Respuesta :
The muon lifetime in the muon reference frame is
[tex]\tau_0 = 2.2 \mu s[/tex]
In the observer's rest frame, the muon lifetime is instead given by
[tex]\tau = \gamma \tau_0[/tex]
where
[tex]\gamma = \frac{1}{ \sqrt{1- \frac{v^2}{c^2} } } [/tex] is the relativistic factor, with v being the muon speed and c the speed of light.
Since the muon is traveling at 70 % of the speed of light,
[tex]v=0.70 c[/tex]
and the relativistic factor is
[tex]\gamma = \frac{1}{ \sqrt{1- \frac{(0.70 c)^2}{c^2} } }=1.4 [/tex]
Therefore, the muon lifetime in the observer's rest frame is
[tex]\tau = \gamma \tau_0 = (1.4)(2.2 \mu s)=3.1 \mu s[/tex]
[tex]\tau_0 = 2.2 \mu s[/tex]
In the observer's rest frame, the muon lifetime is instead given by
[tex]\tau = \gamma \tau_0[/tex]
where
[tex]\gamma = \frac{1}{ \sqrt{1- \frac{v^2}{c^2} } } [/tex] is the relativistic factor, with v being the muon speed and c the speed of light.
Since the muon is traveling at 70 % of the speed of light,
[tex]v=0.70 c[/tex]
and the relativistic factor is
[tex]\gamma = \frac{1}{ \sqrt{1- \frac{(0.70 c)^2}{c^2} } }=1.4 [/tex]
Therefore, the muon lifetime in the observer's rest frame is
[tex]\tau = \gamma \tau_0 = (1.4)(2.2 \mu s)=3.1 \mu s[/tex]
Answer:
Observed lifetime [tex]= 3.0\mu s[/tex]
Explanation:
The lifetime of muon in the muon’s reference frame.
[tex]t^{_{0}}=2.2\mu s[/tex]
The lifetime of muon in observer’s rest frame.
[tex]t=\gamma t_{0}[/tex]
Here the
[tex]\gamma =\dfrac{1}{\sqrt{1-\frac{V^2}{C^2}}}[/tex]
[tex]\gamma[/tex] is the relativistic factor.
V = Speed of muon
C = Speed of light
The muon’s speed of 70% of light speed.
Hence,
[tex]V=\dfrac{70}{100}C[/tex]
V = 0.7C
[tex]=\dfrac{1}{\sqrt{1-\frac{(0.7C)^2}{C^2}}}[/tex]
[tex]=\dfrac{1}{\sqrt{1-0.49}}[/tex]
[tex]=\dfrac{1}{\sqrt{0.51}}[/tex]
[tex]=\dfrac{1}{0.71}[/tex]
= 1.4
The lifetime of muon in observer’s rest frame.
[tex]t=\gamma t_{0}[/tex]
[tex]t=1.4\times 2.2\mu s[/tex]
[tex]t=3.0\mu s[/tex]
Further explanation:
The muon is a lepton which decays to form an electron or positron. The lifetime of the muon is 2.20 microseconds. The muon lifetime in the muon reference frame is .
But the observed lifetime [tex]= \gamma =\frac{1}{\sqrt{1-\frac{V^2}{C^2}}}[/tex]
Learn more:
1. Speed of muon https://brainly.com/question/10048817 (answer by skyluke89)
2. Muon https://brainly.com/question/13198853 answer by skyluke89 )
Keywords: Muon, Speed of light, life time.
