Matter & Interactions 2nd ed. Practice Problems
Aaron Titus | High Point University
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1520001     Energy of a muon     1520001
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Question

 

A muon is an elementary particle with a negative charge, like an electron, but with a larger mass ( ) than an electron. Suppose that a muon has a constant velocity of magnitude 0.9c, where c is the speed of light.

  1. What is the muon's total energy, in both joules and electron-volts?
  2. What is the muon's kinetic energy, in both joules and electron-volts?

 



Solution

 

(a) The total energy of a particle is

Convert this to electron-volts using the appropriate conversion factor which is

The total energy of the muon is 243 MeV. This should be greater than the rest energy of the muon, which is

The rest energy of the muon is 106 MeV. It therefore makes sense that the total energy of the muon (which is the sum of its kinetic energy and rest energy) is greater (243 MeV) than its rest energy. This gives us confidence in our answer.

(b) To find the muon's kinetic energy, write the total energy of the particle as the sum of the muon's rest energy and kinetic energy. Substitute the total energy and rest energy, and solve for the kinetic energy.

The kinetic energy is the difference between the total energy and rest energy and comes out to 137 MeV which is .