Question

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.

Answer 1

Answer:

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

a)

rest mass energy of an electron is 0.511 MeV.

$T =\frac{T_o}{\sqrt{1-\beta^2}}$

Substitute the values:

$7.04 =\frac{2.21}{\sqrt{1-\beta^2}}\\ \beta^2 = 0.90146\\ \beta = 0.95$

b) K = (γ-1) m₀c²

$\gamma = \frac{1}{\sqrt{1-\beta^2}} = 3.185$

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