Question

If a muon decays into an electron and a massless particle, and all the lost mass is converted into the electron's kinetic energy, find γ for the electron.

a)3.0
b)4.0
c)5.0
d)6.0

Answer 1

The muon decays into an electron and a massless particle, converting all the lost mass into the electron's kinetic energy. The gamma factor (γ) for the electron is approximately 207.

Step-by-step explanation:

In this scenario, a muon decays into an electron and a massless particle, and all the lost mass is converted into the electron's kinetic energy. The equation that relates energy and mass is E = mc^2, where E is energy, m is mass, and c is the speed of light. Since we know the rest mass energy of the muon, which is 105.7 MeV, we can use this equation to find the gamma factor (γ) for the electron.

Since the lost mass is converted into the electron's kinetic energy, the energy of the electron is 105.7 MeV. Using the equation E = γmc^2, we can rearrange it to find γ: γ = E / (mc^2). Plugging in the values, we get γ = 105.7 MeV / (0.511 MeV * c^2).

Simplifying this expression, we find that γ is approximately 207. Thus, the correct answer is not provided in the options given. The correct value of γ for the electron is not listed (approximately 207).