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Muons are unstable subatomic particles that decay to electrons with a mean lifetime of 2.2 μs...

Muons are unstable subatomic particles that decay to electrons with a mean lifetime of 2.2 μs . They are produced when cosmic rays bombard the upper atmosphere about 11.1 km above the earth's surface, and they travel very close to the speed of light. The problem we want to address is why we see any of them at the earth's surface.

A. What is the greatest distance a muon could travel during its 2.2 μs lifetime?

B. According to your answer in the previous part, it would seem that muons could never make it to the ground. But the 2.2-μs lifetime is measured in the frame of the muon, and they are moving very fast. At a speed of 0.999 c, what is the mean lifetime of a muon as measured by an observer at rest on the earth?

C. How far would the muon travel in this time?

D. From the point of view of the muon, it still lives for only 2.2 μs , so how does it make it to the ground? What is the thickness of the 11.1 km of atmosphere through which the muon must travel, as measured by the muon?

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