An electron is one of the most fundamental particles in nature.It is everywhere, in all the matter we can see, and it is withelectrons that light interacts when it is emitted, absorbed, orscattered in everyday matter. The electron has a more massivecousin called a muon, also with a charge of -1 e, but with a massof 1.88x10-28 kg. The electron's mass is 9.11x10-31 kg. You can seewhy a muon is called a \"heavy\" electron. A muon is also unstable,and left alone at rest in a lab it will turn into an electron,kinetic energy, and two neutrinos with a lifetime of 2.20x10-6s.

1. Suppose we have a vacuum with two metal plates separated by 2meters. One of the plates has a hole in it so that a chargedparticle coming from the other one can pass through into emptyspace. The plate with a hole is attached to a voltage source of5,000,000 V and electrons and muons are introduced near the otherplate at 0 V. What energies and velocities do the electrons andmuons have when they pass through the hole?

2. If an electron or a muon encounters a magnetic field that isperpendicular to the line the particle is moving on, is their pathchanged? If so how does it depend on whether it is an electron ormuon, and if not, why not?

3. Using an accelerator or some other natural phenomenon,suppose that you could observe a muon traveling through your lab at0.999 times the speed of light. How long would it take todecay?