One of the many fundamental particles in nature is the muon μ. This particle acts very much like a "heavy electron." It has a mass of 106 MeV/c2, compared to the electron's mass of just 0.511 MeV/c2. (We are using E=mc2 to obtain the mass in units of energy and the speed of light c).
Unlike the electron, though, the muon has a finite lifetime, after which it decays into an electron and two very light particles called neutrinos (ν). We'll ignore the neutrinos throughout this problem.
If the muon is at rest, the characteristic time that it takes it to decay is about 2.2μs (τμ=2.2×10−6s). Most of the time, though, particles such as muons are not at rest and, if they are moving relativistically, their lifetimes are increased by time dilation. In this problem we will explore some of these relativistic effects.
Part A: If a muon is traveling at 70% of the speed of light, how long does it take to decay in the observer's rest frame (i.e., what is the observed lifetime τμ of the muon)? Express your answer in microseconds to two significant figures.
Part B: If a muon is traveling at 99.9% the speed of light, how long will it take to decay in the observer's rest frame (i.e., what is the observed lifetime τμ of the muon)? Express your answer in microseconds to two significant figures.
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How far (dμdμd_mu) would the muon travel before it decayed, if there were no time dilation?
Now, let us consider the effects of time dilation. How far would the muon travel, taking time dilation into account?
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