A muon takes to decay in the observer's rest frame is 3.08 μs.
A muon is an unstable subatomic particle that decays into other particles with a mean lifetime of 2.20 μs. This is in the muon reference frame.
The formula for the relativistic factor
[tex]\gamma \:=\: \frac{1}{\sqrt{1 \:-\: (\frac{v}{c})^2}}[/tex]
[tex]\gamma \:=\: \frac{1}{\sqrt{1 \:-\: (\frac{0.7c}{c})^2}}[/tex]
[tex]\gamma \:=\: \frac{1}{\sqrt{1 \:-\: 0.7^2}}[/tex]
[tex]\gamma \:=\: \frac{1}{\sqrt{1 \:-\: 0.49}}[/tex]
[tex]\gamma \:=\: \frac{1}{\sqrt{0.51}}[/tex]
[tex]\gamma \:=\: \frac{1}{\sqrt{1 \:-\: 0.7^2}}[/tex]
[tex]\gamma \:=\: \frac{1}{0.714}[/tex]
γ = 1.4
Relativistic time interval formula
t = γ t₀
t = 1.4 × 2.2
t = 3.08 μs
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