Solve Problem 28.1 for a muon. What are its speed and kinetic energy?

Answer

`0.856c=2.57 xx 10^(8)m//s, 99MeV`.

Explanation

The momentum of a muon is half that of the alpha-particle of the previous problem. It may easily be established after calculating the quantity `beta/sqrt(1-beta^2)=(p)/(m_(0)c)=1.66,` that the muon in this problem is a relativistic particle. We find `beta= 0.856,` from which the velocity of the particle may be found.
The rest energy of a muon is 207 times that of an electron, i.e. `= 207 xx 0.511 =100 MeV` (see Problem 8.1). The total energy is `epsi=(epsi_(0))/sqrt(1-beta^2)` and the kinetic energy is `K= epsi-epsi(0)`