special relativity, what is the mean lifetime of a muon moving at 0.999c, as measured by an observer on earth? d. Now repeat your calculation from part A, using the time you found in Part C. e. For the muons described in this problem, would you expect to detect muons on the surface of the earth? Explain your reasoning.