The mass of a muon is 207 times the electron mass; the average lifetime of muons at rest is 2.21 μs. in a certain experiment, muons moving through a laboratory are measured to have an average lifetime of 7.04 μs. for the moving muons, what are (a) β (b) k, and (c) p? the rest energy of the electron is 0.511 mev.
Given, average lifetime of muons at rest is To = 2.21μs
Average lifetime of moving muons, T = 7.04μs
mass of muon = 207 mass of electron
rest mass energy of an electron is 0.511 MeV.
Substitute the values:
b) K = (γ-1) m₀c²
K = (3.185-1) (207 ×9.1×10⁻³¹) (3×10⁸)² = 3.7×10⁻¹¹J
c) p = γmv = (3.185)((207 ×9.1×10⁻³¹)(0.95×3×10⁸)= 1.71×10⁻¹⁹ N/s