Part A Muons are unstable subatomic particles that decay to electrons with a mea
ID: 1792365 • Letter: P
Question
Part A Muons are unstable subatomic particles that decay to electrons with a mean lifetime of 2.2 . They are produced when cosmic rays bombard the upper atmosphere about 12.3 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 What is the greatest distance a muon could travel during its 2.2 s lifetime? Express your answer using two significant figures. km Submit My Answers Gve Up Incorrect; Try Again; 28 attempts remaining Part B According to your answer in part A, it would seem that muons could never make it to the ground. But the 2.2 lifetime is measured in the frame of the muon, and muons 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? Express your answer using two significant figures Submit My Answers Give Up Part C How far would the muon travel in this time?Explanation / Answer
a) distance d = v t
= 0.999 * 3 * 108 * 2.2 * 10-6
= 659 m = 0.659 km
b) mean life time t = t0 / sqrt [1 - v2/c2]
= 2.2 * 10-6 / sqrt [1 - (0.999 c)2/c2]
= 2.2 * 10-6 / 0.0447
= 4.92 * 10-5 s
c) distance = v * t
= 3 * 108 * 4.92 * 10-5
= 1.48 * 104 m = 14.8 km