1. Muons are unstable subatomic particles with an average lifetime of 2.2 us that decay into electrons and two types of neutrinos. They are produced when cosmic ray protons hit atomic nuclei in the Earth's atmosphere 10. km above sea level. a. At 0.999 c, what is the greatest distance (rest frame) a muon could travel in its average lifetime? b. Thus, the problem: muons could never reach the ground! However, the 2.2 µs average lifetime is from the muon's point of view. To an observer on the ground, what is the average lifetime of a muon? How far could a muon travel in this time? Will the muon reach the ground, from the point of view of an observer on the ground? c. To the muon, how far is the 10. km distance to the ground? In its average lifetime and its speed of 0.999 c, will it be able to make it to the ground?

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1. Muons are unstable subatomic particles with an average lifetime of 2.2 us that decay into
electrons and two types of neutrinos. They are produced when cosmic ray protons hit atomic
nuclei in the Earth's atmosphere 10. km above sea level.
a. At 0.999 c, what is the greatest distance (rest frame) a muon could travel in its average
lifetime?
b. Thus, the problem: muons could never reach the ground! However, the 2.2 µs average lifetime
is from the muon's point of view. To an observer on the ground, what is the average lifetime of
a muon? How far could a muon travel in this time? Will the muon reach the ground, from the
point of view of an observer on the ground?
c. To the muon, how far is the 10. km distance to the ground? In its average lifetime and its
speed of 0.999 c, will it be able to make it to the ground?
Transcribed Image Text:1. Muons are unstable subatomic particles with an average lifetime of 2.2 us that decay into electrons and two types of neutrinos. They are produced when cosmic ray protons hit atomic nuclei in the Earth's atmosphere 10. km above sea level. a. At 0.999 c, what is the greatest distance (rest frame) a muon could travel in its average lifetime? b. Thus, the problem: muons could never reach the ground! However, the 2.2 µs average lifetime is from the muon's point of view. To an observer on the ground, what is the average lifetime of a muon? How far could a muon travel in this time? Will the muon reach the ground, from the point of view of an observer on the ground? c. To the muon, how far is the 10. km distance to the ground? In its average lifetime and its speed of 0.999 c, will it be able to make it to the ground?
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