Question

The elementary particle called a muon is unstable and decays in about 2.20μs2.20μs , as observed in its rest frame, into an electron, a neutrino, and an antineutrino. What lifetime do you observe for muons approaching you at 0.9270.927 the speed of light?

Answer 1

5.865 μs

Step-by-step explanation:

t₀ = Time taken to decay a muon = 2.20 μs

c = Speed of Light in vacuum = 3×10⁸ m/s

v = Velocity of muon = 0.927 c

t = Lifetime observed

Time dilation

`t=\frac{t_0}{\sqrt{1-(v^2)/(c^2)}}\\\Rightarrow t=\frac{2.2* 10^(-6)}{\sqrt{1-((0.927c)^2)/(c^2)}}\\\Rightarrow t=(2.2* 10^(-6))/(√(1-0.927^2))\\\Rightarrow t=(2.2* 10^(-6))/(√(0.140671))\\\Rightarrow t=(2.2* 10^(-6))/(0.3750)\\\Rightarrow t=5.865* 10^(-6)\ seconds`

∴Lifetime observed for muons approaching at 0.927 the speed of light is 5.865 μs